Mathematics
Currently available projects
Air Cushioning in Water Impact
- School:
Mathematics
- Primary Supervisor:
Dr Richard Purvis
Information
- Start date: October 2013
- Programme: PhD
- Mode of Study: Full Time
- Studentship Length: 3 years
How to Apply
- Deadline: 28 February 2013
- Apply online
Fees & Funding
- Funding Status: Competition Funded Project (EU Students Only)
Further Details - Fees: Fees Information (Opens in new window)
Entry Requirements
- Acceptable First Degree:
Mathematics, or other subject with significant mathematical content.
- Minimum Entry Standard: 2:1
Project Description
During the final moments before the impact of a water droplet onto a wall or into a water layer, air cushioning can delay touchdown and cause an air-bubble to be formed near to where the impact occurs. Recent experiments using high speed photography have captured pictures this air-bubble during a solid sphere impact into a water layer [i] (similar experiments have shown the same behaviour for droplet impacts onto both solid surfaces and into water layers).
Mathematical models of this process [ii,iii,iv] have been shown to have surprisingly good agreement to the measured bubble size and are seen to capture much of the behaviour as impact is approached. However, there is still much that is not understood about this air cushioning phenomena. This project will look at some of these open problems, perhaps focusing on stability as touchdown is approached, the influence of surface tension or considering how the local geometry of an impacting solid influences the air cushioning. It would also be interesting to investigate how air influences the splashing behaviour after impact has occurred, as the development of a splash after impact has been shown experimentally to be very different if carried out in a vacuum.
This project is also open to applicants (home, EU or Overseas) who have their own funding.
References
Marston, J. O., Vakarelski, I. U. & Thoroddsen, S. T. 2011 Bubble entrapment during sphere impact onto quiescent liquid surfaces. J. Fluid Mech. 680
Hicks, P. D. & Purvis, R. 2010 Air cushioning and bubble entrapment in three-dimensional droplet impacts. J. Fluid Mech. 649
Hicks, P. D. & Purvis, R. 2011 Air cushioning in droplet impacts with liquid layers and other droplets. Phys. Fluids 23 (6)
P. D. Hicks, E. V. Ermanyuk, N. V. Gavrilov and R. Purvis, 2012, Air trapping at impact of a rigid sphere onto a liquid. J. Fluid Mech. 695
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