Thinning of a liquid film as a small drop or bubble approaches a solid plane

Abstract

When a small drop or bubble approaches a solid surface, a thin liquid film forms between them, drains, until an instability forms and coalescence occurs. A hydrodynamic theory is developed for the first portion of this coalescence process: the drainage of the thin liquid film while it is still sufficiently thick that the effects of London‐van der Waals forces and electrostatic forces can be ignored. This theory describes the time rate of change of the film profile, given only the drop radius and the required physical properties. Predictions are compared with profiles measured by Platikanov (1964) for gas bubbles. It is concluded that, even with only a trace of surfactant present, the liquid‐gas interface may be nearly immobile (tangential components of velocity are zero) and the surface viscosities will have little effect upon the drainage rate.

Numerical Simulation of the Buoyancy-Driven Bouncing of a 2-D Bubble at a Horizontal Wall

“…The bubble motion seems to stop for a moment before rebound. In agreement with the existing literature (Nakamura and Uchida, 1980;Lin and Slattery, 1982), a dimple progressively grows at the top of the bubble (seventh snapshot). A favourable pressure gradient allows the interstitial liquid film entrapped between the bubble and the wall to drain along the wall (typical thickness of about 1 100 of the bubble radius).…”

“…Modelling the thinning of the liquid film is the object of a huge literature (see, e.g. Platikanov, 1964;Nakamura and Uchida, 1980;Lin and Slattery, 1982;Chen and Slattery, 1982;Doubliez, 1991;Bazhlekov et al, 2000). Two competitive scenarios hold:…”

Drainage and stability of foam films during bubble coalescence in aqueous salt solutions

“…This value is in agreement with the reported value of by Lin and Slattery ( 1982) who accounted for the surface deformation of a rising bubble towards a solid surface by the hydrodynamic pressure. We noted that a trace amount of impurities from an old N2 gas used in drying the glassware can change this critical speed to values higher than 100 µm/s and the liquid films can be stable for minutes.…”

Film Drainage between Colliding Drops at Constant Approach Velocity: Experiments and Modeling

“…∂ ∂r r ∂h ∂r [23] tangential stress balance τ d = − h 2 ∂p ∂r [24] coupling between interfacial velocity and interfacial viscous stress…”

“…Then the viscous stress is calculated with a central discretisation scheme of second order using Eq. [24]. Equation [25] is now integrated with the Simpson rule.…”