Abstract
When a drop impacts onto a pool of another liquid, the common interface will move down at a well-defined speed for the first few milliseconds. While simple mechanistic models and experiments with the same fluid used for the drop and pool have predicted this speed to be half the impacting drop speed, this is only one small part in a rich and intricate behavior landscape. Factors such as viscosity and density ratios greatly affect the penetration speed. By using a combination of high-speed photography, high-resolution numerical simulations, and physical modeling, we disentangle the different roles that physical fluid properties play in determining the true value of the postimpact interfacial velocity.
Highlights
Drop impact onto a pool—of the same or a different liquid—is of great interest due to its occurrence in a wide range of natural and technological situations
In this paper we focus on understanding the effect of varying the viscosity ratio μr = μp/μd and density ratio ρr = ρp/ρd between the pool and the impacting drop, respectively, on the penetration velocity V
We constructed a theoretical model accounting for all of these parameters, building on previous simpler single-liquid inviscid approaches. We showed that both trends and quantitative predictions for the impacting front velocity can be encapsulated as part of a simple formula V ≈ [1 + 2.71ρr + (24.3983/Red )μr]−1/2 ≈ (1 + 2.71ρr + 24.3983 Re)−1/2, with predictive capabilities spanning three orders of magnitude in density and viscosity ratios, as well as a wide range of impact conditions described by 50 Red 1110 or 3.27 Re 3344
Summary
Drop impact onto a pool—of the same or a different liquid—is of great interest due to its occurrence in a wide range of natural and technological situations. The underside of the drop and the top of the pool deform as a result of pressure build-up due to the gas between these compliant surfaces. This may lead to the entrapment of a gas film or disk which either collapses into a bubble, splits up and forms bubble rings, or ruptures into microbubbles [6,7,8]. The drop-pool interface will continue to move downwards at a well-defined velocity This penetration velocity is crucial in estimating the volume of the entrapped bubbles postimpact onto liquid pools, films [9,10], and soft solids [11,12,13]
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