Mr James Munro


  • 2014-: PhD student, University of Cambridge
  • 2013-2014: Part III student, University of Cambridge (MMath)
  • 2010-2013: Undergraduate student, University of Cambridge (BA)


I'm a member of the Institute of Theoretical Geophysics at the Department of Applied Mathematics and Theoretical Physics. I'm working on the fluid dynamics of coalescence. For example, when one raindrop runs into another, or when two bubbles meet, or when an emulsion breaks down, there is a fast surface-tension driven flow that pulls the drops or bubbles together into one. These surface-tension driven flows often involve large velocities and small lengthscales, which makes experiments or numerical simulations difficult. I use asymptotic analysis to identify the key lengthscales, and then I solve appropriate forms of the Navier-Stokes equations one each scale.

For example, during the early stages of bubble coalescence, there's a thin sheet of fluid between the bubbles, with a growing hole in the sheet joining the bubbles. Surface tension acting on the tightly-curved edge of this hole quickly pulls the sheet apart and the bubbles together. This motion is opposed by both inertia and viscosity in the fluid sheet. Remarkably, these are both in balance with the driving surface tension force over a radial lengthscale proportional to t^{1/2}. As a result, there's a similarity solution for any Reynolds number which balances all these physical effects. My theoretical solution agrees well with asymptotic results for high and low Reynolds number, with experimental measurements and with simulations of the full Navier-Stokes equations. Going forward, simulations of bubble coalescence don't need to resolve the fine details of bubble coalescence- they can use my simple model for the coalescence event.


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