Viscous sheet retraction

Abstract

We present the results of a combined theoretical and numerical investigation of the rim-driven retraction of flat fluid sheets in both planar and circular geometries. Particular attention is given to the influence of the fluid viscosity on the evolution of the sheet and its bounding rim. In both geometries, after a transient that depends on the sheet viscosity and geometry, the film edge eventually attains the TaylorCulick speed predicted on the basis of inviscid theory. The emergence of this result in the viscous limit is rationalized by consideration of both momentum and energy arguments. We first consider the planar geometry considered by Brenner & Gueyffier (Phys. Fluids, vol. 11, 1999, p. 737) and deduce new analytical expressions for the speed of the film edge at the onset of rupture and the evolution of the maximum film thickness for viscous films. In order to consider the expansion of a circular hole, we develop an appropriate lubrication model that predicts the form of the early stage dynamics of film rupture. Simulations of a broad range of flow parameters confirm the importance of geometry on the dynamics, verifying the exponential hole growth reported in early experimental studies. We demonstrate the sensitivity of the initial retraction speed on the film profile, and so suggest that the anomalous rate of retraction reported in these experiments may be attributed in part to geometric details of the puncture process.

Newtonian pizza: spinning a viscous sheet

“…Eventually, if the thickness decreases to 100 nm or so, intermolecular effects may come into play and cause the sheet to rupture in the central region. In this case, a process of outward sheet retraction should take place, as recently studied by Savva & Bush (2009).…”

“…We also thank John Bush for suggesting the inclusion of surface tension and forwarding a preprint of Savva & Bush (2009). P.D.H.…”

“…The surface-tension-driven radial retraction of fluid sheets is also an active research topic in the context of spray formation as well as in the rupture of a soap film or a liquid curtain (e.g. Savva & Bush 2009). The theoretical framework for modelling thin viscous sheets can been found, for instance, in Buckmaster, Nachman & Ting (1975), Howell (1996) or Ribe (2002).…”

Experimental Investigations of Planar Water Sheets Flowing Under Gravity

“…6 (left) the 2D process of a capillary wave development with time, combined with the lateral sheet retraction, in the case of an initially rectangular liquid film for a small Ohnsorge number [11]. The temporal evolution of this liquid film can be seen as a 2D approximation of the spatial evolution of a horizontal section of the sheet along the vertical axis x.…”

The destabilization of an initially thick liquid sheet edge

“…The receding velocity is clearly not constant, and the rim is continuously accelerated. This is not a slow viscous transient, [6][7][8] since the viscous characteristic time hg/r is negligible in comparison with the inertial characteristic time ffiffiffiffiffiffiffiffiffiffiffiffi ffi qh 3 =r p . This is rather a consequence of the large initial inertia of the rim, which must be absorbed before the terminal velocity V is reached.…”