Welcome to the PoreLab Lecture series with Dhrubaditya MITRA from NORDITA, Stockholm University and KTH, Stockholm, Sweden.!
During this corona time, join us via Zoom with the following link: https://zoom.us/j/234939343
Title : Hydrodynamics with balls : Rheology and transport
We teach our students mostly about Newtonian fluids, but most of the fluids that we meet in real life, e.g., mud, blood, curry and ketchup are complex fluids. A model of complex fluids is objects (often
spheres) immersed in a Newtonian fluid. I shall give a overview of some of my recent work in this field. In particular, I shall talk about four problems of flows with balls in them.
(a) rigid spheres immersed in a plane Couette flow;
(b) rigid spheres confined within thin (a few sphere-diameters) channel.
(c) soft spheres in plane Couette flow 
In the first case we find that the effective viscosity is an universal function of a combination of the volume-fraction and rate-of-strain. The same universal function also works in the third case but it is then a function of a combination of the volume-fraction and the elastic coefficient of the spheres. In the second case we show that if the thickness of the confining channel is a small integer multiple of the diameter of the the spheres the effective viscosity decreases significantly.
(d) Flow through a two-dimensional array (hexagonal lattice with
defects) of soft elastic cylinders. This is model of deformable porous media. We observe that the Darcy flux is a nonlinear function – steeper than linear – of the pressure-difference across the medium.
Furthermore, the flux is larger for a softer medium.
All the results are obtained by numerical and semi-analytical techniques.