From Bouncing to Floating: Noncoalescence of Drops on a Fluid Bath
Original entry: Scott Tsai, APPHY 226, Spring 2009
"From Bouncing to Floating: Noncoalescence of Drops on a Fluid Bath"
Y. Couder, E. Fort, C.H. Gautier, and A. Boudaoud
PRL 94, 177801 (2005)
Soft Matter Keywords
Droplet, coalescence, bounce, float
When a drop of a viscous fluid is deposited on a bath of the same fluid, it is shown that its coalescence with this substrate is inhibited if the system oscillates vertically. Small drops lift off when the peak acceleration of the surface is larger than g. This leads to a steady regime where a drop can be kept bouncing for any length of time. It is possible to inject more fluid into the drop to increase its diameter up to several centimeters. Such a drop remains at the surface, forming a large sunk hemisphere. When the oscillation is stopped, the two fluids remain separated by a very thin air film, which drains very slowly (30 min ). An analysis using lubrication theory accounts for most of the observations.
Soft Matter Examples
The authors describe how a droplet can avoid coalescence when it is sitting on top of a bed of fluid where both the drop and the bed are of the same fluid (ie. water). They can accomplish this by vibrating the bed of fluid in the vertical direction with a forcing acceleration of <math> \gamma = \gamma_m cos \omega t </math>.
For very small drops and large forcing, the drop will continuously bounce (Fig. 1). This is caused by the constant renewing of the air that seperates the drop from the fluid below. The drops also become more and more oblate as the drop sizes increase. Moreover, ocscillations do not occur on the drop surface from its deformation (the drop's surface just changes shape as it approaches the fluid below, but then it goes back to being spherical without oscillation) because the drop's are smaller than the viscous length scale <math> R^* = \mu^2 / \sigma \rho </math>.
When the drop lands on the bed of fluid, the film of air between the drop and the fluid below resists squeezing when it is in a viscous regime, <math> Re = \rho_a h_o^2 \omega / \mu_a </math>, where <math> h_o </math> is the characteristic thickness of the film. Lubrication theory says that the force exerted by the film is <math> F ~ \mu_a r_F^4 \omega / h_o^2 </math>.
When the amplitude of the vibration becomes lower than the threshold amplitude required to avoid coalescence, coalescence occurs immediately for very small drops. For slightly larger drops, at the said vibration amplitude, the drops stop lifting off, and oscillates with a weak amplitude.
For a very large drop, the drop can still avoid coalescence with vibration, but the drop will be sunk into the fluid below and there will be a thin layer of air between the drop and the fluid. Once the drop has sunk into the fluid, the vibrations can be turned off and the drop can avoid coalescence for the same amount of time as if the vibrations continued (Fig. 2).