ICAMS / Interdisciplinary Centre for Advanced Materials Simulation


New developments in lattice Boltzmann modelling of complex fluids: from surface roughening, critical phenomena to suspensions of red blood cells

Date: 24.07.2012
Time: 10:00 a.m.
Place: 21st International Conference on Discrete Simulation of Fluid Dynamics (DSFD), The LaLiT Ashok, Bangalore, India

Fathollah Varnik

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].

[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).

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