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
Abstract:
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[1];
(b) rigid spheres confined within thin (a few sphere-diameters) channel[2].
(c) soft spheres in plane Couette flow [3]
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.
