Description:

Title: A Lubrication Theory for Permeable Particles

Speaker: Michael Loewenberg, Professor of Chemical and Environmental Engineering, Yale University

Abstract: Hard spheres are the quintessential engineering model for particulate systems of all types because it is the simplest model and, at least qualitatively, captures the important features of many systems. Modifications have been implemented from time to time, as needed, to explain certain phenomena not captured by the hard sphere model, such as particle roughness to account for contact between particles in suspensions. In some applications, such as chemical reactors, permeable particles are used. This talk is about the effect of particle permeability on the hydrodynamic interactions of spherical particles immersed in viscous liquids. Even under weak permeability conditions, the near-contact hydrodynamic interactions is qualitatively affected. A lubrication theory will be presented for permeable particles and the physical implications discussed. Competition between liquid draining from the thin gap between two particles and draining into the particles imposes a characteristic length L=K1/5a where K is a dimensionless permeability and a is the particle radius. The leaking of fluid from the lubrication gap into the particles limits the build up of pressure in the near-contact region. By contrast to the singular force preventing the contact of hard spheres, the force resisting the approach of permeable particles with constant velocity is non-singular, allowing contact between permeable particles even in the absence of interparticle forces. Particle permeability also enhances the coupling between rotation and translation, providing access to non-singular rolling motions that are inaccessible to hard spheres at contact.

**Please note, this event will be held in-person, and will be simultaneously broadcast via Zoom at the following link: https://northwestern.zoom.us/j/96991176255. Masks are required to be worn by all in-person attendees per university guidelines and eating and drinking are prohibited. 

-----

To subscribe to the Applied Mathematics Colloquia List send a message to seminar-join@esam.northwestern.edu