MACSI at the department of Mathematics and Statistics at the University of Limerick invites you to a seminar
Speaker: Dr Merlin Etzold (Centre for Mathematical Sciences, Cambridge).
Time & location : Friday 19 October at 4p.m. Room A2-002
Title: Removal of viscous contaminants from gaps and cracks¹
Abstract: Problems of industrial cleaning usually consider equipment optimised to be cleaned easily. Decontamination after accidents or the deployment of chemical weapons, in contrast, requires the treatment of complex, neither smooth nor impermeable, surfaces as they are found on equipment or urban structures. The first step towards understanding realistic surfaces is to consider the implications of cracks and gaps on decontamination time. These common features act as capillary traps for liquid contaminants and hinder decontamination efforts. We consider the removal of a soluble, viscous contaminant droplet from gaps and cracks by a surface washing technique. We consider both rectangular and V-shaped geometries. The mass transfer from the droplets is related to boundary layers and Graetz-type problems (heat transfer in pipe flow), with the added complication of a non-uniform lateral concentration profile due to the lateral variation of the velocity profile. We present 3D solutions for the diffusive boundary layer and demonstrate that a 2D mean-field model, for which we calculate Graetz-type and similarity solutions, predicts the average mass flux with high accuracy. We present also analytical expressions valid in the limit of large and small Péclet numbers. To predict actual decontamination times, the mass transfer model has to be merged with a model for droplet response. We will consider models for the droplet behaviour, one for the shrinking of a bulk contaminant droplet and one model for a diluted contaminant in a polymer-thickened solution. We will also present some experimental data for both cases. Evaporation-driven transport through soft hydrogels in contact with awater-reservoir². I also hope to briefly introduce an intriguing problem where we study the deformation of hydrogels due to evaporative transport. In these experiments, we place a hydrogel bead with an evaporative surface in contact with a water reservoir. Depending on the pressure in the water reservoir and relative humidity of the surrounding air, the bead changes its size… - and we have a model (only 1D at the moment therefore only qualitative) which explains what is going on. This work is part of an effort to understand how tall (> 10 cm) tree scan overcome the problem of cavitation in the xylem.
¹with Julien Landel and Stuart Dalziel.
²with Paul Linden and Grae Worster.
Supported by Science Foundation Ireland funding, MACSI - the Mathematics Applications Consortium for Science and Industry (www.macsi.ul.ie), centred at the University of Limerick, is dedicated to the mathematical modelling and solution of problems which arise in science, engineering and industry in Ireland.