Lattice Boltzmann simulations of sedimentation of a single fiber in a weak vertical shear flow

Abstract

Instability of a suspension is directly related to the problem of the cross-stream migration of a particle relative to its neighboring particle suspension. Such crossstream or lateral migration of a single non-spherical particle (fiber) settling in a bounded weak shear flow with vertical streamlines produced by a perturbation to the fiber number density is studied using lattice Boltzmann simulations. The present simulation results demonstrate that at a given shear rate, the lateral migration can be divided into three phases depending on settling Reynolds number R sd and particle aspect ratio κ. At a low settling Reynolds number R sd , the suspension becomes more stable in phase 1. As R sd increases and excesses a critical settling Reynolds number R sd1 , the fiber suspension becomes unstable in phase 2. In phase 3, at an enough large R sd , the inertia dominates the weak shear flow and it may have little effect on stability. A mechanism of the instability induced by an inertial fiber orientation drift and a shear induced cross-streamline drift, recently proposed by Shin, Koch, and Subramanian ["Structure and dynamics of dilute suspensions of finite reynolds number settling fibers," Phys.

Lattice-Boltzmann lattice-spring simulations of two flexible fibers settling in moderate Reynolds number flows

“…The equations could be solved by many computational fluid dynamics methods [11] . In particular, the lattice Boltzmann (LB) method has been proven to be especially effective for solving the fluid flows interacting with complex solid boundaries when the March number is smaller than 0.3 [12][13][14][15][16][17][18][19][20][21]21,22] .…”

Multi-flexible fiber flows: A direct-forcing immersed boundary lattice-Boltzmann lattice-spring approach

“…Ladd (1994) had firstly proposed a moving boundary condition in the LBM and applied it to particulate flows. Later, Koch and others ( Aidun and Clausen, 2010;Aidun et al, 1998;Benzi et al, 1992;Duenweg and Ladd, 2009;Michaelides, 2004, 2005;Koch and Ladd, 1997;Luo et al, 2017;Qi, 1999;Qi and Gordnier, 2015;Qi et al, 2014aQi et al, , 2014bQi et al, , 2010Whittington, 1998 ) had demonstrated that the LBM is the most simple and efficient method to simulate particle suspensions. Unlike traditional CFD, one of features of the lattice-Boltzmann method (LBM) is that micro-kinetic nature of fluid particle collision and streaming, similar to convection-diffusion of fluid momentum, is presented through the lattice-Boltzmann equation at every time step.…”

“…The present work will focus on studies of effects of fiber concentrations, fiber flexibility, and screen-to-fluid speed ratios on the drainage rates of a screen by using the present approach. Although there are hundreds of articles on topics of fiber suspensions ( Koch, 1994;Koch andShaqfeh, 1989, 1991;Qi, 2006;Qi et al, 2014b;Shin et al, 2009 ), very few of studies on drainage rates exist in the literature. We will demonstrate that the forming process of a flexible fiber network over a wire net/screen can be effectively simulated and that the drainage rate is a nonlinear function of time and is significantly affected by fiber's mass.…”