Investigation of Shear-Driven and Pressure-Driven Liquid Crystal Flow at Microscale: A Quantitative Approach for the Flow Measurement

Abstract

The liquid crystal-based method is a new technology developed for flow visualizations and measurements at microscale with great potentials. It is the priority to study the flow characteristics before implementation of such a technology. A numerical analysis has been applied to solve the simplified dimensionless two-dimensional Leslie-Ericksen liquid crystal dynamic equation. This allows us to analyze the coupling effect of the LC's director orientation and flow field. We will be discussing two classic shear flow cases at microscale, namely Couette and Poiseuille flow. In both cases, the plate drag speed in the state of Couette flow are varied as well as the pressure gradients in Poiseuille flow state are changed to study their effects on the flow field distributions. In Poiseuille flow, with the increase of applied pressure gradient, the influence of backflow significantly affects the flow field. Results show that the proposed method has great advantages on measurement near the wall boundaries which could complement to the current adopted flow measurement technique. The mathematical model proposed in this article could be of great potentials in the development of the quantitatively flow measurement technology.

Keywords: director field; flow measurement; flow visualization; liquid crystal; shear flow.

Figure 1

Schematics and description of the mathematical model of a nematic liquid crystal in the Couette flow. The upper plate is moved to the right at a constant velocity.

Figure 2

Schematics and the mathematical description of a nematic liquid crystal in the Poiseuille flow.

Figure 3

(a) Weak flow director profile across the dimensionless channel width −1≤ z ≤ 1 under strong anchoring and g = 25 (Anderson, T. G. et al., 2015). (b) The calculated director profile of strong anchoring at g = 25.

Figure 4

(a) Director profiles at different velocities of the upper plate. (b) The maximum directional angle at different velocities of the upper plate.

Figure 5

Strong and weak flow solutions at different dimensional pressure gradients. (a–d) correspond to the condition of g = 5, 10, 20, and 25 respectively.

Figure 6

Velocity profiles and director fields at strong anchoring condition. (a–c): The solution of strong anchoring at g = 10. (a) Velocity distributions over the channel width; (b) angle of the director; (c) director distributions over the microchannel. (d–f): Director and flow distributions within the microchannel under the pressure of g = 25.

Figure 7

The solution of strong solution at g = 50. (a) The velocity profile; (b) angle of the director; (c) the distribution of the director at g = 50.

Figure 8

Positional sensitivity of the directional profile of the LC flow. (a) and (b) are sensitivities of the LC in Couette flow at various velocities of the upper plate; (c) and (d) represent the sensitivities at various dimensional pressure gradient in Poiseuille flow.