For the coming academic year, I offer several
projects. The two projects briefly described below should be seen as
examples.

If you have any idea of your own concerning an area in which you would like to
do research, just come to see me. (If after reading this page you haven't got a
clue what the projects are all about, then coming to see me would be also a
clever move.) You are encouraged to have a look at the PG topics to
see where you might be going and start thinking about your research future in
long-term categories.

**Title: **The sliding-plate problem

**Number of credits:** 40

**Prerequisites:** MSM3A03, MSM3A04

**Description:** The project is dealing with a model flow where the
conventional approach of fluid mechanics leads to physically unacceptable singularities.
The essence of the problem is that the process of displacement of a viscous
liquid from one solid plate by another cannot be adequately described in the
framework of the standard fluid-mechanical formulation: the distribution of
viscous stress along the solid planes is nonintegrably
singular leading to an infinite force between the liquid and the solids.
Clearly, this infinite force would not allow the solid planes to move, whilst
in experiments, as we know from our everyday experience, they do move quite
freely. Similar issues emerge in dynamic wetting, fluid motions with
topological transitions of flow domains and some other problems which are of
fundamental academic as well as industrial importance. The goal of the project
is to consider the problem in the framework of both (a) the standard model and
(b) an alternative theory where the singularity can be removed. You are
expected to be able to read and analyse (naturally, with as much help from me
as is necessary) current scientific literature and be interested in the
fundamentals of continuum-mechanical modelling.

**Title:** High-frequency
oscillations of a microbubble

**Number of credits:** 40

**Prerequisites:** MSM3A03, MSM3A04

Description: The nucleation of bubbles and their subsequent evolution is a key element in the dynamics of boiling and a number of other applications. The general area of bubble dynamics is well developed and remains the subject of intensive theoretical and experimental research. However, the very transition in the topology of the flow domain as the bubble appears and its dynamic consequences are poorly understood. In particular, the large surface-to-volume ratio characteristic of microbubbles makes their dynamics different from that of macroscopic bubbles considered in a number of works. The objective of the project is to understand peculiarities of this dynamics and possible ways of their experimental investigation.

**Title: **Pre-breakup evolution of liquid jets

**Number of credits: **40

**Prerequisites: **MSM3A03, MSM3A04

**Description: **The capillarity-driven breakup
of liquid jets is a particular case of a fluid motion where the flow domain
undergoes a topological transition. The relevance of this phenomenon to many industrial and natural processes is obvious, and it
is really surprising that there is practically no understanding of how to
describe it macroscopically. The difficulty is that, as the fluid volume
evolves towards breakup, the flow parameters become singular,
indicating that some important physics is missing in the model. Then the
problem is to identify the `missing physics' and incorporate it into the
mathematical model in a self-consistent way. The goal of this project is to
consider the pre-breakup evolution of a liquid thread
with an emphasis on undestanding how the surface and
bulk parameters behave as the breakup is approached
and what physical processes, if incorporated into the model, could remove the
singularity inherent in the standard formulation.

The above description gives merely three examples of 4th-year projects. They should be viewed as a `gentle introduction' to the subsequent postgraduate research and are aimed at giving you a `flying start'. If you need more information about these (or other) projects, please feel free to contact me at any time.