We develop a first-order and a second-order, coupled, energy stable numerical schemes for a modified Ericksen–Leslie hydrodynamic model for nematic liquid crystals. We then discuss two ways to develop decoupled schemes for the model and show that they are energy stable as well. The coupled schemes are implemented in 2-dimensional space, with which we study defect dynamics in flows of nematic li...

We present an asymptotic analysis of the thickness of the liquid film that coats a smooth solid substrate when it is withdrawn from a bath of non-Newtonian fluid, and compare our results with experimental measurements. The film thickness is, to a good approximation, uniform above the point where the film is withdrawn from the fluid bath, and depends on the rotation rate, the fluid properties an...

The original Ericksen-Leslie consists the conservation laws of nematic liquid crystals, which includes inertial effect. Thus full system has hyperbolic feature. In this paper we study zero inertia limit that is from to parabolic Ericksen-Leslie's crystal flow. By introducing an initial layer and constructing energy norm dissipation functional depending on solutions limiting system, derive a glo...

We consider two elliptic coupled systems of relevance in the fluid dynamics. These are posed on whole space [Formula: see text], and they action external forces. The first system deals with simplified Ericksen–Leslie (SEL) system, which describes dynamics liquid crystal flows. second is time-independent magneto-hydrodynamic (MHD) equations. For SEL we obtain a new criterion to improve regularit...

We study the coupled Navier-Stokes Ginzburg-Landau model of nematic liquid crystals introduced by F.H. Lin, which is a simplified version ofthe Ericksen-Leslie system. We generalize the model to compact n-dimensional Riemannian manifolds, deriving the system from a variational principle, and provide a very simple proof of local well-posedness for this coupled system using a contraction mapping ...

In this paper, the effect of suspended particles on thermal convection in an incompressible Rivlin-Ericksen elastico-viscous fluid in a porous medium is considered. For the porous medium, the Brinkman model is employed. By applying a normal mode analysis method, the dispersion relation has been derived and solved analytically. It is observed that the medium permeability, suspended particles, gr...

Microorganisms often encounter anisotropy, for example in mucus and biofilms. We study how anisotropy and elasticity of the ambient fluid affects the speed of a swimming microorganism with a prescribed stroke. Motivated by recent experiments on swimming bacteria in anisotropic environments, we extend a classical model for swimming microorganisms, the Taylor swimming sheet, actuated by small-amp...