Hydrodynamic Mechanism of Temperature Gradient Formation in Microfluidic Nematic Devices

Abstract

AbstractThe purpose of this chapter is to show some routes in describing the mechanism responsible for the formation of the temperature difference at the boundaries of the microfluidic hybrid aligned nematic (HAN) channel, initially equal to zero, if one sets up the stationary hydrodynamic flow or under the effect of an externally applied shear stress (SS) to the bounding surfaces. Calculations based on the nonlinear extension of the classical Ericksen–Leslie theory, supplemented by thermomechanical correction of the SS \(\sigma _{zx}\) and Rayleigh dissipation function, with accounting the entropy balance equation, show that due to the coupling among the \(\sigma _{zx}\), the gradients of the temperature \(\nabla T\) and the director \(\hat{\mathbf {n}}\) fields in the HAN channel the horizontal nematic flow \({\mathbf {v}}\) is excited. The direction and magnitude of \({\mathbf {v}}\) is influenced by both the heat flux \({\mathbf {q}}\) across the HAN channel and the strength of the \(\sigma _{zx}\).KeywordsLiquid crystalsHydrodynamics of anisotropic systemsThermomechanical force