New Equation Describes Popping of Bubbles

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Researchers from Princeton University developed a formula that describes the collapse of a bubble’s cavity

A jet ejects drops of fluid to form aerosols that are collected above surfaces such as ocean. These aerosols are significant for several disciplines such as atmospheric science and analysis of the conditions of their formation has been a subject of several studies. Now, a team of researchers from Princeton University developed a formula that describes the process such as collapse of a bubble’s cavity and creation of a jet of liquid that shoots from the bubble. The formula applies to bubbles that are smaller than 5 millimeters in diameter and can describe the bubble and jet of liquid over time by using its size, the surface tension, the density and the viscosity of the fluid.

According to the researchers, the collapse of the cavity generates capillary waves when a bubble bursts at a liquid surface. The capillary waves focus on the axis of symmetry to produce a jet. A non-dimensional number called the Laplace number compares capillary inertia and viscous forces and controls the cavity and jet dynamics.  The team showed that the time-dependent profiles of cavity collapse and jet formation both obey an inviscid scaling. The scaling is attributed to a balance between surface tension and inertia forces. Moreover, the team demonstrated a scaling law, which is applicable above a critical Laplace number. The critical viscous force reconciles the time-dependent scaling with the scaling theory that correlates the Laplace number to the final jet velocity and ejected droplet size. The correlation describes a self-similar formula that states the events from cavity collapse to droplet formation in the jetting process.

According to Luc Deike, an assistant professor of mechanical and aerospace engineering at the Princeton Environmental Institute, bubble bursting is ubiquitous in nature and better prediction of the bursting dynamics has broad practical applications in climate and human health and it helps to enhance fundamental understandings of collapsing cavities with singular behavior. Deike helped to develop the equation and was one of the authors of the research that details the new method to describe bursting. The research was published in the journal Physical Review Letters on October 2, 2018.

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