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The purpose of this page is to briefly describe the research I have completed at The Department of Mathematics and Statistics at The University of Melbourne.

Table of contents

• Electrokinetics of porous particles
• Dynamic properties of AFM cantilevers
• Publications

Electrokinetics of porous particles

This is research I undertook towards a Doctor of Philosophy degree. My supervisor was Dr Steven Carnie. I commenced my PhD in April 2002 and my thesis was finally passed in June 2006!!! My thesis can be downloaded from my Publications page.

My PhD thesis is in the area of the electrokinetics of porous particles. Electrokinetics is the study of how micron-sized charged particles that are submerged in an electrolyte solution move in response to an applied electric field. It is natural to expect that the velocity of a charged particle submerged in an electrolyte solution would be proportional to the applied electric field. This is in fact the case if the applied field is not too strong. The constant of proportionality is called the electrophoretic mobility. Traditionally the electrophoretic mobility has been calculated by measuring the velocity of an impermeable particle in a static or an oscillating electric field. The aim of my research is to calculate an expression for the electrophoretic mobility of a porous particle. There is, as yet, no satisfactory theory for the electrophoretic mobility of porous particles that are, for example, used in some paint formulations.

The electrophoretic mobility can be used to determine the stability of suspensions of tiny particles (called colloidal suspensions) and this is extremely useful for industrial applications. One way to characterise a colloidal suspension is via an electroacoustic technique such as Electrokinetic Sonic Amplitude (ESA). ESA operates by applying a high-frequency electric field to a colloidal system. This causes the particles to oscillate, resulting in sound waves being generated. The dynamic electrophoretic mobility is then used to transform the signals obtained from these sound waves into information about the size and charge of the colloidal particles, and hence the stability of the suspension. The main advantage of ESA is that measurements can be obtained in highly concentrated systems where optical techniques fail.

The story so far ...

Next, we studied the transport of an N-component electrolyte in a dilute Newtonian solvent through a rigid, porous body subjected to a static (d.c.) electric field. In this work, the microscopic description is given by the linearized ionic transport (electrokinetic) equations, including the effects of ion diffusion, electromigration and convection. Periodic homogenization is used to derive effective governing equations for the fluid velocity, ionic flux and current density that capture the macroscopic behaviour. Explicit expressions for the transport coefficient tensors are given in terms of solutions to cell problems. Without any additional assumptions, we prove that these transport coefficient tensors obey certain fundamental thermodynamic requirements, namely, Onsager's reciprocal relations and the positive definiteness of the diagonal coefficient tensors. See my Publications page for more details.

And finally ...

Theoretical models for the electrokinetics of weakly permeable porous colloidal particles are absent from the literature. The understanding of this topic is advanced through a systematic analysis of the standard electrokinetic equations. New interfacial boundary conditions are derived using conservation arguments supplemented by Stern-layer theory. When combined with particle-scale transport equations, these boundary conditions incorporate four principal effects into the standard electrokinetic model: solvent slip and Stern-layer ionic conduction at the interface, and macroscopic ionic conduction together with the electroosmotic flow of solvent through the particle. The method of matched asymptotic expansions is then used to construct an approximate solution to the aforementioned system, in the thin double-layer limit. An expression for the electrophoretic mobility of a weakly permeable colloidal sphere is produced that consists of a generalization of Smoluchowski's formula to encompass porous particles, and a next order correction. For the first time, the effects of solvent slip and Stern-layer ionic conduction within the porous/free-fluid interface, in conjunction with macroscopic ionic conduction and electroosmosis through the particle, are exhibited. It is shown that solvent slip at the porous interface is overwhelmingly the dominant effect on the mobility of weakly permeable porous colloidal particles. See my Publications page for more details.

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Dynamic properties of AFM cantilevers

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