Surface-Tension- and Injection-Driven Thin-Film Flow

Gore’s GMCS filter removes sulphur dioxide from flue gases by passing the gas through a
filter comprising a porous structure. The gas adsorbs onto microscopic sorbent pellets and reacts producing liquid sulphuric acid, which drains away along a network of fibres. Understanding the drainage mechanism and its driving forces is key to designing an effective filter. In this talk we consider a paradigm fluids problem of a surface-tension-driven spreading of a viscous fluid
on a flat surface from part of the surface through which fluid is injected. This set-up is
designed to mimic the production and accumulation of liquid sulphuric acid on a pellet
within the filter and the subsequent drainage along a fibre. We use asymptotic
techniques for a thin viscous layer to obtain power-law dependencies of the film thickness
and the position of the apparent contact line on time, which agree with the numerical
solution to the full problem. Further, we look at some generalisations in terms of temporally and thickness-dependent injection rates and present a simple inverse problem for determining the functional form of the injection rate by measuring the motion of the contact-line
position.