Flow and Nematic Director Profiles in a Microfluidic Channel: The Interplay of Nematic Material Constants and Backflow

Abstract

We numerically and analytically study the flow and nematic order parameter profiles in a microfluidic channel, within the Beris–Edwards theory for nematodynamics, with two different types of boundary conditions—strong anchoring/Dirichlet conditions and mixed boundary conditions for the nematic order parameter. We primarily study the effects of the pressure gradient, the effects of the material constants and viscosities modelled by a parameter L 2 and the nematic elastic constant L ∗ , along with the effects of the choice of the boundary condition. We study continuous and discontinuous solution profiles for the nematic director and these discontinuous solutions have a domain wall structure, with a layered structure that offers new possibilities. Our main results concern the onset of flow reversal as a function of L ∗ and L 2 , including the identification of certain parameter regimes with zero net flow rate. These results are of value in tuning microfluidic geometries, boundary conditions and choosing liquid crystalline materials for desired flow properties.

Keywords

• nematic liquid crystal
• Beris–Edwards
• flow hydrodynamics
• asymptotic analysis