Rim destabilization and re-formation upon severance from its expanding sheet

Abstract

Upon radial liquid sheet expansion, a bounding rim forms, with a thickness and stability governed, in part, by the liquid influx from the unsteady connected sheet. We examine how the thickness and fragmentation of such a radially expanding rim change upon its severance from its sheet, absent of liquid influx. To do so, we design an experiment enabling the study of rims pre and post severance by vaporizing the thin neck connecting the rim. We confirm that the severed rim follows a ballistic motion, with a radial velocity inherited from the sheet at severance time. We identify that the severed rim undergoes fragmentation in two types of junctions: the base of inherited, pre-severance, ligaments and the junction between nascent rim corrugations, with no significant distinction between the two associated timescales. The number of ligaments and fragments formed is captured well by the theoretical prediction of rim corrugation and ligament wavenumbers established for unsteady expanding sheets upon droplet impact on surfaces of comparable size to the droplet, and with the sheet thickness profiles in both systems having the same functional form. Our findings are robust to changes in impacting laser energy and initial droplet size. Finally, we report and analyze the re-formation of the rim on the expanding sheet and propose a prediction for its characteristic corrugation timescale. Our findings highlight the fundamental mechanisms governing interfacial destabilization of connected fluid-fed expanding rims that become severed, thereby clarifying destabilization of freely radially expanding toroidal fluid structures absent of fluid influx.

Figures (2)

• Figure 1: (a) Top view of the experimental setup. Individual tin droplets are subjected to irradiation by multiple laser pulses. The synchronization system, triggered by the scattered light from a He-Ne laser, employs a delay generator to control the arrival time of all laser pulses. The energy of the pre-pulse (PP; seeded Nd:YAG Q-switched laser, Amplitude/Continuum Surelite) is tuned using a half-wave plate and a thin film-polarizer (TFP). A low-energy vaporization pulse (VP; Nd:YAG, quasi-continuous-wave diode-pumped Meijer:17) is used to vaporize the tin, releasing the rim from the sheet. The remaining energy reflected from the TFP is blocked by a beam dump (BD). A stroboscopic imaging system is used to track the expansion of the tin sheet from the side (90°) and front (30°) with two probe pulses, $\textrm{SP}_\textrm{1}$ and $\textrm{SP}_\textrm{2}$ (see insets for the corresponding shadowgraphs). (b) Illustration of the sequences of laser pulses and camera exposures. The onset of the vaporization with VP is denoted by $t$. Subsequently, $\textrm{SP}_\textrm{1}$ is scanned over time at different moments after vaporization ($t_\textrm{vp}$). For the side view, only the first probe pulse is recorded whereas for the front view, a double-framing camera is used, where $\textrm{SP}_\textrm{1}$ falls within the first exposure time of the PCO camera $t_\textrm{exp,1}$ while $\textrm{SP}_\textrm{2}$ aligns with the second exposure time $t_\textrm{exp,2}$. See the main text for further details. (c) Conceptual sketch of the rim release. The formed rim is detached after VP impact. Later, the remaining sheet develops a new rim that grows over time.
• Figure 2: Phenomenological description of rim severance and subsequent destabilization. (a) Front-view images depict the sheet before ($t_{\textrm{vp}}$=0 ns) and after ($t$=100--600 ns) interaction with the VP laser. Two side-view images (for $t_{\textrm{vp}}$=0 and 600 ns) are additionally shown. Shadowgraphs were captured using a droplet with an initial size of $d_{0}$=40 $\mu$m, PP laser energy of $E_{\textrm{pp}}$=21 mJ, leading to $\textrm{We}_\textrm{d}$=3702, and using a VP laser energy $E_{\textrm{pp}}$=3.2 mJ. Recall that the VP laser pulse energy is adjusted independently for each droplet size and Weber number to achieve, just, a clear rim severance. Quantification of breaking is done on the left-hand side of the sheet, since the front view shadowgraphs are recorded with $30\degree$ resulting in a partially out-of-focus view of fragments on one side of the sheet. (b--f) Illustration of the sequence of hydrodynamic destabilization following rim detachment, progressing in time from left to right. (b) VP laser impact detaches the rim already at the end of the VP and initiates a ballistic expansion of the rim, manifested as a translucent gap (red arrows), observable some 50 ns after VP impact. Previously formed ligaments exhibit base merging (yellow arrows). (c) By 200 ns, a typical event of end-pinching fragmentation of the ligament occurs. The finite (spatial) coherence of the backlighting is the origin of minor diffraction effects producing slightly brighter regions near sharp or small features. (d and e) The breakup of the rim at two distinct points: the base of the ligaments at $t_l$=500 ns, and the rest of the corrugated rim at $t_b$=700 ns. (f) Around $t$=950 ns, inner sheet corrugation and further formation of ligaments are observed.