ChBE Lecture: Instability at the Interface – Patterns by Competition

Armour College of Engineering’s Department of Chemical and Biological Engineering will host a lecture by Dr. Ranga Narayanan entitled Instability at the Interface – Patterns by Competition. Dr. Narayanan is the Bonnie and Fed Edie Chair and Distinguished Professor of Chemical Engineering at the University of Florida.

Abstract:

In this general talk aimed toward students we shall focus on the interfacial instability that may arise when two contiguous phases are in contact with each other. An interface my become unstable by changing its shape or by generating flow as a control variable exceeds its critical value. For example when a heavy liquid overlies a lighter one the interface can undulate and break as the width of the container exceeds a critical value. This is the familiar Rayleigh Taylor instability where patterns can be generated. Similarly, when a bilayer is parametrically excited, a pattern will be generated at a critical excitation. These patterns require competition of effects one of which is connected to interfacial tension. We will discuss these effects, physically and mathematically.

Now, there are multiple roles played by interfacial tension. For example, interfacial tension affects the pressure difference between phases whether in motion or not; it affects the melting point in a solidification problem and it even affects the reaction rates in an electrochemical reaction. In all of these cases the role of interfacial tension is to stabilize the interface so that the pattern formation is delayed. Yet there are situations where the gradient of interfacial tension generates instability even though the tension plays its usual role of stabilization. This gradient in interfacial tension can be generated on account of potential gradients that can themselves arise from concentration or temperature fields.

For example, in convection of multiple fluid phases gravity and interfacial tension interact with enforced potentials such as temperature gradients and under certain conditions the flow is oscillatory. The oscillations manifest themselves when the destabilizing forces themselves compete with one another. But more is needed. The competition in time must be triggered by competition in space. And the competition in space occurs at certain aspect ratios called co-dimension 2 points. We will discuss this phenomenon where competing time scales interact with competing length scales to generate oscillations. The application to materials processing problems will also be made evident.