A Numerical Study on the Performance of Liquid Crystal Biosensor Microdroplets

The numerical results from the modeling of liquid crystals dispersed in aqueous solutions in the form of axially symmetric droplets, with the aim of helping to facilitate the development of liquid crystal biosensors, were obtained. We developed a transient two-dimensional nonlinear model obtained via torque balance that incorporates Frank's elastic free energy. In order to perform parametric studies, we defined the scaled parameters based on the surface viscosity and the homeotropic anchoring energy at the droplet interface. To evaluate the performance of the biosensor, the average angle and characteristic time were defined as performance criteria. Using these results, we studied the bulk reorientation of liquid crystal droplets in aqueous solutions caused by biomolecular interaction. Furthermore, we examined how surface viscosity affects the performance of a biosensor in the case of weak planar anchoring. The droplet interface ordering was modeled using the Euler-Lagrange equation. The droplets' equilibrium was determined by minimizing their total distortion energy based on the interaction between their surface and bulk elastic energy. Two factors that contributed to the biosensor performance were homeotropic strength and surface viscosity. This highlights the importance of controlling the surface and physicochemical properties to achieve the desired liquid crystal orientation. In addition, our results provide insight into the role that surface viscosity plays in controlling radial configuration.