Dimple-assisted dewetting in rotating superfluid films

Abstract

A superfluid wetting film on a solid substrate responds to rotation above a threshold velocity by formation of vortices which connect the free film surface with the substrate. The vortices cause localized deformations ͑''dimples''͒ at the film surface. It is proposed that surface dimples can support the heterogeneous nucleation of critical holes upon undercooling of the wetting film into a nonwet state, leading to a reduction of the lifetime of the metastable wetting layer. ͓S0163-1829͑98͒52622-7͔It was recently observed in experiment that 4 He undergoes first-order wetting and prewetting transitions on the weak binding substrates Cs and Rb. 1 An even richer wetting behavior is displayed by 3 He-4 He mixtures on Cs. [2][3][4][5] The hysteresis associated with the first-order wetting transitions was found to be unusually asymmetric: while an overheated thin film decays rapidly by nucleation of critical droplets, an undercooled thick film remains on the substrate in a longlived metastable state. 6 This feature, which is also present in interfacial dewetting transitions in binary liquid mixtures, 7 was recently explained on the basis of the topology of the wetting phase diagram. 8 As indicated in Fig. 1 by a doubleheaded arrow, an overheating experiment leads away from the prewetting line h p (T) for TϾT w , while the path of undercooling runs parallel to the bulk coexistence line for T ϽT w . In either direction the path crosses h p (T) so that, in general, the decay of the initial state will occur by homogeneous nucleation of critical nuclei, i.e., critical droplets on the nonwet wall or critical holes in the thick wetting layer. Both the size and the excess free energy E c of the critical nuclei are infinite at the prewetting line h p (T), and at the bulk coexistence line hϵϪ c ϭ0 for TϽT w . 8-10 The latter has been interpreted as a line of first-order surface transitions between a microscopic liquid layer on the wall for h→Ϫ0, and an infinitely thick liquid layer on the wall for h→ϩ0, while at hϭ0 wet and nonwet regions can coexist at the surface. 8 The finite distance of the endpoint of the overheating path from the solid line in Fig. 1 leads to a finite value of E c drop , while E c hole is practically infinite for the endpoint of the undercooling path. Since the nucleation rate behaves as Iϳexp(ϪE c /kT), thermal fluctuations are not sufficient in this situation to bring about the decay of the metastable thick film.In order to facilitate hole formation, energy can be transferred to the system from some external source, e.g., by heating 4 or by laser irradiation. 12 The purpose of the present paper is to point out that when the helium film is superfluid, its rotation can be used to assist hole formation. As Feynman pointed out, 13 a vortex deforms the fluid-fluid interface locally into a surface dimple, i.e., a macroscopic depression of the interface in the vicinity of the vortex. The presence of the dimple affects the nucleation kinetics: the initial state from which a critical hole forms upon undercooling i...

Dimple‐assisted dewetting: heterogeneous nucleation in undercooled wetting films

“…Recently, it has been proposed that for a superfluid helium film a controlled deformation of the liquid-vapor interface ('surface dimple') could be a suitable candidate for the reduction of the nucleation barrier [66,67]. The presence of a surface deformation affects the nucleation kinetics: the nucleation of a hole can now occur from an already existing 'hole'-like excitation of the interface.…”

“…The consideration of a nucleation process in the presence of surface deformations might therefore open up the possibility of performing quantitative experiments on the nucleation of holes in undercooled wetting layers and therefore allow a test of the predictions of the scaling theory of critical holes. This thesis develops theoretical scenarios of such an interface-defect mediated process, for which the term 'dimple-assisted dewetting' was introduced [66].…”

“…The profile of the vortex dimple can be determined from the linear variational equation to (2.14) in closed form by Green's function methods [69]. The depth of the dimple and its radius at half-depth are found to behave according to [66] F d jzð0Þj % n 2 ½ln ð2a=xÞ 2 ; ð2:17Þ R d jrðz ¼ zð0Þ=2Þj % x exp ½ðF d =nÞ 1=2 ; ð2:18Þ while for the dimple free energy one has from eq. (2.14)…”

“…It is based on the latest available precise estimates of the Hamaker constants of 4 He on weak-binding substrates [82]. These estimates generally yield larger values of the Hamaker constant than the original predictions, so that the results for the dimple differ slightly from previous estimates [66]. Since the results for the dimple depend on the value of the Hamaker constant only through the combination A=F 4 , they are easily reinterpreted for a system with Hamaker constant A 0 in terms of a different film thickness through the relation…”