Fluctuation assisted spreading of a fluid filled elastic blister

Abstract

In this theoretical and numerical study, we show how spatially extended fluctuations can influence and dominate the dynamics of a fluid filled elastic blister as is deforms onto a pre-wetted solid substrate. To describe the blister dynamics, we develop a stochastic elastohydrodynamic framework that couples the viscous flow, the elastic bending of the interface and the noise from the environment. We deploy a scaling analysis to find the elastohydrodynamic spreading lawR ∼t 1/11 a direct analogue to the capillary spreading of drops, while the inclusion of noise in our model highlights that the dynamics speed-up significantlyR ∼t 1/6 as local changes in curvature enhance the peeling of the elastic interface from the substrate. Moreover, our analysis identifies a distinct criterion for the transition between the deterministic and stochastic spreading regime, which is further illustrated by numerical simulations.

Asymptotic regimes in elastohydrodynamic and stochastic leveling on a viscous film

“…For the macroscopic system provided in our experiment and described in detail below, i.e., T A = 300 K, h i = 2.5 µm, R i = 20 µm, µ = 10 4 Pa s and B = 1.3 · 10 −12 Nm we get the noise prefactor Γ = 2.5 · 10 −13 ms −1/2 and the energy ratio N = 1.75 · 10 −6 which is well within the elastic bending dominated regime. However, a transition from a dominant elastohydrodynamic leveling to a dominant stochastic leveling would occur for a system with temperature T A = 300 K, membrane perturbation height h i = 10 nm and radius R i = 5 µm for a bending modulus B in the range of 10 − 100 k B T A where k B T A = 4 × 10 −21 Nm which corresponds to N in the range of 0 − 8 [36].…”

“…quasi-static solution to obtain the correct scaling [22], i.e., constant pressure in the bump, leading to [36] h 0 (t) ∼ τ t…”

“…( 1). This term mimics the stress generated by thermal fluctuations, originates from an additional symmetric random stress term in the Navier-Stokes equations and is obtained by an integration in the z-direction (for details see [36,[39][40][41]). The noise term η(x, t), is multiplied by a prefactor Γ = k B T A /(6µb) where k B is the Boltzmann constant, T A is the ambient temperature, b is the width of the plate along the y-direction, and η(x, t) is modelled as a spatiotemporal Gaussian white noise such that η(x, t) = 0 and η(x, t)η(x , t ) = δ(x − x )δ(t − t ), where the symbols indicate average quantities.…”

“…how do the system transition from one to another? At the nanoscale, thermal fluctuations are expected to contribute and may even dominate the dynamics [33][34][35][36][37], which we quantify in the leveling dynamics. To answer these questions, we combine numerical solutions of a mathematical model based on the lubrication theory [28] with scaling analysis and experiments.…”

Universal Self-Similar Attractor in the Bending-Driven Leveling of Thin Viscous Films

“…(1). Intermediate asymptotics has been employed in such elastohydrodynamic flows [13,48,49], with in particular the use of asymptotic matching to obtain power-law solutions in non-linear geometries [50,51]. In the latter geometries, as the profiles eventually approach their final flat equilibrium configuration, a crossover towards a different power law was predicted and tested numerically [52].…”