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Register a new userShape changes and motion of a vesicle in a fluid using a lattice Boltzmann model
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We study the deformation and motion of an erythrocyte in fluid flows via a lattice Boltzmann method. To this purpose, the bending rigidity and the elastic modulus of isotropic dilation are introduced and incorporated with the lattice Boltzmann simulation, and the membrane-flow interactions on both sides of the membrane are carefully examined. We find that the static biconcave shape of an erythrocyte is quite stable and can effectively resist the pathological changes on their membrane. Further, our simulation results show that in shear flow, the erythrocyte will be highly flattened and undergo tank tread-like motion. This phenomenon has been observed by experiment very long time ago, but it has feazed the boundary integral and singularity methods up to the present. Because of its intrinsically parallel dynamics, this lattice Boltzmann method is expected to find wide applications for both single and multi-vesicles suspension as well as complex open membranes in various fluid flows for a wide range of Reynolds numbers.
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In this paper, we propose a lattice Boltzmann (LB) model for the generalized coupled cross-diffusion-fluid system. Through the direct Taylor expansion method, the proposed LB model can correctly recover the macroscopic equations. The cross diffusion terms in the coupled system are modeled by introducing additional collision operators, which can be used to avoid special treatments for the gradient terms. In addition, the auxiliary source terms are constructed properly such that the numerical diffusion caused by the convection can be eliminated. We adopt the developed LB model to study two important systems, i.e., the coupled chemotaxis-fluid system and the double-diffusive convection system with Soret and Dufour effects. We first test the present LB model through considering a steady-state case of coupled chemotaxis-fluid system, then we analyze the influences of some physical parameters on the formation of sinking plumes. Finally, the double-diffusive natural convection system with Soret and Dufour effects is also studied, and the numerical results agree well with some previous works.
The squirmer is a simple yet instructive model for microswimmers, which employs an effective slip velocity on the surface of a spherical swimmer to describe its self-propulsion. We solve the hydrodynamic flow problem with the lattice Boltzmann (LB) method, which is well-suited for time-dependent problems involving complex boundary conditions. Incorporating the squirmer into LB is relatively straight-forward, but requires an unexpectedly fine grid resolution to capture the physical flow fields and behaviors accurately. We demonstrate this using four basic hydrodynamic tests: Two for the far-field flow---accuracy of the hydrodynamic moments and squirmer-squirmer interactions---and two that require the near field to be accurately resolved---a squirmer confined to a tube and one scattering off a spherical obstacle---which LB is capable of doing down to the grid resolution. We find good agreement with (numerical) results obtained using other hydrodynamic solvers in the same geometries and identify a minimum required resolution to achieve this reproduction. We discuss our algorithm in the context of other hydrodynamic solvers and present an outlook on its application to multi-squirmer problems.
A lattice Boltzmann model is considered in which the speed of sound can be varied independently of the other parameters. The range over which the speed of sound can be varied is investigated and good agreement is found between simulations and theory. The onset of nonlinear effects due to variations in the speed of sound is also investigated and good agreement is again found with theory. It is also shown that the fluid viscosity is not altered by changing the speed of sound.
Conventional lattice Boltzmann models for the simulation of fluid dynamics are restricted by an error in the stress tensor that is negligible only for vanishing flow velocity and at a singular value of the temperature. To that end, we propose a unified formulation that restores Galilean invariance and isotropy of the stress tensor by introducing an extended equilibrium. This modification extends lattice Boltzmann models to simulations with higher values of the flow velocity and can be used at temperatures that are higher than the lattice reference temperature, which enhances computational efficiency by decreasing the number of required time steps. Furthermore, the extended model remains valid also for stretched lattices, which are useful when flow gradients are predominant in one direction. The model is validated by simulations of two- and three-dimensional benchmark problems, including the double shear layer flow, the decay of homogeneous isotropic turbulence, the laminar boundary layer over a flat plate and the turbulent channel flow.
In this work we consider theoretically the problem of a Newtonian droplet moving in an otherwise quiescent infinite viscoelastic fluid under the influence of an externally applied temperature gradient. The outer fluid is modelled by the Oldroyd-B equation, and the problem is solved for small Weissenberg and Capillary numbers in terms of a double perturbation expansion. We assume microgravity conditions and neglect the convective transport of energy and momentum. We derive expressions for the droplet migration speed and its shape in terms of the properties of both fluids. In the absence of shape deformation, the droplet speed decreases monotonically for sufficiently viscous inner fluids, while for fluids with a smaller inner-to-outer viscosity ratio, the droplet speed first increases and then decreases as a function of the Weissenberg number. For small but finite values of the Capillary number, the droplet speed behaves monotonically as a function of the applied temperature gradient for a fixed ratio of the Capillary and Weissenberg numbers. We demonstrate that this behaviour is related to the polymeric stresses deforming the droplet in the direction of its migration, while the associated changes in its speed are Newtonian in nature, being related to a change in the droplets hydrodynamic resistance and its internal temperature distribution. When compared to the results of numerical simulations, our theory exhibits a good predictive power for sufficiently small values of the Capillary and Weissenberg numbers.
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