My work notes
Landau Levich analysis
Date:
Some ideas for the future
Multiple thin film instability
Level: MS or PhD
My understanding: Minimal
Description:
Stability of oscillating wake
Level: MS or PhD
My understanding: Basic question is well defined
Description: If we study the stability of a Gaussian vortex profile, we can show that symmetric modes are unstable and only antisymmetric modes are stable. This can be shown either on a Gaussian vortex profile or with a broken-line plug-type flow profile. What happens if this profile is made to oscillate streamwise. We'll need a Floquet theory to study this problem. Simulations show that the symmetric mode becomes stable. Can we get this from stability analysis as well? This will be a good problem for a Masters student to begin with.
Splitting of a vortex into a dipole with tilt to the container (effect of bottom topography?)
Level: Initially Summer student level, and then probably MS or PhD
My understanding: Minimal and based on kitchen experiments
Description:
Aggregation of rough colloidal particles
Level: MS or PhD
My understanding: Moderate
Description:
Detailed analysis of surfactant effects on Landau-Levich coating
Level: MS or PhD
My understanding: Not too bad
Description:
Coating flows with viscoplastic materials (also discuss with IJ Hewitt)
Level: MS or PhD
My understanding: Minimal
Description:
Stability analysis of a 3D vortex with radial and axial stratification
Level: MS or PhD
My understanding: More sure about this
Description:
Flow structure beneath an interface caused by a rapid accumulation of surfactants or particles
Level: Summer/MS/PhD
My understanding: Moderate. I have intuitive notions at this point.
Description:
Bubbly turbulent flow: the receding motion of a bubbly-clean interface, detailed undersding
Level: Summer/MS/PhD
My understanding: No clue at this point. Idea based on kitchen experiments.
Description:
Effect of anisotropic surface tension
Level: MS/PhD
My understanding: Unclear at this point
Description: It has been observed that particle-laden interface tend to have elasticity. In addition, recent measurements (see the paper by Dominic Vella's group) has revealed that these interfaces also have an anisotropic surface tension, i.e. surface tension is different in different directions. It was speculated that these such a surface tension is necessary to create non-spherical drops/bubbles. It would be interesting to study the effect of such an anisotropic surface tension in other interfacial flows. Even in the case of drops and bubbles, can analytical solutions be obtained for drop shapes.
Non-Boussinesq effects in flow past a cylinder
Level: MS/PhD
My understanding: Basic question is clear
Description: Consider a hyperbolic flow like in the saddle point flow at the end of the recirculation bubble. The simplest example of a hyperbolic flow is the extensional flow (similar to stagnation point flow, but in all four quadrants). This flow is an exact solution of inviscid homogenous flows. We have to see if there is such a solution of inviscid stratified (Boussinesq) flows. My gut feeling is that this may be possible. If yes, then we define non-Boussinesq effects as a small parameter (at this point, I don't know how to do this). Note that only the essential non-Boussinesq term has to be retained in the problem. The problem should be set up in such a way that at leading order, the flow is like the Boussinesq problem. At first order, we have the non-Boussinesq term. I am interested in seeing if the non-Boussinesq term breaks this saddle point. If yes, then I would imagine that non-Boussinesq effects break the recirculation bubble in flow past a cylinder, thus lowering the critical Re.
Old Courses Homeworks, Solutions and Exams
Math 215: Jan-April 2012