Relevance of angular momentum conservation in mesoscale hydrodynamics simulations

Mesoscale simulations of hydrodynamic squirmer interactions

The swimming behavior of self-propelled microorganisms is studied by particle-based mesoscale simulations. The simulation technique includes both hydrodynamics and thermal fluctuations that are both essential for the dynamics of microswimmers. The swimmers are modeled as squirmers, i.e., spherical objects with a prescribed tangential surface velocity, where the focus of thrust generation can be tuned from pushers to pullers. For passive squirmers (colloids), we show that the velocity autocorrelation function agrees quantitatively with the Boussinesq approximation. Single active squirmers show a persistent random-walk behavior, determined by forward motion, lateral diffusion, and orientational fluctuations, in agreement with theoretical predictions. For pairs of squirmers, which are initially swimming in parallel, we find an attraction for pushers and a repulsion for pullers, as expected. The hydrodynamic force between squirmer pairs is calculated as a function of the center-to-center distances d(cm) and is found to be consistent with a logarithmic distance dependence for d(cm) less than about two sphere diameters; here, the force is considerably stronger than expected from the far-field expansion. The dependence of the force strength on the asymmetry of the polar surface velocity is obtained. During the collision process, thermal fluctuations turn out to be very important and to strongly affect the postcollision velocity directions of both squirmers.

Fluid-solid boundary conditions for multiparticle collision dynamics

The simulation of colloidal particles suspended in solvent requires an accurate representation of the interactions between the colloids and the solvent molecules. Using the multiparticle collision dynamics method, we examine several proposals for stick boundary conditions, studying their properties in both plane Poiseuille flow (where fluid interacts with the boundary of a stationary macroscopic solid) and particle-based colloid simulations (where the boundaries are thermally affected and in motion). In addition, our simulations compare various collision rules designed to remove spurious slip near solid surfaces, and the effects of these rules on the thermal motion of colloidal particles. Furthermore, we demonstrate that stochastic reflection of the fluid at solid boundaries fails to faithfully represent stick boundary conditions, and conclude that bounce-back conditions should be applied at both mobile and stationary surfaces. Finally, we generalize these ideas to create partial slip boundary conditions at both stationary and mobile surfaces.

Spatially resolved simulations of membrane reactions and dynamics: multipolar reaction DPD

Biophysical chemistry of mesoscale systems and quantitative modeling in systems biology now require a simulation methodology unifying chemical reaction kinetics with essential collective physics. This will enable the study of the collective dynamics of complex chemical and structural systems in a spatially resolved manner with a combinatorially complex variety of different system constituents. In order to allow a direct link-up with experimental data (e.g. high-throughput fluorescence images) the simulations must be constructed locally, i.e. mesoscale phenomena have to emerge from local composition and interactions that can be extracted from experimental data. Under suitable conditions, the simulation of such local interactions must lead to processes such as vesicle budding, transport of membrane-bounded compartments and protein sorting, all of which result from a sophisticated interplay between chemical and mechanical processes and require the link-up of different length scales. In this work, we show that introducing multipolar interactions between particles in dissipative particle dynamics (DPD) leads to extended membrane structures emerging in a self-organized manner and exhibiting the necessary mechanical stability for transport, correct scaling behavior, and membrane fluidity so as to provide a two-dimensional self-organizing dynamic reaction environment for kinetic studies in the context of cell biology.

Dynamical regimes and hydrodynamic lift of viscous vesicles under shear

The dynamics of two-dimensional viscous vesicles in shear flow, with different fluid viscosities etain and etaout inside and outside, respectively, is studied using mesoscale simulation techniques. Besides the well-known tank-treading and tumbling motions, an oscillatory swinging motion is observed in the simulations for large shear rate. The existence of this swinging motion requires the excitation of higher-order undulation modes (beyond elliptical deformations) in two dimensions. Keller-Skalak theory is extended to deformable two-dimensional vesicles, such that a dynamical phase diagram can be predicted for the reduced shear rate and the viscosity contrast etain/etaout. The simulation results are found to be in good agreement with the theoretical predictions, when thermal fluctuations are incorporated in the theory. Moreover, the hydrodynamic lift force, acting on vesicles under shear close to a wall, is determined from simulations for various viscosity contrasts. For comparison, the lift force is calculated numerically in the absence of thermal fluctuations using the boundary-integral method for equal inside and outside viscosities. Both methods show that the dependence of the lift force on the distance ycm of the vesicle center of mass from the wall is well described by an effective power law ycm(-2) for intermediate distances 0.8Rp< approximately ycm< approximately 3Rp with vesicle radius Rp. The boundary-integral calculation indicates that the lift force decays asymptotically as 1/[ycm ln(ycm)] far from the wall.

Simulation of a model microswimmer

We discuss the modelling of a microswimmer that operates in a 'squirmer' mode, by means of stochastic rotation dynamics. The squirmer that we model can easily be tuned between a 'pusher' and a 'puller'. We examine the flows produced by the squirmer and find that there is good agreement between both the predicted and simulated velocities of locomotion and the resulting flow field.

Transport coefficients of off-lattice mesoscale-hydrodynamics simulation techniques

The viscosity and self-diffusion constant of particle-based mesoscale hydrodynamic methods, multiparticle collision dynamics (MPC), and dissipative particle dynamics, are investigated, both with and without angular-momentum conservation. Analytical results are derived for fluids with an ideal-gas equation of state and a finite-time-step dynamics, and compared with simulation data. In particular, the viscosity is derived in a general form for all variants of the MPC method. In general, very good agreement between theory and simulations is obtained.