Electrically modulated capillary filling imbibition of nematic liquid crystals

The flow of nematic liquid crystals (NLCs) in the presence of an electric field is typically characterized by the variation in its rheological properties due to transition in its molecular arrangements. Here, we bring out a nontrivial interplay of a consequent alteration in the resistive viscous effects and driving electrocapillary interactions, toward maneuvering the capillary filling dynamics over miniaturized scales. Considering a dynamic interplay of the relevant bulk and interfacial forces acting in tandem, our results converge nicely to previously reported experimental data. Finally, we attempt a scaling analysis to bring forth further insight to the reported observations. Our analysis paves the way for the development of microfluidic strategies with previously unexplored paradigms of interaction between electrical and fluidic phenomenon, providing with an augmented controllability on capillary filling as compared to tthose reported to be achievable by the existing strategies. This, in turn, holds utilitarian scopes in improved designs of functional capillarities in electro-optical systems, electrorheological utilities, electrokinetic flow control, as well as in interfacing and imaging systems for biomedical microdevices.

Figure 1

Schematic of the setup for electrocapillary imbibitions of NLC medium rising through a parallel-plate channel. The viscosity variation is the manifestation of different director configurations for open- and closed-switch conditions. Inset: The topological defect is situated at the contact line that demarcates the solid (S), nematic (N), and vapor (V) phases. The defect core has a radius ($r_c$) in order of molecular dimensions (hence not shown in the figure) and a normal $\widehat{\mathbf{k}}$.

Figure 2

The comparison between the semianalytical expressions of the present theory and previous experimental findings [29] for (a) capillary filling and filling rate and (b) filling rate through two different capillary pores of NLC 5CB medium in the absence of an external electric field.

Figure 3

Depicts the variation of (a) dimensionless viscosity and (inset) director angle as a function of the channel width for $\mathrm{Er}=1$ for varying $\overline{q}$ and $\overline{q}=10$ for varying Er. Plot (b) depicts the variation of gross viscosity as a function of the channel width for various combinations of the dielectric strength parameter $\overline{q}$ and Ericksen number Er.

Figure 4

The capillary front propagation and its rate as a function of dimensionless time for different values of the dielectric strength parameter $\overline{q}$ for (a) $\mathrm{Bo}={10}^{-6}$ and (b) $\mathrm{Bo}=0.02$. The other dimensionless parameters involved are for case (a) $\mathrm{Ca}=0.01$, $\mathrm{Er}=20$, and $\mathrm{E}{\mathrm{a}}_c=5$ and (b) $\mathrm{Ca}=0.002$, $\mathrm{Er}=100$, and $\mathrm{E}{\mathrm{a}}_c=5$.

Figure 5

Depicts the different capillary filling regimes for the NLC medium. The approximations from the scaling analysis are compared to the numerical solution for two values of $\overline{q}$. The other parameters for the present case include $\mathrm{Bo}={10}^{-6}$, $\mathrm{Ca}=0.01$, $\mathrm{Er}=20$, and $\mathrm{E}{\mathrm{a}}_c=5$.