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.
Highlights
Nematic liquid crystals are classical examples of partially ordered complex liquids for which the constituent molecules have translational freedom but exhibit a degree of long-range orientational ordering or certain preferred directions of averaged molecular alignment, that vary in space and time [1]
We work in a reduced Beris–Edwards framework to model a microfluidic channel, with an applied pressure gradient to induce fluid flow, and different types of boundary conditions for a reduced Q-tensor on the channel walls with the usual no-slip boundary conditions for the flow field
We look at two different cases: (i) symmetric Dirichlet conditions for θ on ỹ = ±1 consistent with strong anchoring and in the spirit of [8], (ii) a Neumann-type boundary condition modelling weak anchoring on ỹ = −1 accompanied by a Dirichlet condition on y = 1 as shown below
Summary
Nematic liquid crystals are classical examples of partially ordered complex liquids for which the constituent molecules have translational freedom but exhibit a degree of long-range orientational ordering or certain preferred directions of averaged molecular alignment, that vary in space and time [1]. In the Ericksen–Leslie framework, we have two variables—the flow field and the nematic director, which is interpreted as the direction of preferred averaged molecular alignment in space. The Beris–Edwards theory is more general than the Ericksen–Leslie since it employs the Landau-de Gennes Q-tensor order parameter to describe the nematic orientational ordering. We work in a reduced Beris–Edwards framework to model a microfluidic channel, with an applied pressure gradient to induce fluid flow, and different types of boundary conditions for a reduced Q-tensor on the channel walls with the usual no-slip boundary conditions for the flow field. The various dynamical theories of nematic liquid crystals and the key results are surveyed in [26] and in [27]; the authors rigorously derive the Ericksen–Leslie equations from the Beris–Edwards model.
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