Direct measurement of the permeability of the meniscus bordering a free-standing smectic-Afilm

Abstract

A smectic-A free-standing film is always connected by a meniscus to the frame on which it has been stretched. The meniscus acts as a dissipative reservoir and is characterized by its permeability. We propose a method to measure directly this quantity by equilibrating two menisci in correspondence with the same free-standing film. The permeability is shown to depend on the film thickness, in full agreement with previous indirect measurements obtained by analyzing the growth dynamics of dislocation loops. An improved model of the meniscus is proposed to interpret all the data.

Collapse dynamics of smectic-A bubbles

“…It turns out that C has already been measured in the quasi-static regime. In the following, we shall denote by C qs the corresponding value, which we recall is usually much larger than 1 and strongly dependent on the film thickness [1,6,11,12]. In the following subsection, we analyze the direct consequences of the previous theory under the assumption that C = C qs during the collapse.…”

“…For a film of thickness N > 100, C qs ≈ (N G /N ) 2 where N G ≈ 2700 [12]. This result allows us to calculate the pressure increase inside the film just after the valve opening by using equations (6) and (34):…”

“…Nevertheless, we need to know the rheological behavior of the meniscus to solve explicitly the problem of the collapse dynamics. In the rest of this theoretical section, we shall assume, to simplify, that there exists, as in the quasistatic regime [1,11,12], a linear relation between ∆P f ilm and v m :…”

“…This mechanism was then evidenced experimentally, first by analyzing the slowing-down of pores when their diameter approaches that of the meniscus [11], and, second, by measuring the equilibration time of two menisci connected by a film [12]. In these two experiments, the velocities involved in the film around the core of the dislocations and at the entrance of the menisci were so small (of the order of µm/min or less) that it was possible to assume linear relations between the stress σ in the film and the dislocation velocity v (v = mσ, where m is the above-mentioned mobility), and between the pressure difference ∆P f ilm between the film and its meniscus and the material velocity v m at the entrance of the meniscus Fig.…”

“…We recall that in this quasi-static regime, m is a constant, whereas the meniscus permeability C is a quantity that strongly depends on the film thickness H = N d, where N is the number of layers in the film and d the layer thickness [1,9,11,12].…”