Research Projects

Transport of micro-objects under Brownian diffusion and osmotic effects does not provide the required speed or direction. Improved delivery of therapeutic agents in the affected cells in body based on drug-loaded nanoparticles has drawn wide interest in nanotechnology-enabled drug delivery systems. The surface of the colloids acquires electrostatic charge (surface charge), which depends on several electrostatic conditions such as, functional group of the colloids, surface reaction constant, dielectric permittivity etc. The directed transport of colloids suspended in an aqueous medium can be made either by imposing a voltage drop across, which is termed as the electrophoresis or by creating a chemical concentration gradient (diffusiophoresis). Electrophoresis and diffusiophoresis are established to be the most convenient mechanisms in translocating colloids in a fluid medium. Another class of phoretic motion, termed as autophoresis, in which through the surface reactions colloids create a heterogeneous distribution of ions. This leads to creation of an induced electric filed, which propels the colloids. The influence of the wettability of the bounding surface is an important issue in the context of microfluidics. The surface wetting condition is characterized by the slip length which is measured through the macroscopic contact angle of the aqueous solution on the substrate. The influence of surface charge on the velocity condition has not been perfectly resolved. This effect becomes pronounced when surface charge creates the zeta-potential much higher than the thermal potential. In this project the phoretic transport of hydrophobic colloids will be analysed under different electrostatic conditions. The goal of this project is to gain further insights on the mechanisms of auto-propulsions as well as electrophoresis of rigid micro- or nano-sized. Mathematical modelling based on the first principles and analysis through numerical simulations supplemented by theoretical analysis is proved to be a useful tool to design and understand complicated nanoscale transport phenomena. Molecular dynamic simulations near a charged surface may provide an intricate analysis of the electrokinteics. However, the large computation cost and lack of the choice of a suitable force potential for the non-equilibrium situation creates a bottleneck. For this, the continuum based mathematical model is found to be the most effective and less complicated way to analyze the electrokinetic near charged surface. Most of the theories on electrokinetics are developed by considering ions as point charge and neglects the ion-solvent interactions. Those mathematical models cannot explain several nonlinear phenomena manifest for non-dilute situations. In addition, a mean-filed based approach is adopted in most of the existing theories, in which the many-body interactions of finite-sized ions are neglected. These mean-field based approach often fails to explain several experimental as well as atomistic simulation results. The short-range ion-ion and ion-solvent interactions as well as subtle nonlinearity in the electrokinetics will be elucidated in the present project. We will adopt modified electrokinetic models incorporating those short-range effects to illustrate the lacuna between the existing continuum models and experimental hypothesis. The mathematical model is governed by a coupled set of partial differential equations, which needs to be solved numerically supplemented by asymptotic analysis. Efficient numerical schemes to resolve sharp changes of the variables near the bounding surface gradient will be demonstrated. The slower rate of convergence of the diffusion dominated processes is a bottle-neck in simulating the electrokinetics. We will adopt numerical techniques for faster rate of convergence. Numerical simulations will be supplemented with thin-layer analysis as well as hybrid method by adopting Lagrangian based approach for ion distribution.