Lattice Boltzmann algorithm to simulate isotropic-nematic emulsions

Abstract

We present lattice Boltzmann simulations of the dynamical equations of motion of a drop of isotropic fluid in a nematic liquid crystal solvent, both in the absence and in the presence of an electric field. The coupled equations we solve are the Beris-Edward equations for the dynamics of the tensor order parameter describing the nematic solvent, the Cahn-Hilliard equation for the concentration evolution, and the Navier-Stokes equations for the determination of the instantaneous velocity field. We implement the lattice Boltzmann algorithm to ensure that spurious velocities are close to zero in equilibrium. We first study the effects of the liquid crystal elastic constant, K, anchoring strength, W, and surface tension, sigma, on the shape of the droplet and on the director field texture in equilibrium. We then consider how the drop behaves as the director field is switched by an applied electric field. We also show that the algorithm allows us to follow the motion of a drop of isotropic fluid placed in a liquid crystal cell with a tilted director field at the boundaries.

Steady-state hydrodynamic instabilities of active liquid crystals: Hybrid lattice Boltzmann simulations

“…This we interpret as a discretisation error, as this method in 2D is known (for conventional i.e. passive liquid crystals) to lead to discretization errors causing small spurious velocities even in the steady state [43].…”

“…Ref. [43]). It can be seen that the LB treatment with the double gradient terms entered in the second moment constraint leads to a small deviation at intermediate times.…”

Electric-field-induced shape transition of nematic tactoids

“…The last term couples the concentration gradient to the liquid crystal orientation, modelling interfacial anchoring of the liquid crystal. L 0 > 0 encourages the director to align parallel to the isotropicnematic interface (planar anchoring), whereas L 0 < 0 encourages perpendicular (homeotropic) anchoring [39]. To reproduce the experimental results qualitatively, we choose A 0 =1.5, A ϕ =0.28, K=0.093, ǫ a =1, k ϕ =0.05 and L 0 =0.06.…”

Channel flow of a tensorial shear-thinning Maxwell model: Lattice Boltzmann simulations

“…In the steady state, we did not find significant differences to our scheme, which we believe to be easier to justify in the non-steady case. There are applications of LB to complex fluids where the route using a forcing term F i is empirically found to be more robust compared to the modification of the distribution function 38 . A number of schemes exploit the equivalence of ∂ · Σ with an external force density in Eq.…”

“…One may also exploit that the gradient of the non-Newtonian stresses appears equivalently to an external force density in the Navier-Stokes equations. The dynamics of the non-Newtonian forces is then traced either by a modified LB scheme at the cost of introducing an enlarged set of lattice-node densities [37][38][39] , or through suitable finite-difference solvers in hybrid-LB schemes [40][41][42] . In this paper, we present a modified LB scheme that allows to naturally incorporate non-Newtonian stresses, including flow-induced pressure and normal-stress differences relevant close to the glass transition.…”