#### Dr. Fathollah Varnik

Scale Bridging Thermodynamic and Kinetic Simulation at ICAMS

Ruhr-Universität Bochum

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- fathollah.varnik@rub.de
- +4923432194
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**A mechanical analysis of chemically stimulated linear shape memory polymer actuation**

Dumlu, H. and Marquardt, A. and Zirdehi, E.M. and Varnik, F. and Shen, Y. and Neuking, K. and Eggeler, G.*Materials*14 (2021)In the present work, we study the role of programming strain (50% and 100%), end loads (0, 0.5, 1.0, and 1.5 MPa), and chemical environments (acetone, ethanol, and water) on the exploitable stroke of linear shape memory polymer (SMP) actuators made from ESTANE ETE 75DT3 (SMP-E). Dynamic mechanical thermal analysis (DMTA) shows how the uptake of solvents results in a decrease in the glass temperature of the molecular switch component of SMP-E. A novel in situ technique allows chemically studying triggered shape recovery as a function of time. It is found that the velocity of actuation decreases in the order acetone > ethanol > water, while the exploitable strokes shows the inverse tendency and increases in the order water > ethanol > acetone. The results are interpreted on the basis of the underlying chemical (how solvents affect thermophysical properties) and micromechanical processes (the phenomenological spring dashpot model of Lethersich type rationalizes the behavior). The study provides initial data which can be used for micromechanical modeling of chemically triggered actuation of SMPs. The results are discussed in the light of underlying chemical and mechanical elementary processes, and areas in need of further work are highlighted. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.view abstract 10.3390/ma14030481 **On the size effect of additives in amorphous shape memory polymers**

Zirdehi, E.M. and Dumlu, H. and Eggeler, G. and Varnik, F.*Materials*14 (2021)Small additive molecules often enhance structural relaxation in polymers. We explore this effect in a thermoplastic shape memory polymer via molecular dynamics simulations. The additiveto-monomer size ratio is shown to play a key role here. While the effect of additive-concentration on the rate of shape recovery is found to be monotonic in the investigated range, a non-monotonic dependence on the size-ratio emerges at temperatures close to the glass transition. This work thus identifies the additives’ size to be a qualitatively novel parameter for controlling the recovery process in polymer-based shape memory materials. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.view abstract 10.3390/ma14020327 **A crossover in spatio-temporal correlations of strain fluctuations in glass forming liquids**

Hassani, M. and Bruns, M. and Varnik, F.*Journal of Statistical Mechanics: Theory and Experiment*2020 (2020)Via molecular dynamics simulations of a generic glass former in the supercooled and normal liquid states, it is shown that spatial correlations of strain fluctuations exhibit a crossover from the well-established power-law ∼1/r 3-decay at long wavelengths to an exponential behavior, ∼&esp(-r/lc) at intermediate distances. The characteristic length of the exponential decay grows both with temperature and time via, l2 c ∝ D(T)t, with D(T) being the temperature-dependent diffusion coefficient. This suggests that the crossover between the power-law and exponential decays is governed by a diffusion process. © 2020 IOP Publishing Ltd and SISSA Medialab srl.view abstract 10.1088/1742-5468/ab5366 **Controlling bubble coalescence in metallic foams: A simple phase field-based approach**

Vakili, S. and Steinbach, I. and Varnik, F.*Computational Materials Science*173 (2020)The phase-field method is used as a basis to develop a strictly mass conserving, yet simple, model for simulation of two-phase flow. The model is aimed to be applied for the study of structure evolution in metallic foams. In this regard, the critical issue is to control the rate of bubble coalescence compared to concurrent processes such as their rearrangement due to fluid motion. In the present model, this is achieved by tuning the interface energy as a free parameter. The model is validated by a number of benchmark tests. First, stability of a two dimensional bubble is investigated by the Young-Laplace law for different values of the interface energy. Then, the coalescence of two bubbles is simulated until the system reaches equilibrium with a circular shape. To address the major capability of the present model for the formation of foam structure, the bubble coalescence is simulated for various values of interface energy in order to slow down the merging process. These simulations are repeated in the presence of a rotational flow to highlight the fact that the model allows to suppress the coalescence process compared to the motion of bubbles relative to each other. Moreover, since density is treated as an auxiliary variable “slaved” to the volume occupied by a given phase, the present model allows realization of arbitrarily large liquid-gas density ratios. This property is demonstrated by simulation of a system with ρl/ρg=10,000. © 2019 Elsevier B.V.view abstract 10.1016/j.commatsci.2019.109437 **Diffuse interface models of solidification with convection: The choice of a finite interface thickness**

Subhedar, A. and Galenko, P.K. and Varnik, F.*European Physical Journal: Special Topics*229 (2020)The thin interface limit aims at minimizing the effects arising from a numerical interface thickness, inherent in diffuse interface models of solidification and microstructure evolution such as the phase field model. While the original formulation of this problem is restricted to transport by diffusion, we consider here the case of melt convection. Using an analysis of the coupled phase field-fluid dynamic equations, we show here that such a thin interface limit does also exist if transport contains both diffusion and convection. This prediction is tested by comparing simulation studies, which make use of the thin-interface condition, with an analytic sharp-interface theory for dendritic tip growth under convection. © 2020, The Author(s).view abstract 10.1140/epjst/e2019-900099-5 **Effects of size and elasticity on the relation between flow velocity and wall shear stress in side-wall aneurysms: A lattice Boltzmann-based computer simulation study**

Wang, H. and Krüger, T. and Varnik, F.*PLoS ONE*15 (2020)Blood flow in an artery is a fluid-structure interaction problem. It is widely accepted that aneurysm formation, enlargement and failure are associated with wall shear stress (WSS) which is exerted by flowing blood on the aneurysmal wall. To date, the combined effect of aneurysm size and wall elasticity on intra-aneurysm (IA) flow characteristics, particularly in the case of side-wall aneurysms, is poorly understood. Here we propose a model of three-dimensional viscous flow in a compliant artery containing an aneurysm by employing the immersed boundary-lattice Boltzmann-finite element method. This model allows to adequately account for the elastic deformation of both the blood vessel and aneurysm walls. Using this model, we perform a detailed investigation of the flow through aneurysm under different conditions with a focus on the parameters which may influence the wall shear stress. Most importantly, it is shown in this work that the use of flow velocity as a proxy for wall shear stress is well justified only in those sections of the vessel which are close to the ideal cylindrical geometry. Within the aneurysm domain, however, the correlation between wall shear stress and flow velocity is largely lost due to the complexity of the geometry and the resulting flow pattern. Moreover, the correlations weaken further with the phase shift between flow velocity and transmural pressure. These findings have important implications for medical applications since wall shear stress is believed to play a crucial role in aneurysm rupture. © 2020 Wang et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.view abstract 10.1371/journal.pone.0227770 **Interface tracking characteristics of color-gradient lattice Boltzmann model for immiscible fluids**

Subhedar, A. and Reiter, A. and Selzer, M. and Varnik, F. and Nestler, B.*Physical Review E*101 (2020)We study the interface tracking characteristics of a color-gradient-based lattice Boltzmann model for immiscible flows. Investigation of the local density change in one of the fluid phases, via a Taylor series expansion of the recursive lattice Boltzmann equation, leads to the evolution equation of the order parameter that differentiates the fluids. It turns out that this interface evolution follows a conservative Allen-Cahn equation with a mobility which is independent of the fluid viscosities and surface tension. The mobility of the interface, which solely depends upon lattice speed of sound, can have a crucial effect on the physical dynamics of the interface. Further, we find that, when the equivalent lattice weights inside the segregation operator are modified, the resulting differential operators have a discretization error that is anisotropic to the leading order. As a consequence, the discretization errors in the segregation operator, which ensures a finite interface width, can act as a source of the spurious currents. These findings are supported with the help of numerical simulations. © 2020 American Physical Society.view abstract 10.1103/PhysRevE.101.013313 **Multi-phase-field simulation of microstructure evolution in metallic foams**

Vakili, S. and Steinbach, I. and Varnik, F.*Scientific Reports*10 (2020)This paper represents a model for microstructure formation in metallic foams based on the multi-phase-field approach. The model allows to naturally account for the effect of additives which prevent two gas bubbles from coalescence. By applying a non-merging criterion to the phase fields and at the same time raising the free energy penalty associated with additives, it is possible to completely prevent coalescence of bubbles in the time window of interest and thus focus on the formation of a closed porous microstructure. On the other hand, using a modification of this criterion along with lower free energy barriers we investigate with this model initiation of coalescence and the evolution of open structures. The method is validated and used to simulate foam structure formation both in two and three dimensions. © 2020, The Author(s).view abstract 10.1038/s41598-020-76766-z **Multiple character of non-monotonic size-dependence for relaxation dynamics in polymer-particle and binary mixtures**

Zirdehi, E.M. and Voigtmann, T. and Varnik, F.*Journal of Physics Condensed Matter*32 (2020)Adding plasticizers is a well-known procedure to reduce the glass transition temperature in polymers. It has been recently shown that this effect shows a non-monotonic dependence on the size of additive molecules (2019 J. Chem. Phys. 150 024903). In this work, we demonstrate that, as the size of the additive molecules is changed at fixed concentration, multiple extrema emerge in the dependence of the system's relaxation time on the size ratio. The effect occurs on all relevant length scales including single monomer dynamics, decay of Rouse modes and relaxation of the chain's end-to-end vector. A qualitatively similar trend is found within mode-coupling theoretical results for a binary hard-sphere mixture. An interpretation of the effect in terms of local packing efficiency and coupling between the dynamics of minority and majority species is provided. © 2020 The Author(s). Published by IOP Publishing Ltd.view abstract 10.1088/1361-648X/ab757c **Simulation of capillary-driven kinetics with multi-phase-field and lattice Boltzmann method**

Schiedung, R. and Tegeler, M. and Medvedev, D. and Varnik, F.*Modelling and Simulation in Materials Science and Engineering*28 (2020)We propose a combined computational approach based on the multi-phase-field and the lattice Boltzmann method for the motion of solid particles under the action of capillary forces. The accuracy of the method is analyzed by comparison with the analytic solutions for the motion of two parallel plates of finite extension connected by a capillary bridge. The method is then used to investigate the dynamics of multiple spherical solid bodies connected via capillary bridges. The amount of liquid connecting the spheres is varied, and the influence of the resulting liquid-morphology on their dynamics is investigated. It is shown that the method is suitable for a study of liquid-phase sintering which includes both phase transformation and capillary driven rigid body motion. © 2020 The Author(s). Published by IOP Publishing Ltd.view abstract 10.1088/1361-651X/ab9bb3 **Thin interface limit of the double-sided phase-field model with convection**

Subhedar, A. and Galenko, P.K. and Varnik, F.*Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences*378 (2020)The thin interface limit of the phase-field model is extended to include transport via melt convection. A double-sided model (equal diffusivity in liquid and solid phases) is considered for the present analysis. For the coupling between phase-field and Navier-Stokes equations, two commonly used schemes are investigated using a matched asymptotic analysis: (i) variable viscosity and (ii) drag force model. While for the variable viscosity model, the existence of a thin interface limit can be shown up to the second order in the expansion parameter, difficulties arise in satisfying no-slip boundary condition at this order for the drag force model. Nevertheless, detailed numerical simulations in two dimensions show practically no difference in dendritic growth profiles in the presence of forced melt flow obtained for the two coupling schemes. This suggests that both approaches can be used for the purpose of numerical simulations. Simulation results are also compared to analytic theory, showing excellent agreement for weak flow. Deviations at higher fluid velocities are discussed in terms of the underlying theoretical assumptions. © 2020 The Author(s) Published by the Royal Society. All rights reserved.view abstract 10.1098/rsta.2019.0540 **Non-monotonic effect of additive particle size on the glass transition in polymers**

Zirdehi, E.M. and Varnik, F.*Journal of Chemical Physics*150 (2019)Effect of small additive molecules on the structural relaxation of polymer melts is investigated via molecular dynamics simulations. At a constant external pressure and a fixed number concentration of added molecules, the variation of the particle diameter leads to a non-monotonic change of the relaxation dynamics of the polymer melt. For non-entangled chains, this effect is rationalized in terms of an enhanced added-particle-dynamics which competes with a weaker coupling strength upon decreasing the particle size. Interestingly, cooling simulations reveal a non-monotonic effect on the glass transition temperature also for entangled chains, where the effect of additives on polymer dynamics is more intricate. This observation underlines the importance of monomer-scale packing effects on the glass transition in polymers. In view of this fact, size-adaptive thermosensitive core-shell colloids would be a promising candidate route to explore this phenomenon experimentally. © 2019 Author(s).view abstract 10.1063/1.5063476 **Probing the Degree of Heterogeneity within a Shear Band of a Model Glass**

Hassani, M. and Lagogianni, A.E. and Varnik, F.*Physical Review Letters*123 (2019)Recent experiments provide evidence for density variations along shear bands in metallic glasses with a length scale of a few hundred nanometers. Via molecular dynamics simulations of a generic binary glass model, here we show that this is strongly correlated with variations of composition, coordination number, viscosity, and heat generation. Individual shear events along the shear band path show a mean distance of a few nanometers, comparable to recent experimental findings on medium range order. The aforementioned variations result from these localized perturbations, mediated by elasticity. © 2019 American Physical Society.view abstract 10.1103/PhysRevLett.123.195502 **Long-range strain correlations in 3D quiescent glass forming liquids**

Hassani, M. and Zirdehi, E.M. and Kok, K. and Schall, P. and Fuchs, M. and Varnik, F.*EPL*124 (2018)Recent two-dimensional computer simulations and experiments indicate that even supercooled liquids exhibit long-lived, long-range strain correlations expected only in solids. Here we investigate this issue in three dimensions via Newtonian molecular-dynamics simulations, by a generalized hydrodynamics approach, and by experiments on Brownian hard-sphere colloids. Both in the glassy state and in liquid regimes, strain correlations are predicted to decay with a power law, reminiscent of elastic fields around an inclusion. In contrast, the temporal evolution of the correlation amplitude is distinct in the liquid state, where it grows linearly with time, and in the glass, where it reaches a time-independent plateau. These predictions are assessed via molecular-dynamics simulations and experiments. In simple liquids, the size of the cooperative strain patterns is of the order of the distance traveled by (high-frequency) transverse sound prior to structural relaxation. This length is of the order of nanometers in a normal liquid and grows to macroscale upon approaching the glass transition. © CopyrightEPLA, 2018.view abstract 10.1209/0295-5075/124/18003 **Multi-phase-field method for surface tension induced elasticity**

Schiedung, R. and Steinbach, I. and Varnik, F.*Physical Review B*97 (2018)A method, based on the multi-phase-field framework, is proposed that adequately accounts for the effects of a coupling between surface free energy and elastic deformation in solids. The method is validated via a number of analytically solvable problems. In addition to stress states at mechanical equilibrium in complex geometries, the underlying multi-phase-field framework naturally allows us to account for the influence of surface energy induced stresses on phase transformation kinetics. This issue, which is of fundamental importance on the nanoscale, is demonstrated in the limit of fast diffusion for a solid sphere, which melts due to the well-known Gibbs-Thompson effect. This melting process is slowed down when coupled to surface energy induced elastic deformation. © 2018 American Physical Society.view abstract 10.1103/PhysRevB.97.035410 **Shear-density coupling for a compressible single-component yield-stress fluid**

Gross, M. and Varnik, F.*Soft Matter*14 (2018)Flow behavior of a single-component yield stress fluid is addressed on the hydrodynamic level. A basic ingredient of the model is a coupling between fluctuations of density and velocity gradient via a Herschel-Bulkley-type constitutive model. Focusing on the limit of low shear rates and high densities, the model approximates well - but is not limited to - gently sheared hard sphere colloidal glasses, where solvent effects are negligible. A detailed analysis of the linearized hydrodynamic equations for fluctuations and the resulting cubic dispersion relation reveals the existence of a range of densities and shear rates with growing flow heterogeneity. In this regime, after an initial transient, the velocity and density fields monotonically reach a spatially inhomogeneous stationary profile, where regions of high shear rate and low density coexist with regions of low shear rate and high density. The steady state is thus maintained by a competition between shear-induced enhancement of density inhomogeneities and relaxation via overdamped sound waves. An analysis of the mechanical equilibrium condition provides a criterion for the existence of steady state solutions. The dynamical evolution of the system is discussed in detail for various boundary conditions, imposing either a constant velocity, shear rate, or stress at the walls. © 2018 The Royal Society of Chemistry.view abstract 10.1039/c8sm00495a **The influence of water and solvent uptake on functional properties of shape-memory polymers**

Ghobadi, E. and Marquardt, A. and Zirdehi, E.M. and Neuking, K. and Varnik, F. and Eggeler, G. and Steeb, H.*International Journal of Polymer Science*2018 (2018)In this contribution, diffusion of water, acetone, and ethanol into a polymer matrix has been studied experimentally and numerically by finite element approaches. Moreover, the present study reports an assessment of different thermomechanical conditions of the shape-memory (SM) performance, for example, stress-or strain-holding times in stress-or strain-controlled thermomechanical cycles and the effect of maximum strain. According to the results presented here, the uptake of acetone in Estane is much higher than ethanol and follows classical Fickian diffusion. Further, a series of thermomechanical measurements conducted on dry and physically (hydrolytically) aged polyether urethanes revealed that incorporation of water seems to have an appreciable impact on the shape recovery ratios which can be attributed to the additional physical crosslinks. However, no obvious difference in shape fixation of dry and physically (hydrolytically) aged samples could be recognized. Furthermore, by decreasing the strain-holding time, shape recovery improves significantly. Moreover, the shape fixity is found to be independent of holding time. The shape recovery ratio decreased dramatically with an increase in the stress-holding time. Copyright © 2018 Ehsan Ghobadi et al.view abstract 10.1155/2018/7819353 **Wall effects on spatial correlations of non-affine strain in a 3D model glass**

Hassani, M. and Engels, P. and Varnik, F.*EPL*121 (2018)Effects of hard planar walls with a particle scale roughness on the spatial correlations of non-affine strain in amorphous solids are investigated via molecular dynamics simulations. When determined within layers parallel to the wall plane, normalized non-affine strain correlations are enhanced within layers closer to the wall. The amplitude of these correlations, on the other hand, is found to be suppressed by the wall. While the former is connected to the effects of a hard boundary on the continuum mechanics scale, the latter is attributed to molecular scale wall effects on the size of the region (nearest-neighbor cage), explored by particles on intermediate times scales. © CopyrightEPLA, 2018.view abstract 10.1209/0295-5075/121/18005 **Molecular dynamics simulations of entangled polymers: The effect of small molecules on the glass transition temperature**

Mahmoudinezhad, E. and Marquardt, A. and Eggeler, G. and Varnik, F.*Procedia Computer Science*108 (2017)Effect of small molecules, as they penetrate into a polymer system, is investigated via molecular dynamics simulations. It is found that small spherical particles reduce the glass transition temperature and thus introduce a softening of the material. Results are compared to experimental findings for the effect of different types of small molecules such as water, acetone and ethanol on the glass transition temperature of a polyurethane-based shape memory polymer. Despite the simplicity of the simulated model, MD results are found to be in good qualitative agreement with experimental data. © 2017 The Authors. Published by Elsevier B.V.view abstract 10.1016/j.procs.2017.05.152 **Multi-phase-field model for surface and phase-boundary diffusion**

Schiedung, R. and Kamachali, R.D. and Steinbach, I. and Varnik, F.*Physical Review E*96 (2017)The multi-phase-field approach is generalized to treat capillarity-driven diffusion parallel to the surfaces and phase boundaries, i.e., the boundaries between a condensed phase and its vapor and the boundaries between two or multiple condensed phases. The effect of capillarity is modeled via curvature dependence of the chemical potential whose gradient gives rise to diffusion. The model is used to study thermal grooving on the surface of a polycrystalline body. Decaying oscillations of the surface profile during thermal grooving, postulated by Hillert long ago but reported only in few studies so far, are observed and discussed. Furthermore, annealing of multi-nanoclusters on a deformable free surface is investigated using the proposed model. Results of these simulations suggest that the characteristic craterlike structure with an elevated perimeter, observed in recent experiments, is a transient nonequilibrium state during the annealing process. © 2017 American Physical Society.view abstract 10.1103/PhysRevE.96.012801 **On the numerical evaluation of local curvature for diffuse interface models of microstructure evolution**

Vakili, S. and Steinbach, I. and Varnik, F.*Procedia Computer Science*108 (2017)Within diffuse interface models for multiphase problems, the curvature of the phase boundary can be expressed as the difference of two terms, a Laplacian and a second, gradient, term of the diffuse interface variable, ø. In phase field simulations of microstructure evolution, the second term is often replaced by f'(ø) = df/dø, where f(ø) is the potential function in the free energy functional of the underlying physical model. We show here that this replacement systematically deteriorates the accuracy in local curvature evaluation as compared to a discretized evaluation of the second term. Analytic estimates reveal that the discretization errors in the Laplacian and in the second term have roughly the same spatial dependence across the interface, thus leading to a cancellation of errors in k. This is confirmed in a test case, where the discretization error can be determined via comparison to the exact solution. If, however, the second term is replaced by a quasi exact expression, the error in δø enters k without being compensated and can obscure the behavior of the local curvature. Due to the antisymmetric variations of this error term, approaches using the average curvature, as obtained from an integral along the interface normal, are immune to this problem. © 2017 The Authors. Published by Elsevier B.V.view abstract 10.1016/j.procs.2017.05.256 **Diffusion of small molecules in a shape memory polymer**

Marquardt, A. and Mogharebi, S. and Neuking, K. and Varnik, F. and Eggeler, G.*Journal of Materials Science*51 (2016)The present work studies the diffusion of small molecules (acetone, ethanol, and water) in a shape memory polymer (SMP) of type Estane ETE 75DT3 (SMP-E), which represents a thermoplastic polyurethane. The work aims at providing background information on the chemical reaction between SMPs and small molecules which can limit the service life of SMP actuators operating in harsh chemical environments. Weight gain studies after immersion of plate specimens in liquid acetone, ethanol, and water yield data which can be assessed on the basis of analytical and numerical solutions of Fick’s second law. The diffusion coefficients which are obtained for 21, 30, and 40 °C in the present study scale as Dacetone > Dethanol > Dwater. The diffusion coefficients show Arrhenius types of temperature dependencies with apparent activation energies of 33 (acetone), 59 (ethanol), and 58 (water) kJ mol−1. The diffusion coefficients and the apparent activation energies obtained in the present work are in reasonable agreement with data which were reported for the reaction of the three small molecules with similar polymers in the literature. It is not straightforward to correlate differences in molecular mobility with individual physical properties. The Hansen solubility parameter (originally derived to explain solubility not mobility) qualitatively rationalizes the observed differences. © 2016, Springer Science+Business Media New York.view abstract 10.1007/s10853-016-0213-0 **Localized plastic deformation in a model metallic glass: A survey of free volume and local force distributions**

Hassani, M. and Engels, P. and Raabe, D. and Varnik, F.*Journal of Statistical Mechanics: Theory and Experiment*2016 (2016)Plastic deformation of a model glass is investigated via large scale molecular dynamics simulations. The role of microscopic fluctuations of the structure for the deformation behavior is highlighted by demonstrating that statistically independent samples prepared via an identical protocol develop qualitatively distinct deformation paths. As a quantitative measure, the spatial distribution of the particle based excess volume is monitored via Voronoi tesselation. While the fluctuations of the thus defined single-particle based excess volume do not seem to show any signature of the strain field, a non-local definition of the excess volume clearly correlates with the observed shear deformation field. The distribution of the force acting on individual particles also shows a pattern strongly similar to that of the strain. In line with other studies, these results underline the importance of both the structural heterogeneities as well as the fluctuations of the locally acting forces and stresses for plastic deformation in amorphous solids. © 2016 IOP Publishing Ltd and SISSA Medialab srl.view abstract 10.1088/1742-5468/2016/08/084006 **Non-monotonic effect of confinement on the glass transition**

Varnik, F. and Franosch, T.*Journal of Physics Condensed Matter*28 (2016)The relaxation dynamics of glass forming liquids and their structure are influenced in the vicinity of confining walls. This effect has mostly been observed to be a monotonic function of the slit width. Recently, a qualitatively new behaviour has been uncovered by Mittal and coworkers, who reported that the single particle dynamics in a hard-sphere fluid confined in a planar slit varies in a non-monotonic way as the slit width is decreased from five to roughly two particle diametres (Mittal et al 2008 Phys. Rev. Lett. 100 145901). In view of the great potential of this effect for applications in those fields of science and industry, where liquids occur under strong confinement (e.g. nano-technology), the number of researchers studying various aspects and consequences of this non-monotonic behaviour has been rapidly growing. This review aims at providing an overview of the research activity in this newly emerging field. We first briefly discuss how competing mechanisms such as packing effects and short-range attraction may lead to a non-monotonic glass transition scenario in the bulk. We then analyse confinement effects on the dynamics of fluids using a thermodynamic route which relates the single particle dynamics to the excess entropy. Moreover, relating the diffusive dynamics to the Widom's insertion probability, the oscillations of the local dynamics with density at moderate densities are fairly well described. At high densities belonging to the supercooled regime, however, this approach breaks down signaling the onset of strongly collective effects. Indeed, confinement introduces a new length scale which in the limit of high densities and small pore sizes competes with the short-range local order of the fluid. This gives rise to a non-monotonic dependence of the packing structure on confinement, with a corresponding effect on the dynamics of structural relaxation. This non-monotonic effect occurs also in the case of a cone-plate type channel, where the degree of confinement varies with distance from the apex. This is a very promising issue for future research with the possibility of uncovering the existence of alternating glassy and liquid-like domains. © 2016 IOP Publishing Ltd.view abstract 10.1088/0953-8984/28/13/133001 **Response to "Comment on 'Viscous coalescence of droplets: A lattice Boltzmann study'" [Phys. Fluids 28, 079101 (2016)]**

Gross, M. and Steinbach, I. and Raabe, D. and Varnik, F.*Physics of Fluids*28 (2016)view abstract 10.1063/1.4958828 **Aging in amorphous solids: A study of the first-passage time and persistence time distributions**

Siboni, N.H. and Raabe, D. and Varnik, F.*EPL*111 (2015)The time distribution of relaxation events in an aging system is investigated via molecular-dynamics simulations. The focus is on the distribution functions of the first-passage time, p1(δt), and the persistence time, p(τ ). In contrast to previous reports, both p1 and p are found to evolve with time upon aging. The age dependence of the persistence time distribution is shown to be sensitive to the details of the algorithm used to extract it from particle trajectories. By updating the reference point in event detection algorithm and accounting for the event specific aging time, we uncover the age dependence of p(τ), hidden to previous studies. Moreover, the apparent age dependence of p1 in continuous time random walk with an age-independent p(τ) is shown to result from an implicit synchronization of all the random walkers at the starting time.view abstract 10.1209/0295-5075/111/48004 **Fluctuating multicomponent lattice Boltzmann model**

Belardinelli, D. and Sbragaglia, M. and Biferale, L. and Gross, M. and Varnik, F.*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*91 (2015)Current implementations of fluctuating lattice Boltzmann equations (FLBEs) describe single component fluids. In this paper, a model based on the continuum kinetic Boltzmann equation for describing multicomponent fluids is extended to incorporate the effects of thermal fluctuations. The thus obtained fluctuating Boltzmann equation is first linearized to apply the theory of linear fluctuations, and expressions for the noise covariances are determined by invoking the fluctuation-dissipation theorem directly at the kinetic level. Crucial for our analysis is the projection of the Boltzmann equation onto the orthonormal Hermite basis. By integrating in space and time the fluctuating Boltzmann equation with a discrete number of velocities, the FLBE is obtained for both ideal and nonideal multicomponent fluids. Numerical simulations are specialized to the case where mean-field interactions are introduced on the lattice, indicating a proper thermalization of the system. © 2015 American Physical Society.view abstract 10.1103/PhysRevE.91.023313 **Modeling the flow in diffuse interface methods of solidification**

Subhedar, A. and Steinbach, I. and Varnik, F.*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*92 (2015)Fluid dynamical equations in the presence of a diffuse solid-liquid interface are investigated via a volume averaging approach. The resulting equations exhibit the same structure as the standard Navier-Stokes equation for a Newtonian fluid with a constant viscosity, the effect of the solid phase fraction appearing in the drag force only. This considerably simplifies the use of the lattice Boltzmann method as a fluid dynamics solver in solidification simulations. Galilean invariance is also satisfied within this approach. Further, we investigate deviations between the diffuse and sharp interface flow profiles via both quasiexact numerical integration and lattice Boltzmann simulations. It emerges from these studies that the freedom in choosing the solid-liquid coupling parameter h provides a flexible way of optimizing the diffuse interface-flow simulations. Once h is adapted for a given spatial resolution, the simulated flow profiles reach an accuracy comparable to quasiexact numerical simulations. © 2015 American Physical Society.view abstract 10.1103/PhysRevE.92.023303 **Shear-flow-controlled mode selection in a nonlinear autocatalytic medium**

Ayodele, S.G. and Raabe, D. and Varnik, F.*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*91 (2015)The effect of shear flow on mode selection and the length scale of patterns formed in a nonlinear autocatalytic reaction-diffusion model is investigated. We predict analytically the existence of transverse and longitudinal modes. The type of the selected mode strongly depends on the difference in the flow rates of the participating species, quantified by the differential flow parameter. Spatial structures are obtained by varying the length scale of individual modes and superposing them via the differential flow parameter. Our predictions are in line with numerical results obtained from lattice Boltzmann simulations. © 2015 American Physical Society.view abstract 10.1103/PhysRevE.91.022913 **Correlations of plasticity in sheared glasses**

Varnik, F. and Mandal, S. and Chikkadi, V. and Denisov, D. and Olsson, P. and Vågberg, D. and Raabe, D. and Schall, P.*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*89 (2014)In a recent paper [Mandal, Phys. Rev. E 88, 022129 (2013)PLEEE81539-375510. 1103/PhysRevE.88.022129], the nature of spatial correlations of plasticity in hard-sphere glasses was addressed both via computer simulations and in experiments. It was found that the experimentally obtained correlations obey a power law, whereas the correlations from simulations are better fitted by an exponential decay. We here provide direct evidence - via simulations of a hard-sphere glass in two dimensions (2D) - that this discrepancy is a consequence of the finite system size in the 3D simulations. By extending the study to a 2D soft disk model at zero temperature [Durian, Phys. Rev. Lett. 75, 4780 (1995)PRLTAO0031-900710.1103/PhysRevLett.75.4780], the robustness of the power-law decay in sheared amorphous solids is underlined. Deviations from a power law occur when either reducing the packing fraction towards the supercooled regime in the case of hard spheres or changing the dissipation mechanism from contact dissipation to a mean-field-type drag in the case of soft disks. © 2014 American Physical Society.view abstract 10.1103/PhysRevE.89.040301 **Fluctuations and diffusion in sheared athermal suspensions of deformable particles**

Gross, M. and Krüger, T. and Varnik, F.*EPL*108 (2014)We analyze fluctuations of particle displacements and stresses in a sheared athermal suspension of elastic capsules (red blood cells). Upon variation of the volume fraction from the dilute up to the highly concentrated regime, our numerical simulations reveal different characteristic power-law regimes of the fluctuation variances and relaxation times. In the jammed phase and at high shear rates, anomalous scaling exponents are found that deviate from pure dimensional predictions. The observed behavior is rationalized via kinetic arguments and a dissipation balance model that takes into account the local fluid flows between the particles. Our findings support the view that the rheology of dense suspensions is essentially governed by the non-affine displacements. © CopyrightEPLA, 2014.view abstract 10.1209/0295-5075/108/68006 **Multiple reentrant glass transitions in confined hard-sphere glasses**

Mandal, S. and Lang, S. and Gross, M. and Oettel, M. and Raabe, D. and Franosch, T. and Varnik, F.*Nature Communications*5 (2014)Glass-forming liquids exhibit a rich phenomenology upon confinement. This is often related to the effects arising from wall-fluid interactions. Here we focus on the interesting limit where the separation of the confining walls becomes of the order of a few particle diameters. For a moderately polydisperse, densely packed hard-sphere fluid confined between two smooth hard walls, we show via event-driven molecular dynamics simulations the emergence of a multiple reentrant glass transition scenario upon a variation of the wall separation. Using thermodynamic relations, this reentrant phenomenon is shown to persist also under constant chemical potential. This allows straightforward experimental investigation and opens the way to a variety of applications in micro-and nanotechnology, where channel dimensions are comparable to the size of the contained particles. The results are in line with theoretical predictions obtained by a combination of density functional theory and the mode-coupling theory of the glass transition. © 2014 Macmillan Publishers Limited.view abstract 10.1038/ncomms5435 **Polyelectrolytes polarization in nonuniform electric fields**

Farahpour, F. and Ejtehadi, M.R. and Varnik, F.*International Journal of Modern Physics C*25 (2014)Stretching dynamics of polymers in microfluidics is of particular interest for polymer scientists. As a charged polymer, a polyelectrolyte (PE) can be deformed from its coiled equilibrium configuration to an extended chain by applying uniform or nonuniform electric fields. By means of hybrid lattice Boltzmann (LB)-molecular dynamics (MD) simulations, we investigate how the condensed counterions (CIs) around the PE contribute to the polymer stretching in inhomogeneous fields. As an application, we discuss the translocation phenomena and entropic traps, when the driving force is an applied external electric field. © 2014 World Scientific Publishing Company.view abstract 10.1142/S0129183114410101 **Rheology of dense suspensions of elastic capsules: Normal stresses, yield stress, jamming and confinement effects**

Gross, M. and Krüger, T. and Varnik, F.*Soft Matter*10 (2014)We study the shearing rheology of dense suspensions of elastic capsules, taking aggregation-free red blood cells as a physiologically relevant example. Particles are non-Brownian and interact only via hydrodynamics and short-range repulsive forces. An analysis of the different stress mechanisms in the suspension shows that the viscosity is governed by the shear elasticity of the capsules, whereas the repulsive forces are subdominant. Evidence for a dynamic yield stress above a critical volume fraction is provided and related to the elastic properties of the capsules. The shear stress is found to follow a critical jamming scenario and is rather insensitive to the tumbling-to-tank- treading transition. The particle pressure and normal stress differences display some sensitivity to the dynamical state of the cells and exhibit a characteristic scaling, following the behavior of a single particle, in the tank-treading regime. The behavior of the viscosity in the fluid phase is rationalized in terms of effective medium models. Furthermore, the role of confinement effects, which increase the overall magnitude and enhance the shear-thinning of the viscosity, is discussed. © 2014 the Partner Organisations.view abstract 10.1039/c4sm00081a **Spreading dynamics of nanodrops:A lattice boltzmann study**

Gross, M. and Varnik, F.*International Journal of Modern Physics C*25 (2014)Spreading of nano-droplets is an interesting and technologically relevant phenomenon, where thermal fluctuations lead to unexpected deviations from well-known deterministic laws. Here, we apply the newly developed fluctuating nonideal lattice Boltzmann (LB) method [M. Gross, M. E. Cates, F. Varnik and R. Adhikari, J. Stat. Mech. 2011, P03030 (2011)] for the study of this issue. Confirming the predictions of Davidovich and coworkers [Phys. Rev. Lett. 95, 244905 (2005)], we provide the first independent evidence for the existence of an asymptotic, self-similar noise-driven spreading regime in both two-(2D) and three-dimensional (3D) geometry. The cross over from the deterministic Tanner's law, where the drop's base radius b grows (in 3D) with time as b ∼ t 1/10 and the noise dominated regime, where b ∼ t1/6 is also observed by tuning the strength of thermal noise. © 2014 World Scientific Publishing Company.view abstract 10.1142/S0129183113400196 **Chain deformation in translocation phenomena**

Farahpour, F. and Maleknejad, A. and Varnik, F. and Ejtehadi, M.R.*Soft Matter*9 (2013)Deformation of single stranded DNA in a translocation process before reaching the pore is investigated. By solving the Laplace equation in a suitable coordinate system and with appropriate boundary conditions, an approximate solution for the electric field inside and outside a narrow pore is obtained. With an analysis based on the "electrohydrodynamic equivalence" we determine the possibility of the extension of a charged polymer due to the presence of an electric field gradient in the vicinity of the pore entrance. With a multi-scale hybrid simulation (LB-MD), it is shown that an effective deformation before reaching the pore occurs, which facilitates the process of finding the entrance for the end monomers. We also highlight the role of long range hydrodynamic interactions via comparison of the LB-MD results with those obtained using a Langevin thermostat instead of the LB solver. © 2013 The Royal Society of Chemistry.view abstract 10.1039/c2sm27416g **Crossover from tumbling to tank-treading-like motion in dense simulated suspensions of red blood cells**

Krüger, T. and Gross, M. and Raabe, D. and Varnik, F.*Soft Matter*9 (2013)Via computer simulations, we provide evidence that the shear rate induced red blood cell tumbling-to-tank-treading transition also occurs at quite high volume fractions, where collective effects are important. The transition takes place as the ratio of effective suspension stress to the characteristic cell membrane stress exceeds a certain value and does not explicitly depend on volume fraction or cell deformability. This value coincides with that for a transition from an orientationally less ordered to a highly ordered phase. The average cell deformation does not show any signature of transition, but rather follows a simple scaling law independent of volume fraction. © 2013 The Royal Society of Chemistry.view abstract 10.1039/c3sm51645h **Flow heterogeneity and correlations in a sheared hard sphere glass: Insight from computer simulations**

Mandal, S. and Gross, M. and Raabe, D. and Varnik, F.*AIP Conference Proceedings*1518 (2013)Understanding the origin of flow heterogeneity in glassy systems is of high interest both due to its importance from theoretical standpoint as well as due to its occurrence in a large number of practical situations such as the flow of the so-called soft-glassy materials (foams, colloidal suspensions, granular media, etc). Detailed experimental investigations do indeed confirm that the flow of driven amorphous solids is not homogeneous, even if the macroscopic stress is constant across the system. We study this issue via large scale event driven molecular dynamics simulations of a hard sphere glass. We observe significant fluctuations of the velocity profile with a time scale of the order of a few hundreds percent strain. Furthermore, there appears to be a correlation between the fluctuations of the local volume fraction and the fluctuations of the local shear rate. The time scales of the fluctuations of density and shear rate are practically identical. These observations motivate an interpretation of our results via the shear concentration coupling (SCC) theory. A detailed comparison, however, reveals serious inconsistencies. In particular, the amplitude of the fluctuations of the shear rate seems to be decoupled from that of density, a feature which is rather unexpected within the SCC picture. An alternative interpretation of our observations is also discussed invoking dynamic heterogeneity. © 2013 American Institute of Physics.view abstract 10.1063/1.4794578 **Interfacial roughening in nonideal fluids: Dynamic scaling in the weak- and strong-damping regime**

Gross, M. and Varnik, F.*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*87 (2013)Interfacial roughening denotes the nonequilibrium process by which an initially flat interface reaches its equilibrium state, characterized by the presence of thermally excited capillary waves. Roughening of fluid interfaces has been first analyzed by Flekkoy and Rothman, where the dynamic scaling exponents in the weakly damped case in two dimensions were found to agree with the Kardar-Parisi-Zhang universality class. We extend this work by taking into account also the strong-damping regime and perform extensive fluctuating hydrodynamics simulations in two dimensions using the Lattice Boltzmann method. We show that the dynamic scaling behavior is different in the weakly and strongly damped case. © 2013 American Physical Society.view abstract 10.1103/PhysRevE.87.022407 **Lattice Boltzmann modeling of advection-diffusion-reaction equations: Pattern formation under uniform differential advection**

Ayodele, S.G. and Raabe, D. and Varnik, F.*Communications in Computational Physics*13 (2013)A lattice Boltzmann model for the study of advection-diffusion-reaction (ADR) problems is proposed. Via multiscale expansion analysis, we derive from the LB model the resulting macroscopic equations. It is shown that a linear equilibrium distribution is sufficient to produce ADR equations within error terms of the order of the Mach number squared. Furthermore, we study spatially varying structures arising fromthe interaction of advective transportwith a cubic autocatalytic reaction-diffusion process under an imposed uniform flow. While advecting all the present species leads to trivial translation of the Turing patterns, differential advection leads to flow induced instability characterized with traveling stripes with a velocity dependent wave vector parallel to the flow direction. Predictions from a linear stability analysis of the model equations are found to be in line with these observations. © 2013 Global-Science Press.view abstract 10.4208/cicp.441011.270112s **Maintaining the equipartition theorem in small heterogeneous molecular dynamics ensembles**

Siboni, N.H. and Raabe, D. and Varnik, F.*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*87 (2013)It has been reported recently that the equipartition theorem is violated in molecular dynamics simulations with periodic boundary condition. This effect is associated with the conservation of the total momentum. Here, we propose a fluctuating center of mass molecular dynamics approach to solve this problem. Using the analogy to a system exchanging momentum with its surroundings, we work out - and validate via simulations - an expression for the rate at which fluctuations shall be added to the system. It is shown that the proposed method maintains equipartition both at equilibrium and beyond equilibrium in the linear response regime. © 2013 American Physical Society.view abstract 10.1103/PhysRevE.87.030101 **Simulating mobile dendrites in a flow**

Medvedev, D. and Varnik, F. and Steinbach, I.*Procedia Computer Science*18 (2013)We propose a scheme for simulation of the solute-driven dendritic solidification which accounts for the flows of liquid and motion of growing dendrites. The scheme is based on the multiphase-field method for calculating the solidification and the lattice Boltzmann method to simulate the fluid flows. Motion and rotation of solid grains is possible. © 2013 The Authors. Published by Elsevier B.V.view abstract 10.1016/j.procs.2013.05.431 **Simulation of viscous sintering using the lattice Boltzmann method**

Varnik, F. and Rios, A. and Gross, M. and Steinbach, I.*Modelling and Simulation in Materials Science and Engineering*21 (2013)The viscous flow is one of the important mass transport mechanisms in sintering powder materials such as porous glass. The main underlying driving force here is the tendency of the system to minimize the overall surface free energy. In this work, we first address the fundamental problem of the coalescence of two suspending drops and provide an alternative derivation of Frenkel's formula by explicitly taking account of driving forces which arise from the curvature of the contact zone. The result thus obtained is compared with non-ideal (two phase) fluid lattice Boltzmann simulations. Furthermore, we use this simulation tool to address the more complex case of the sintering of a compact of viscous spherical particles. We observe a significantly faster densification dynamics than in experiments but obtain qualitative agreement upon rescaling the unit of time. We attribute this faster dynamics in simulations to the absence of intergranular friction and discuss a possible improvement of the model. We also propose, for the present LB model, a simple way of imposing shear flow to determine the time dependence of the effective viscosity during the sintering process. The method is benchmarked via a simple analytic case and first simulation results are presented for situations for which no analytic theory exists. © 2013 IOP Publishing Ltd.view abstract 10.1088/0965-0393/21/2/025003 **Single-particle fluctuations and directional correlations in driven hard-sphere glasses**

Mandal, S. and Chikkadi, V. and Nienhuis, B. and Raabe, D. and Schall, P. and Varnik, F.*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*88 (2013)Via event-driven molecular dynamics simulations and experiments, we study the packing-fraction and shear-rate dependence of single-particle fluctuations and dynamic correlations in hard-sphere glasses under shear. At packing fractions above the glass transition, correlations increase as shear rate decreases: the exponential tail in the distribution of single-particle jumps broadens and dynamic four-point correlations increase. Interestingly, however, upon decreasing the packing fraction, a broadening of the exponential tail is also observed, while dynamic heterogeneity is shown to decrease. An explanation for this behavior is proposed in terms of a competition between shear and thermal fluctuations. Building upon our previous studies, we further address the issue of anisotropy of the dynamic correlations. © 2013 American Physical Society.view abstract 10.1103/PhysRevE.88.022129 **Viscous coalescence of droplets: A lattice Boltzmann study**

Gross, M. and Steinbach, I. and Raabe, D. and Varnik, F.*Physics of Fluids*25 (2013)The coalescence of two resting liquid droplets in a saturated vapor phase is investigated by Lattice Boltzmann simulations in two and three dimensions. We find that, in the viscous regime, the bridge radius obeys a t1/2-scaling law in time with the characteristic time scale given by the viscous time. Our results differ significantly from the predictions of existing analytical theories of viscous coalescence as well as from experimental observations. While the underlying reason for these deviations is presently unknown, a simple scaling argument is given that describes our results well. © 2013 AIP Publishing LLC.view abstract 10.1063/1.4803178 **Critical dynamics of an isothermal compressible nonideal fluid**

Gross, M. and Varnik, F.*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*86 (2012)A pure fluid at its critical point shows a dramatic slow-down in its dynamics, due to a divergence of the order-parameter susceptibility and the coefficient of heat transport. Under isothermal conditions, however, sound waves provide the only possible relaxation mechanism for order-parameter fluctuations. Here we study the critical dynamics of an isothermal, compressible nonideal fluid via scaling arguments and computer simulations of the corresponding fluctuating hydrodynamics equations. We show that, below a critical dimension of 4, the order-parameter dynamics of an isothermal fluid effectively reduces to "model A," characterized by overdamped sound waves and a divergent bulk viscosity. In contrast, the shear viscosity remains finite above two dimensions. Possible applications of the model are discussed. © 2012 American Physical Society.view abstract 10.1103/PhysRevE.86.061119 **Flow and Rheological Response of Model Glasses**

Varnik, F. and Mandal, S. and Gross, M.*Transactions of the Indian Ceramic Society*71 (2012)Results of molecular dynamics simulations on the response of glassy materials to an externally imposed steady shear are presented. The work highlights on one hand how the competition of the time scale imposed by the flow and the inherent structural relaxation time determines the linear or non-linear nature of the rheological response. On the other hand, the issue of flow heterogeneity in a shear melted glass is also studied. © 2012 Copyright The Indian Ceramic Society.view abstract 10.1080/0371750X.2013.772745 **Heterogeneous shear in hard sphere glasses**

Mandal, S. and Gross, M. and Raabe, D. and Varnik, F.*Physical Review Letters*108 (2012)There is growing evidence that the flow of driven amorphous solids is not homogeneous, even if the macroscopic stress is constant across the system. Via event-driven molecular dynamics simulations of a hard sphere glass, we provide the first direct evidence for a correlation between the fluctuations of the local volume fraction and the fluctuations of the local shear rate. Higher shear rates do preferentially occur at regions of lower density and vice versa. The temporal behavior of fluctuations is governed by a characteristic time scale, which, when measured in units of strain, is independent of shear rate in the investigated range. Interestingly, the correlation volume is also roughly constant for the same range of shear rates. A possible connection between these two observations is discussed. © 2012 American Physical Society.view abstract 10.1103/PhysRevLett.108.098301 **Shear-induced anisotropic decay of correlations in hard-sphere colloidal glasses**

Chikkadi, V. and Mandal, S. and Nienhuis, B. and Raabe, D. and Varnik, F. and Schall, P.*EPL*100 (2012)Spatial correlations of microscopic fluctuations are investigated via real-space experiments and computer simulations of colloidal glasses under steady shear. It is shown that while the distribution of one-particle fluctuations is always isotropic regardless of the relative importance of shear as compared to thermal fluctuations, their spatial correlations show a marked sensitivity to the competition between shear-induced and thermally activated relaxation. Correlations are isotropic in the thermally dominated regime, but develop strong anisotropy as shear dominates the dynamics of microscopic fluctuations. We discuss the relevance of this observation for a better understanding of flow heterogeneity in sheared amorphous solids. © Copyright EPLA, 2012.view abstract 10.1209/0295-5075/100/56001 **Simulation of static critical phenomena in nonideal fluids with the lattice Boltzmann method**

Gross, M. and Varnik, F.*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*85 (2012)A fluctuating nonideal fluid at its critical point is simulated with the lattice Boltzmann method. It is demonstrated that the method, employing a Ginzburg-Landau free energy functional, correctly reproduces the static critical behavior associated with the Ising universality class. A finite-size scaling analysis is applied to determine the critical exponents related to the order parameter, compressibility and specific heat. A particular focus is put on finite-size effects and issues related to the global conservation of the order parameter. © 2012 American Physical Society.view abstract 10.1103/PhysRevE.85.056707 **Contact angle dependence of the velocity of sliding cylindrical drop on flat substrates**

Moradi, N. and Varnik, F. and Steinbach, I.*EPL*95 (2011)Via numerical simulations, we investigate the dynamics of cylindrical drops on flat substrates. In agreement with the common understanding, in the limit of Stokes flow and negligible drop deformation, the drop's centre-of-mass velocity scales linearly with the applied force and with the second power of drop radius. In this paper, we go a step further and perform a detailed study of dissipation loss inside the drop. An important result is that the dominant part of viscous dissipation arises from the region below the drop's centre of mass. Based on this observation, we propose a simple analytic model which allows capturing the dependence of the steady-state drop velocity on the equilibrium contact angle. Simulation results are in good agreement with the predictions of this model. © 2011 Europhysics Letters Association.view abstract 10.1209/0295-5075/95/44003 **Efficient and accurate simulations of deformable particles immersed in a fluid using a combined immersed boundary lattice Boltzmann finite element method**

Krüger, T. and Varnik, F. and Raabe, D.*Computers and Mathematics with Applications*61 (2011)The deformation of an initially spherical capsule, freely suspended in simple shear flow, can be computed analytically in the limit of small deformations [D. Barths-Biesel, J.M. Rallison, The time-dependent deformation of a capsule freely suspended in a linear shear flow, J. Fluid Mech. 113 (1981) 251267]. Those analytic approximations are used to study the influence of the mesh tessellation method, the spatial resolution, and the discrete delta function of the immersed boundary method on the numerical results obtained by a coupled immersed boundary lattice Boltzmann finite element method. For the description of the capsule membrane, a finite element method and the Skalak constitutive model [R. Skalak, A. Tozeren, R.P. Zarda, S. Chien, Strain energy function of red blood cell membranes, Biophys. J. 13 (1973) 245264] have been employed. Our primary goal is the investigation of the presented model for small resolutions to provide a sound basis for efficient but accurate simulations of multiple deformable particles immersed in a fluid. We come to the conclusion that details of the membrane mesh, as tessellation method and resolution, play only a minor role. The hydrodynamic resolution, i.e., the width of the discrete delta function, can significantly influence the accuracy of the simulations. The discretization of the delta function introduces an artificial length scale, which effectively changes the radius and the deformability of the capsule. We discuss possibilities of reducing the computing time of simulations of deformable objects immersed in a fluid while maintaining high accuracy. © 2011 Elsevier Ltd. All rights reserved.view abstract 10.1016/j.camwa.2010.03.057 **Langevin theory of fluctuations in the discrete Boltzmann equation**

Gross, M. and Cates, M.E. and Varnik, F. and Adhikari, R.*Journal of Statistical Mechanics: Theory and Experiment*2011 (2011)The discrete Boltzmann equation for both the ideal and a non-ideal fluid is extended by adding Langevin noise terms in order to incorporate the effects of thermal fluctuations. After casting the fluctuating discrete Boltzmann equation in a form appropriate to the Onsager-Machlup theory of linear fluctuations, the statistical properties of the noise are determined by invoking a fluctuation-dissipation theorem at the kinetic level. By integrating the fluctuating discrete Boltzmann equation, a fluctuating lattice Boltzmann equation is obtained, which provides an efficient way to solve the equations of fluctuating hydrodynamics for ideal and non-ideal fluids. Application of the framework to a generic force-based non-ideal fluid model leads to ideal gas-type thermal noise. Simulation results indicate proper thermalization of all degrees of freedom. © 2011 IOP Publishing Ltd and SISSA.view abstract 10.1088/1742-5468/2011/03/P03030 **Lattice Boltzmann study of pattern formation in reaction-diffusion systems**

Ayodele, S.G. and Varnik, F. and Raabe, D.*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*83 (2011)Pattern formation in reaction-diffusion systems is of great importance in surface micropatterning, self-organization of cellular micro-organisms, and in developmental biology. In this work, we apply the lattice Boltzmann method to study pattern formation in reaction-diffusion systems. As a first methodological step, we consider the case of a single species undergoing transformation reaction and diffusion. In this case, we perform a third-order Chapman-Enskog multiscale expansion and study the dependence of the lattice Boltzmann truncation error on the diffusion coefficient and the reaction rate. These findings are in good agreement with numerical simulations. Furthermore, taking the Gray-Scott model as a prominent example, we provide evidence for the maturity of the lattice Boltzmann method in studying pattern formation in nonlinear reaction-diffusion systems. For this purpose, we perform linear stability analysis of the Gray-Scott model and determine the relevant parameter range for pattern formation. Lattice Boltzmann simulations allow us not only to test the validity of the linear stability phase diagram including Turing and Hopf instabilities, but also permit going beyond the linear stability regime, where large perturbations give rise to interesting dynamical behavior such as the so-called self-replicating spots. We also show that the length scale of the patterns may be tuned by rescaling all relevant diffusion coefficients in the system with the same factor while leaving all the reaction constants unchanged. © 2011 American Physical Society.view abstract 10.1103/PhysRevE.83.016702 **Microfluidic emulsion separation - Simultaneous separation and sensing by multilayer nanofilm structures**

Uhlmann, P. and Varnik, F. and Truman, P. and Zikos, G. and Moulin, J.-F. and Müller-Buschbaum, P. and Stamm, M.*Journal of Physics Condensed Matter*23 (2011)Emulsion separation is of high relevance for filtration applications, liquid-liquid-partitioning of biomolecules like proteins and recovery of products from droplet microreactors. Selective interaction of various components of an emulsion with substrates is used to design microfluidic flow chambers for efficient separation of emulsions into their individual components. Our lab-on-a-chip device consists of an emulsion separation cell with an integrated silicon sensor chip, the latter allowing the detection of liquid motion via the field-effect signal. Thus, within our lab-on-a-chip device, emulsions can be separated while the separation process is monitored simultaneously. For emulsion separation a surface energy step gradient, namely a sharp interface between the hydrophobic and hydrophilic parts of the separation chamber, is used. The key component of the lab-on-a-chip system is a multilayer and multifunctional nanofilm structure which not only provides the surface energy step gradient for emulsion separation but also constitutes the functional parts of the field-effect transistors. The proof-of-principle was performed using a model emulsion consisting of immiscible aqueous and organic solvent components. Droplet coalescence was identified as a key aspect influencing the separation process, with quite different effects during separation on open surfaces as compared to slit geometry. For a detailed description of this observation, an analytical model was derived and lattice Boltzmann computer simulations were performed. By use of grazing incidence small angle x-ray scattering (GISAXS) interfacial nanostructures during gold nanoparticle deposition in a flow field were probed to demonstrate the potential of GISAXS for insitu investigations during flow. © 2011 IOP Publishing Ltd.view abstract 10.1088/0953-8984/23/18/184123 **Modelling thermal fluctuations in non-ideal fluids with the lattice Boltzmann method**

Gross, M. and Adhikari, R. and Cates, M.E. and Varnik, F.*Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences*369 (2011)Recently, we proposed a theoretical framework to include thermal fluctuations into the Lattice Boltzmann (LB) method for non-ideal fluids. Here, we apply a variant thereof toa certain class of force-based non-ideal fluid LB models. We find that ideal-gas-like noise is an exact result of the fluctuation-dissipation theorem in the hydrodynamic regime.It is shown that satisfactory equilibration of the density and fluid momentum can be obtained in a simulation over a wide range of length scales. © 2011 The Royal Society.view abstract 10.1098/rsta.2011.0091 **Morphologies of small droplets on patterned hydrophobic substrates**

Moradi, N. and Gross, M. and Varnik, F. and Zikos, G. and Steinbach, I.*Modelling and Simulation in Materials Science and Engineering*19 (2011)For situations, in which the size of a droplet is comparable to the roughness scale of the solid substrate, we explore possible wetting morphologies on patterned hydrophobic substrates and investigate their dependence on the initial droplet position, droplet volume and the surface geometry. For a regular array of cubical pillars, small perturbations of a symmetric droplet state are restored by capillary forces. Larger deviations, on the other hand, may lead to completely new morphologies. Our studies also suggest that the previously reported 'reentrant transition' upon quasi-static evaporation (a transition from the suspended state to partial penetration and then back to the suspended state) (Gross, et al. 2009 Europhys. Lett. 88 26002) is not restricted to a symmetric initial state but may occur for quite non-symmetric morphologies as well. In contrast, a change in the substrate geometry may lead to a completely different behavior, fully precluding the reentrant transition. This underlines the importance of substrate design for the use of reentrant transition as a self-cleaning mechanism. © 2011 IOP Publishing Ltd.view abstract 10.1088/0965-0393/19/4/045005 **Particle stress in suspensions of soft objects**

Krüger, T. and Varnik, F. and Raabe, D.*Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences*369 (2011)In a suspension of extended objects such as colloidal particles, capsules or vesicles, the contribution of particles to the stress is usually evaluated by first determining the stress originating from a single particle (e.g. via integrating the fluid stress over the surface of a particle) and then adding up the contributions of individual particles. While adequate for a computation of the average stress over the entire system, this approach fails to correctly reproduce the local stress. In this work, we propose and validate a variant of the method of planes which overcomes this problem. The method is particularly suited for many-body interactions arising from, for example, shear and bending rigidity of red blood cells. © 2011 The Royal Society.view abstract 10.1098/rsta.2011.0090 **Shear stress in nonideal fluid lattice Boltzmann simulations**

Gross, M. and Moradi, N. and Zikos, G. and Varnik, F.*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*83 (2011)The viscous stress in nonideal fluid lattice Boltzmann methods is investigated theoretically and by simulations. Three representative liquid-gas models are compared in a steady-state situation, where an analytical expression for the viscous stress is available. It is shown that, in the presence of nonideal fluid interactions or strong body forces, the accuracy of the computed viscous stress depends strongly on the underlying model. © 2011 American Physical Society.view abstract 10.1103/PhysRevE.83.017701 **Stability and dynamics of droplets on patterned substrates: Insights from experiments and lattice Boltzmann simulations**

Varnik, F. and Gross, M. and Moradi, N. and Zikos, G. and Uhlmann, P. and Müller-Buschbaum, P. and Magerl, D. and Raabe, D. and Steinbach, I. and Stamm, M.*Journal of Physics Condensed Matter*23 (2011)The stability and dynamics of droplets on solid substrates are studied both theoretically and via experiments. Focusing on our recent achievements within the DFG-priority program 1164 (Nano-and Microfluidics), we first consider the case of (large) droplets on the so-called gradient substrates. Here the term gradient refers to both a change of wettability (chemical gradient) or topography (roughness gradient). While the motion of a droplet on a perfectly flat substrate upon the action of a chemical gradient appears to be a natural consequence of the considered situation, we show that the behavior of a droplet on a gradient of topography is less obvious. Nevertheless, if care is taken in the choice of the topographic patterns (in order to reduce hysteresis effects), a motion may be observed. Interestingly, in this case, simple scaling arguments adequately account for the dependence of the droplet velocity on the roughness gradient (Moradi et al 2010 Europhys. Lett. 8926006). Another issue addressed in this paper is the behavior of droplets on hydrophobic substrates with a periodic arrangement of square shaped pillars. Here, it is possible to propose an analytically solvable model for the case where the droplet size becomes comparable to the roughness scale (Gross et al 2009 Europhys. Lett. 8826002). Two important predictions of the model are highlighted here. (i)There exists a state with a finite penetration depth, distinct from the full wetting (Wenzel) and suspended (Cassie-Baxter, CB) states. (ii)Upon quasi-static evaporation, a droplet initially on the top of the pillars (CB state) undergoes a transition to this new state with a finite penetration depth but then (upon further evaporation) climbs up the pillars and goes back to the CB state again. These predictions are confirmed via independent numerical simulations. Moreover, we also address the fundamental issue of the internal droplet dynamics and the terminal center of mass velocity on a flat substrate. © 2011 IOP Publishing Ltd.view abstract 10.1088/0953-8984/23/18/184112 **Structure and flow of droplets on solid surfaces**

Müller-Buschbaum, P. and Magerl, D. and Hengstler, R. and Moulin, J.-F. and Körstgens, V. and Diethert, A. and Perlich, J. and Roth, S.V. and Burghammer, M. and Riekel, C. and Gross, M. and Varnik, F. and Uhlmann, P. and Stamm, M. and Feldkamp, J.M. and Schroer, C.G.*Journal of Physics Condensed Matter*23 (2011)The structure and flow of droplets on solid surfaces is investigated with imaging and scattering techniques and compared to simulations. To access nanostructures at the liquid-solid interface advanced scattering techniques such as grazing incidence small-angle x-ray scattering (GISAXS) with micro-and nanometer-sized beams, GISAXS and insitu imaging ellipsometry and GISAXS tomography are used. Using gold nanoparticle suspensions, structures observed in the wetting area due to deposition are probed insitu during the drying of the droplets. After drying, nanostructures in the wetting area and inside the dried droplets are monitored. In addition to drying, a macroscopic movement of droplets is caused by body forces acting on an inclined substrate. The complexity of the solid surfaces is increased from simple silicon substrates to binary polymer brushes, which undergo a switching due to the liquid in the droplet. Nanostructures introduced in the polymer brush due to the movement of droplets are observed. © 2011 IOP Publishing Ltd.view abstract 10.1088/0953-8984/23/18/184111 **Acoustic driven flow and lattice Boltzmann simulations to study cell adhesion in biofunctionalized μ-fluidic channels with complex geometry**

Fallah, M.A. and Myles, V.M. and Krüger, T. and Sritharan, K. and Wixforth, A. and Varnik, F. and Schneider, S.W. and Schneider, M.F.*Biomicrofluidics*4 (2010)Accurately mimicking the complexity of microvascular systems calls for a technology which can accommodate particularly small sample volumes while retaining a large degree of freedom in channel geometry and keeping the price considerably low to allow for high throughput experiments. Here, we demonstrate that the use of surface acoustic wave driven microfluidics systems successfully allows the study of the interrelation between melanoma cell adhesion, the matrix protein collagen type I, the blood clotting factor von Willebrand factor (vWF), and microfluidic channel geometry. The versatility of the tool presented enables us to examine cell adhesion under flow in straight and bifurcated microfluidic channels in the presence of different protein coatings. We show that the addition of vWF tremendously increases (up to tenfold) the adhesion of melanoma cells even under fairly low shear flow conditions. This effect is altered in the presence of bifurcated channels demonstrating the importance of an elaborate hydrodynamic analysis to differentiate between physical and biological effects. Therefore, computer simulations have been performed along with the experiments to reveal the entire flow profile in the channel. We conclude that a combination of theory and experiment will lead to a consistent explanation of cell adhesion, and will optimize the potential of microfluidic experiments to further unravel the relation between blood clotting factors, cell adhesion molecules, cancer cell spreading, and the hydrodynamic conditions in our microcirculatory system. © 2010 American Institute of Physics.view abstract 10.1063/1.3396449 **Roughness-gradient-induced spontaneous motion of droplets on hydrophobic surfaces: A lattice Boltzmann study**

Moradi, N. and Varnik, F. and Steinbach, I.*EPL*89 (2010)The effect of a step-wise change in the pillar density on the dynamics of droplets is investigated via three-dimensional lattice Boltzmann simulations. For the same pillar density gradient but different pillar arrangements, both motion over the gradient zone as well as complete arrest are observed. In the moving case, the droplet velocity scales approximately linearly with the texture gradient. A simple model is provided reproducing the observed linear behavior. The model also predicts a linear dependence of droplet velocity on surface tension. This prediction is clearly confirmed via our computer simulations for a wide range of surface tensions. Copyright © 2010 EPLA.view abstract 10.1209/0295-5075/89/26006 **Second-order convergence of the deviatoric stress tensor in the standard Bhatnagar-Gross-Krook lattice Boltzmann method**

Krüger, T. and Varnik, F. and Raabe, D.*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*82 (2010)It is shown numerically that the deviatoric stress tensor is second-order accurate in the bulk Bhatnagar-Gross-Krook lattice Boltzmann (LB) method. In an earlier work, we have already predicted the second-order convergence. However, numerical simulations using a duct flow were not fully in line with this prediction. In particular, the convergence rate of the stress tensor was observed to depend on the LB boundary condition. In the present paper, we examine a pure bulk system, the decaying Taylor-Green vortex flow. Our prediction on the second-order accuracy of the stress tensor is unambiguously evidenced via these studies. © 2010 The American Physical Society.view abstract 10.1103/PhysRevE.82.025701 **Small droplets on superhydrophobic substrates**

Gross, M. and Varnik, F. and Raabe, D. and Steinbach, I.*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*81 (2010)We investigate the wetting behavior of liquid droplets on rough hydrophobic substrates for the case of droplets that are of comparable size to the surface asperities. Using a simple three-dimensional analytical free-energy model, we have shown in a recent letter that, in addition to the well-known Cassie-Baxter and Wenzel states, there exists a further metastable wetting state where the droplet is immersed into the texture to a finite depth, yet not touching the bottom of the substrate. Due to this new state, a quasistatically evaporating droplet can be saved from going over to the Wenzel state and instead remains close to the top of the surface. In the present paper, we give an in-depth account of the droplet behavior based on the results of extensive computer simulations and an improved theoretical model. In particular, we show that releasing the assumption that the droplet is pinned at the outer edges of the pillars improves the analytical results for larger droplets. Interestingly, all qualitative aspects, such as the existence of an intermediate minimum and the "reentrant transition," remain unchanged. We also give a detailed description of the evaporation process for droplets of varying sizes. Our results point out the role of droplet size for superhydrophobicity and give hints for achieving the desired wetting properties of technically produced materials. © 2010 The American Physical Society.view abstract 10.1103/PhysRevE.81.051606 **Thermal fluctuations in the lattice Boltzmann method for nonideal fluids**

Gross, M. and Adhikari, R. and Cates, M.E. and Varnik, F.*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*82 (2010)We introduce thermal fluctuations in the lattice Boltzmann method for nonideal fluids. A fluctuation-dissipation theorem is derived within the Langevin framework and applied to a specific lattice Boltzmann model that approximates the linearized fluctuating Navier-Stokes equations for fluids based on square-gradient free-energy functionals. The obtained thermal noise is shown to ensure equilibration of all degrees of freedom in a simulation to high accuracy. Furthermore, we demonstrate that satisfactory results for most practical applications of fluctuating hydrodynamics can already be achieved using thermal noise derived in the long-wavelength limit. © 2010 The American Physical Society.view abstract 10.1103/PhysRevE.82.056714

#### fluid dynamics

#### glass transition

#### lattice boltzmann method

#### microfluidics

#### modelling and simulation