Heat Driven Flows in Microsized Nematic Volumes: Computational Studies and Analysis

Abstract

The nematic fluid pumping mechanism responsible for the heat driven flow in microfluidic nematic channels and capillaries is described in a number of applications. This heat driven flow can be generated either by a laser beam focused inside the nematic microvolume and at the nematic channel boundary, or by inhomogeneous heating of the nematic channel or capillary boundaries. As an example, the scenario of the vortex flow excitation in microsized nematic volume, under the influence of a temperature gradient caused by the heat flux through the bounding surface of the channel, is described. In order to clarify the role of heat flux in the formation of the vortex flow in microsized nematic volume, a number of hydrodynamic regimes based on a nonlinear extension of the Ericksen–Leslie theory, supplemented by thermomechanical correction of the shear stress and Rayleigh dissipation function, as well as taking into account the entropy balance equation, are analyzed. It is shown that the features of the vortex flow are affected not only by the power of the laser radiation, but also by the duration of the energy injection into the microsized nematic channel.

Shear-Driven Mechanism of Temperature Gradient Formation in Microfluidic Nematic Devices: Theory and Numerical Studies

“…By means of other hydrodynamic flow with profiles, which cannot demonstrate the sharp growth of u st across the HAN channel, one can achieve the same result only by using of the "high-speed" hydrodynamic flow ∼0.1 µm/s [22]. However, taking into account that some LC systems driven by external SS exhibit such non-equilibrium phenomena as a tumbling behavior [7,8,23], the mechanical description can shed some light on the problem of temperature gradient formation; when under certain conditions, the thermomechanical force can overcome elastic, viscous, and anchor forces and cause a temperature gradient across the HAN channel.…”

“…It has been shown that, due to the temperature gradient ∇T, the horizontal hybrid aligned nematic (HAN) microfluidic channel, being initially at rest, starts moving in the horizontal direction if heated from below or above [6][7][8]. In the case when the director n is anchored homeotropically to the cooler (T lw ), lower boundaries and homogeneously to the hotter (T up ) upper boundaries, due to coupling between ∇T ∼ ∆T d and ∇ n, the hydrodynamic flow v = v x î = u î [7] in the horizontal direction is excited.…”

“…Here, ∆T = T up − T lw is the temperature difference on the HAN boundaries, d is the thickness of the HAN channel, and î is the unit vector taken parallel to the horizontal boundaries of the HAN channel (see Figure 1). The magnitude of the flow v x is proportional to ∼ d η σ tm zx [6][7][8], where σ tm zx ∼ ξ ∆T d 2 is the tangential component of the thermomechanical stress tensor σ tm ij , η is the viscosity, and ξ is the thermomechanical constant [6]. The direction of the hydrodynamic flow v is influenced by the character of the preferred anchoring of the average molecular direction n to the boundaries of the HAN channel and the heat flux q across the bounding surface [7,8].…”

“…The magnitude of the flow v x is proportional to ∼ d η σ tm zx [6][7][8], where σ tm zx ∼ ξ ∆T d 2 is the tangential component of the thermomechanical stress tensor σ tm ij , η is the viscosity, and ξ is the thermomechanical constant [6]. The direction of the hydrodynamic flow v is influenced by the character of the preferred anchoring of the average molecular direction n to the boundaries of the HAN channel and the heat flux q across the bounding surface [7,8]. Measurements of the temperature of the induced flow were performed on the HAN cell [9], and the main result of that experimental study is the estimation of the thermomechanical constant ξ ∼ 10 −12 J/K m [9].…”

“…Despite the fact that the possibility of formation of hydrodynamic flows in nematic channels under the influence of temperature gradients has been theoretically described since [6][7][8], only detailed numerical simulations performed within the framework of the extended Ericksen-Leslie theory [10,11] allowed us to recreate the complete picture of the formation of flows in nematic microchannels and capillaries. One of the aims of this paper is to describe the various regimes of hydrodynamic flow formation due to the interaction between the temperature and director field gradients obtained by numerical modeling of these processes.…”