Modelling & Simulation
Scale bridging modelling of complex fluids: From nano-scale flow to suspension rheology
Fathollah Varnik, ICAMS, Ruhr-Universität, Bochum, Germany
Complex fluids cover a wide range of materials from binary fluid mixtures through emulsions to suspensions of rigid and soft particles [1-4]. Flow properties, structure and rheological response in these materials are mutually connected and determined by the interplay of processes on different length and time scales. This includes on the one hand forces and transport on the particle or droplet scale and the long range hydrodynamic effects on the microstructure on the other hand. The presence of various scales poses a challenge to numerical modelling of these systems.
We present a number of successful strategies which allow to efficiently bridge this gap [5-8]. Among these, a model to simulate the flow of suspensions of red blood cells is presented and validated against available theories [2,3,7]. The second example brings us to the deformation behaviour of amorphous solids where results of molecular dynamics simulations serve as input to larger continuum-scale models, allowing one to predict flow instability and a rich dynamic behaviour for the apparently simple case of flow in a planar Couette geometry .
 S. Mandal, S. Lang, M. Gross, M. Oettel, D. Raabe, T. Franosch, F. Varnik, Multiple reentrant glass transitions in confined hard-sphere glasses, Nature Com. 5, 4435 (2014).
 T. Krüger, M. Gross, D. Raabe, F. Varnik, Crossover from tumbling to tank-treading-like motion in dense simulated suspensions of red blood cells, Soft Matter 9, 9008 (2013).
 M. Gross, T. Krüger, F. Varnik, Fluctuations and diffusion in sheared athermal suspensions of deformable particles, Europhys. Letters 108, 68006 (2014).  M. Gross, F. Varnik, Spreading dynamics of nanodrops: A lattice Boltzmann study, Int. J. Modern Physics C 25, 1340019 (2014).
 M. Gross, M. E. Cates, F. Varnik, R. Adhikari, Langevin theory of fluctuations in the discrete Boltzmann equation, J. Stat. Mech. P03030 (2011).
 D. Belardinelli, M. Sbragaglia, L. Biferale, M. Gross, F. Varnik, Fluctuating multicomponent lattice Boltzmann model, Phys. Rev. E 91, 023313 (2015).
 T. Krüger, F. Varnik, D. Raabe, Efficient and accurate simulations of deformable particles immersed in a fluid using a combined immersed boundary lattice Boltzmann finite element method, Comp. and Mathematics w. Appl., 61, 3485 (2011).
 S. Mandal, M. Gross, D. Raabe, F. Varnik, Heterogeneous shear in hard sphere glasses, Phys. Rev. Lett. 108, 098301 (2012).