Some two-phase mixed boundary value problems in electrostatics and fluid mechanics.

Two distinct mixed boundary problems are investigated: the parallel disk capacitor with a dielectric layer between the plates and the circular disk viscometer on or below the interface, between 2 immiscible liquids. In the first chapter a brief historical review of prime contributions in each of these fields is given; then,in the second, the parallel disk capacitor,with a dielectric layer confined to the space between the plates, is analysed using asymptotic methods and a formula for the capacity, to order log e,is derived. The third chapter contains an analysis of the parallel plate capacitor with an infinite dielectric layer leading to a Fredholm equation of the second kind which may be solved only numerical techniques. The methods of the third chapter are applied to the viscometer problem in chapter 4, and again numerical techniques are needed to complete the solution. A computer program suitable for solving these numerical problems is given in Appendix 1. In each of these two chapters, some allied problems are examined and appropriate Fredholm equations produced. Also in chapter 4 some alternative, approximate series solutions are found. This dissertation extends the work of many researchers over the last 100 years and utilises the well known similarities between problems in electrostatics and in fluid dynamics, of the so called mixed boundary value type