Search Results (5)

In this study, two numerical schemes with second-order accuracy in time for a modified Ericksen–Leslie model are constructed. The highlight is based on a novel convex splitting method for dealing with the nonlinear potentials, which is integrated with the second-order backward differentiation formula (BDF2) and leap frog method for temporal discretization and the finite element method for spatial discretization. The unconditional energy stability of both schemes is further demonstrated. Finally, several numerical examples are presented to demonstrate the efficiency and accuracy of the proposed schemes. Full article

Elongated ellipsoidal liquid crystal microdroplet reorientation dynamics are discussed in this paper for biosensor applications. To investigate the effect of elongated droplets on nematic liquid crystal droplet biosensors, we simulated a model of a liquid crystal droplet using ellipse geometry. Director reorientation is examined in relation to the elongated droplet shape. In addition, we examined aspect ratio as a factor affecting biosensor response time in relation to surface viscosity and anchoring energy. Finally, the findings suggest that the aspect ratio should be taken into account when designing biosensors. These results can be used to develop more effective biosensors for a variety of applications. This model then predicts the director reorientation angle, which is dependent on the anchoring energy and surface viscosity. This model further suggests that both surface viscosity and homeotropic anchoring energy play an important role when it comes to the director reorientation angle. We developed and applied a nonlinear unsteady-state mathematical model utilizing torque balance and Frank free energy according to the Leslie–Ericksen continuum theory for simulating elongated nematic liquid crystal biosensor droplets with aqueous interfaces. Using the Euler–Lagrange equation, a transient liquid crystal–aqueous interface realignment is modeled by changing the easy axis when surfactant molecules are added to the interface. The realignment at the surface of the droplet is assumed to be driven by the effect of the surfactant, which causes an anchoring transition. According to the results, the response time of the biosensor depends on the aspect ratio. Therefore, the elongation has the potential to control biosensing response time. The result of our study provides a better understanding of director reorientation in elongated liquid crystal droplets in biosensing applications through the numerical results which are presented in this paper. Full article

A nonlinear unsteady-state mathematical model employing torque balance and Frank free energy according to the Leslie-Ericksen continuum theory is developed and implemented to simulate the performance of nematic liquid crystal biosensor films with aqueous interfaces. A transient liquid crystal-aqueous interface realignment is modeled using the Euler–Lagrange equation by changing the easy axis when the surfactant molecules at the interface are introduced. In our study, we evaluated the dynamics between bulk and interface by controlling surface properties of the interface, such as homeotropic anchoring energy and surface viscosity. In addition, transient optical interference and response time have been examined in this study. Our parametric study results indicated that both homeotropic anchoring energy and surface viscosity at the interface contribute to bulk reorientation. Furthermore, the obtained numerical results indicate that as homeotropic anchoring strength increases, the effective birefringence decreases more gradual due to the increasing surfactant concentration at the aqueous interface, consistent with available experimental observations. Our results have been validated and compared to experimental results from thin-film liquid crystal biosensors in this study. Full article

In this article, we consider the Qian–Sheng model in the Landau–de Gennes framework describing nematic liquid crystal flows when the inertial effect is neglected. By taking the limit of elastic constant to zero (also called the uniaxial limit) and utilizing the so-called Hilbert expansion method, we provide a rigorous derivation from the non-inertial Qian–Sheng model to the Ericksen–Leslie model. Full article

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. Full article