Universal Rim Thickness in Unsteady Sheet Fragmentation

Abstract

Unsteady fragmentation of a fluid bulk into droplets is important for epidemiology as it governs the transport of pathogens from sneezes and coughs, or from contaminated crops in agriculture. It is also ubiquitous in industrial processes such as paint, coating, and combustion. Unsteady fragmentation is distinct from steady fragmentation on which most theoretical efforts have been focused thus far. We address this gap by studying a canonical unsteady fragmentation process: the breakup from a drop impact on a finite surface where the drop fluid is transferred to a free expanding sheet of time-varying properties and bounded by a rim of time-varying thickness. The continuous rim destabilization selects the final spray droplets, yet this process remains poorly understood. We combine theory with advanced image analysis to study the unsteady rim destabilization. We show that, at all times, the rim thickness is governed by a local instantaneous Bond number equal to unity, defined with the instantaneous, local, unsteady rim acceleration. This criterion is found to be robust and universal for a family of unsteady inviscid fluid sheet fragmentation phenomena, from impacts of drops on various surface geometries to impacts on films. We discuss under which viscous and viscoelastic conditions the criterion continues to govern the unsteady rim thickness.

Comparison of Surface Tension Models for the Volume of Fluid Method

“…During processes such as gas evolution during electrochemical reactions and boiling, nucleated bubbles grow by mass transfer across the interface [15,16] or coalescence [8], but once the bubble detaches it may deform as it rises up and/or interacts with other bubbles [53]. Other complex processes, such as splashing, involve droplet spreading on a surface which is accompanied by formation of secondary smaller droplets at the rim [81]. To reliably model these processes, surface tension models must be able to accurately handle flow scenarios with both small and large capillary numbers.…”

Mass Loss from a Stretching Semitransparent Sheet of Liquid Tin

“…To better understand the temporal and spatial distribution of the tin mass, we again revisit studies of droplet impact on a pillar [16][17][18]20,26] or on a solid substrate [27,29]. In these studies, the Weber number We = ρ U 2 R 0 /σ is the pertinent parameter to describe the expansion dynamics.…”

“…As discussed above, a bounding rim on the edge of the sheet develops during sheet expansion, which has a volume V rim = π 2 R(t)b 2 /2, where b is the rim diameter. Recently, it has been shown that the rim diameter b of an expanding liquid sheet that undergoes unsteady fragmentation is universally governed by a local instantaneous Bond number Bo ≡ −R(t)ρb 2 /σ = 1 [18]. We again refer to Eq.…”

“…[16,17]. Droplet deformation and fragmentation upon impact, be it onto a solid substrate or by a laser pulse, is a topic of particular current interest in fields ranging from epidemiology, governing the transport of pathogens from sneezes and coughs [17,18], through sprays relevant in, e.g., agriculture [18,19], to state-of-the-art nanolithography [7,[10][11][12][13][14]. Knowledge of the thickness profile of the thin liquid sheet formed upon impact is crucial for understanding the deformation and complex fragmentation processes involved.…”

“…Finally, we use the measurement data to determine the fraction of the volume-or, equivalently, mass-that is retained in the target at times relevant for main laser-pulse impact. Channels for mass loss from the sheet are subsequently identified and quantified using existing models [18,20].…”