Modeling Transport Phenomena of Microparticles

The aim of this course is to introduce the transport phenomena of microparticles like viscous drops, microorganisms, rigid colloids, soft particles involve in miro- and nano-fluidics. The course provides basic understanding of particular solutions of Navier-Stokes equations, application of Stokes stream function, introduction to governing equations of porous media and electro-hydrodynamics. Subsequently, glimpses of important applications like migration of viscous drops under external gradients, active motion of particles that model swimming microorganisms will be provided. Electrically driven flow in micro- and nano-scale will be introduced. Motion of charged colloids, soft particles mimicking bacteria, humic substances, under electric field in electrolyte or gel medium will be modelled. Numerical techniques to solve the equations governing the advection-diffusion transport will be introduced. The course will be supplemented with assignments on simpler problems related to transport phenomena.

Pre-requisites

Partial differential equations, Basic Fluid Mechanics,

Numerical Methods.

Week 1: Basics of transport phenomena, Navier-Stokes equations

Week 2: Stokes Flow and applications

Week 3: Hydrodynamic phenomena of droplets

Week 4: Flow through porous media,  Darcy equation, Brinkman equation

Week 5: Electrokinetic Transport , Nernst-Planck equations, Debye-Huckel Approximation

Week 6: Electroosmosis, Debye layer overlap

Week 7: Numerical Methods for BVPs and PDEs

Week 8: Electrophoresis of colloids, Double layer polarization, Gel elctrophoresis