Impact of interfacial slip on the stability of liquid two-layer polymer films

Abstract

In this work we derive systems of coupled thin-film equations for immiscible liquid polymer layers on a solid substrate. We take into account slip between liquids and solids and also slip between both liquids. On the scale of tens of nanometres such two-layer systems are susceptible to instability and may rupture and dewet due to intermolecular forces. The stability of the two-layer system and its significant dependence on the order of magnitude of slip is investigated via these thin-film models. With weak slip at both the liquid-liquid and liquid-solid interface and polymer layers of comparable thickness, the dispersion relation typically shows two local maxima, one in the long-wave regime and the other at moderate wavenumbers. The former is associated with perturbations that mainly affect the gas-liquid interface and the latter with larger relative perturbation amplitudes at the liquid-liquid interface. Increasing the slip at the liquid-liquid interface generally favours the long-wave regime and can in fact revert the mode of the instability and thus significantly change the spinodal patterns. Moreover, the maxima shift to small wavenumbers for increasing slip.

Weak solutions to lubrication systems describing the evolution of bilayer thin films

“…corresponding to the weak-slip conditions at the both interfaces. As it was shown recently in [14] the latter model incorporates both the no-slip and the Navier-slip models (1.5),(1.6) as limiting cases as the slip lengths b, b 1 tend simultaneously to zero or infinity, respectively. One needs to point out that we obtained a slight difference between the weak formulations in the no-slip and Navier-slip cases (compare Theorems 2.1 and 4.1).…”

“…The mobility function has the form M (h) = h 3 or M (h) = bh 2 for the no-slip or Navier-slip conditions considered at the solid-liquid interface, respectively, where b > 0 denotes the slip-length parameter. Recently, this model was generalized to a coupled lubrication system describing evolution of a layered system of two viscous, immiscible, nanoscopic Newtonian fluids evolving on a solid substrate [1,9,14] and subsequently analysed in [2,13,14,16,18]. The latter system can be stated in the form:…”

Capillary levelling of immiscible bilayer films

“…2004; Merabia & Bonet Avalos 2008; Jachalski et al. 2014). Liquid–liquid interfaces, in particular those between two polymers, often exhibit apparent slip (de Gennes 1989; Brochard-Wyart & de Gennes 1990; de Gennes & Brochard-Wyart 1990), and have been studied with molecular dynamics simulations (Koplik & Banavar 2006; Razavi, Koplik & Kretzschmar 2014; Poesio, Damone & Matar 2017) and experiments (Lee et al.…”

“…2011; Jachalski et al. 2014). The capillary-levelling technique was applied to a variety of geometries and configurations, which range from imprinted nano-patterns (Stillwagon & Larson 1988; Buck et al.…”

Dewetting of a pre-patterned thin polymer bilayer: influence of the instability mode

“…The instabilities of the thin polymer bilayers are generally governed by the thermodynamic forces. However, some recent studies [36][37][38][39][40][41][42][43][44] have indicated that kinetic forces also greatly inuence the instability of the thin polymer bilayer, as a result the instability could become a kinetically controlled one. Bandyopadhyay et al 36 have shown that a marked decrease in the viscosity of the upper layer increases the rate of deformation of the upper interface, causing the instability shiing back to the upper interface.…”