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Mechanics of an elastic cell under flow conditions (BLYTHU16SF)

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  • Full or part time
    Dr Blyth
  • Application Deadline
    No more applications being accepted
  • Self-Funded PhD Students Only
    Self-Funded PhD Students Only

Project Description

The deformation of an elastic cell placed into an inviscid flow field is a fundamental problem of key importance to a number of technological applications (e.g. miniaturised self-flying vehicles, blood flow, football technology). In this PhD project we will investigate how an elastic cell (comprising a fluid-filled closed elastic membrane) deforms when placed in a variety of prototype flows which mimic those likely to be encountered in reality, including a uniform stream, and a vortex flow, and a linear combination of these. Mathematically this problem poses a significant challenge not least because the boundary of the domain (here, the cell membrane) is unknown in advance and must be found as part of the solution. Specifically, we will tackle the following problems: (1) a bubble or cell placed into a uniform stream-vortex flow ; (2) A 3D cell placed in a uniform stream. The objective in each case is to compute the shape of the deformed cell boundary.

Funding Notes

This PhD project is offered on a self-funding basis. It is open to applicants with funding or those applying to funding sources. Details of tuition fees can be found at http://bit.ly/1Jf7KCr

A bench fee is also payable on top of the tuition fee to cover specialist equipment or laboratory costs required for the research. The amount charged annually will vary considerably depending on the nature of the project and applicants should contact the primary supervisor for further information about the fee associated with the project.

References

i) 2013 M. G. Blyth & E. I. Parau, Deformation of an elastic cell in a uniform stream and in a circulatory flow, IMA. J. Appl. Math., 78.
ii) 1981 J-M. Vanden-Broeck & J. B. Keller, Axisymmetric bubble or drop in a uniform flow, J. Fluid Mech, 108.

iii) 1996 S Tanveer, Some analytical properties of solutions to a two-dimensional steadily translating inviscid bubble, P. Roy. Soc. Lond. A., 452.

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