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Abstract

Due to the presence of many time and length scales, modelling complex fluids is a real challenge for modern scientific computing. Rigorous and predictive bottom-up approaches are quite rare and largely remain a task for future research.  In this context, it is of great interest to develop models which allow to efficiently incorporate the essential effects originating from a smaller scale in a larger scale description. In this talk, I present two of such approaches which allow the  study a large variety of physical phenomena. In the first part of the talk, a model based on the lattice Boltzmann (LB) method is developed that allows to simulate a non-ideal, van-der-Waals-like fluid including thermal fluctuations [1,2]. It is shown in detail how a Langevin theory of a non-ideal fluid LB model can be constructed that respects all basic laws of equilibrium statistical mechanics. A fluctuation-dissipation theorem is obtained by first transferring the Onsager's regression hypothesis to the discrete Boltzmann equation for non-ideal fluids in the moment space and then deriving from it the desired LB model [1]. The theory is general and can be applied to any existing deterministic lattice Boltzmann model. The method is then applied to a variety of physical phenomena such as spreading of nanodrops (where a cross-over from nano- to macroscale behavior is observed by tuning thermal fluctuations), surface roughening and static and dynamic critical fluctuations [3]. The second part of the presentation deals with modelling suspensions of deformable objects such as, e.g., red blood cells and capsules. The approach combines the lattice Boltzmann method --for the dynamics of the fluid-- with the finite element method --which solves the membrane dynamics. For the coupling between the two, the immersed boundary method is used. The method is implemented and successfully benchmarked in the case of a single cell under simple shear [4]. It is then applied to the study of particle stress in a dense suspension, where a new approach for accurate determination of local stress is proposed and tested [5]. Moreover, using this hybrid-method, the collective dynamics of dense suspensions of red blood cells is investigated uncovering the onset of tank-treading even in highly dense suspensions upon an increase of the suspension stress [6].

References:
[1] M. Gross,  M. E. Cates, F. Varnik, R. Adhikari, Langevin theory of fluctuations in the discrete Boltzmann equation, J. Stat. Mech. P03030 (2011).
[2] M. Gross, R. Adhikari, M. E. Cates, F. Varnik, Thermal fluctuations in the lattice Boltzmann method for non-ideal fluids, Phys. Rev. E 82, 056714 (2010).
[3] M. Gross, F. Varnik, Simulation of static critical phenomena with the lattice Boltzmann method, Phys. Rev. E. 85, 056707 (2012).
[4] 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, Computers and Mathematics with Applications 61, 3485 (2011).
[5] T. Krüeger, F. Varnik, D. Raabe, Particle stress in suspensions of soft objects, Phil. Trans. R. Soc. A 369, 2414 (2011).
[6] T. Krüger, D. Raabe, F. Varnik, Crossover from tumbling to tank-treading-like motion in dense suspensions of red blood cells (submitted).