1,274 research outputs found
Lattice Boltzmann simulations of a viscoelastic shear-thinning fluid
We present a hybrid lattice Boltzmann algorithm for the simulation of flow
glass-forming fluids, characterized by slow structural relaxation, at the level
of the Navier-Stokes equation. The fluid is described in terms of a nonlinear
integral constitutive equation, relating the stress tensor locally to the
history of flow. As an application, we present results for an integral
nonlinear Maxwell model that combines the effects of (linear) viscoelasticity
and (nonlinear) shear thinning. We discuss the transient dynamics of
velocities, shear stresses, and normal stress differences in planar
pressure-driven channel flow, after switching on (startup) and off (cessation)
of the driving pressure. This transient dynamics depends nontrivially on the
channel width due to an interplay between hydrodynamic momentum diffusion and
slow structural relaxation
Channel Flow of a Tensorial Shear-Thinning Maxwell Model: Lattice Boltzmann Simulations
We introduce a nonlinear generalized tensorial Maxwell-type constitutive
equation to describe shear-thinning glass-forming fluids, motivated by a recent
microscopic approach to the nonlinear rheology of colloidal suspensions. The
model captures a nonvanishing dynamical yield stress at the glass transition
and incorporates normal-stress differences. A modified lattice-Boltzmann (LB)
simulation scheme is presented that includes non-Newtonian contributions to the
stress tensor and deals with flow-induced pressure differences. We test this
scheme in pressure-driven 2D Poiseuille flow of the nonlinear generalized
Maxwell fluid. In the steady state, comparison with an analytical solution
shows good agreement. The transient dynamics after startup and cessation of the
pressure gradient are studied; the simulation reproduces a finite stopping time
for the cessation flow of the yield-stress fluid in agreement with previous
analytical estimates
Mesoscopic simulation of diffusive contaminant spreading in gas flows at low pressure
Many modern production and measurement facilities incorporate multiphase
systems at low pressures. In this region of flows at small, non-zero Knudsen-
and low Mach numbers the classical mesoscopic Monte Carlo methods become
increasingly numerically costly. To increase the numerical efficiency of
simulations hybrid models are promising. In this contribution, we propose a
novel efficient simulation approach for the simulation of two phase flows with
a large concentration imbalance in a low pressure environment in the low
intermediate Knudsen regime. Our hybrid model comprises a lattice-Boltzmann
method corrected for the lower intermediate Kn regime proposed by Zhang et al.
for the simulation of an ambient flow field. A coupled event-driven
Monte-Carlo-style Boltzmann solver is employed to describe particles of a
second species of low concentration. In order to evaluate the model, standard
diffusivity and diffusion advection systems are considered.Comment: 9 pages, 8 figure
Steady-state hydrodynamic instabilities of active liquid crystals: Hybrid lattice Boltzmann simulations
We report hybrid lattice Boltzmann (HLB) simulations of the hydrodynamics of
an active nematic liquid crystal sandwiched between confining walls with
various anchoring conditions. We confirm the existence of a transition between
a passive phase and an active phase, in which there is spontaneous flow in the
steady state. This transition is attained for sufficiently ``extensile'' rods,
in the case of flow-aligning liquid crystals, and for sufficiently
``contractile'' ones for flow-tumbling materials. In a quasi-1D geometry, deep
in the active phase of flow-aligning materials, our simulations give evidence
of hysteresis and history-dependent steady states, as well as of spontaneous
banded flow. Flow-tumbling materials, in contrast, re-arrange themselves so
that only the two boundary layers flow in steady state. Two-dimensional
simulations, with periodic boundary conditions, show additional instabilities,
with the spontaneous flow appearing as patterns made up of ``convection
rolls''. These results demonstrate a remarkable richness (including dependence
on anchoring conditions) in the steady-state phase behaviour of active
materials, even in the absence of external forcing; they have no counterpart
for passive nematics. Our HLB methodology, which combines lattice Boltzmann for
momentum transport with a finite difference scheme for the order parameter
dynamics, offers a robust and efficient method for probing the complex
hydrodynamic behaviour of active nematics.Comment: 18 eps figures, accepted for publication in Phys. Rev.
Efficient and accurate simulations of deformable particles immersed in a fluid using a combined immersed boundary lattice Boltzmann finite element method
The deformation of an initially spherical capsule, freely suspended in simple
shear flow, can be computed analytically in the limit of small deformations [D.
Barthes-Biesel, J. M. Rallison, The Time-Dependent Deformation of a Capsule
Freely Suspended in a Linear Shear Flow, J. Fluid Mech. 113 (1981) 251-267].
Those analytic approximations are used to study the influence of the mesh
tessellation method, the spatial resolution, and the discrete delta function of
the immersed boundary method on the numerical results obtained by a coupled
immersed boundary lattice Boltzmann finite element method. For the description
of the capsule membrane, a finite element method and the Skalak constitutive
model [R. Skalak et al., Strain Energy Function of Red Blood Cell Membranes,
Biophys. J. 13 (1973) 245-264] have been employed. Our primary goal is the
investigation of the presented model for small resolutions to provide a sound
basis for efficient but accurate simulations of multiple deformable particles
immersed in a fluid. We come to the conclusion that details of the membrane
mesh, as tessellation method and resolution, play only a minor role. The
hydrodynamic resolution, i.e., the width of the discrete delta function, can
significantly influence the accuracy of the simulations. The discretization of
the delta function introduces an artificial length scale, which effectively
changes the radius and the deformability of the capsule. We discuss
possibilities of reducing the computing time of simulations of deformable
objects immersed in a fluid while maintaining high accuracy.Comment: 23 pages, 14 figures, 3 table
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