Evolution of nonconformal Landau-Levich-Bretherton films of partially wetting liquids

We experimentally and theoretically describe the dynamics of evolution and eventual rupture of Landau-Levich-Bretherton films of partially wetting liquids in microchannels in terms of nonplanar interface curvatures and disjoining pressure. While both the early-stage dynamics of film evolution and near-collapse dynamics of rupture are understood, we match these regimes and find theoretically that the dimensionless rupture time, $T_r$, scales with ${\kappa }^{-10/7}$. Here, $\kappa$ is the dimensionless curvature given by the ratio of the Laplace-pressure discontinuity that initiates film thinning to the initial strength of the disjoining pressure that drives the rupture. We experimentally verify the rupture times and highlight the crucial consequences of early film rupture in digital microfluidic contexts: pressure drop in segmented flow and isolation of droplets from the walls.

Figure 1

(a) Sketch of the experimental setup. (b) Top-view micrograph of a flowing bubble; dark regions in the image indicate corner menisci. (c)–(g) Microscope observations of Landau-Levich-Bretherton (LLB) film deposition dynamics; films are deposited at capillary numbers $\mathcal{C}>2.5\times {10}^{-5}$. (h)–(j) Observations of dewetting dynamics: films rupture at the corners and move along circular fronts; $z_r$ is a speed-dependent length of unruptured film. (k) Schematic three-dimensional cutout near the nose of the bubble (left) and $x-y$ cross sections of the lubricating film at increasing distance from the nose, depicting the important events, including film deposition, rupture, and dewetting (right).

Figure 2

(a) Dimensionless film height profiles $H$ in the dimple region at various times $T=(0.01,0.03,0.08,0.15,0.27,0.45,0.75,1.28,2.0,2.5)\times {10}^{-3}$ from numerical solutions of Eq. (1) for $\kappa =50$. The highlighted profile indicates a transition from an early drainage dominated regime [9] to a long-range force induced rupture regime [10]. (b), (c) Minimum film height $H_{\min }$ values extracted from numerical solutions of Eq. (1) for various $\kappa$ are well described by the two self-similar expressions for minimum film height $H_{\min }$ provided in (a) at early and late times, respectively.

Figure 3

Film rupture time versus dimensionless meniscus curvature $\kappa$. The red markers are numerical calculations. The dotted line is the theoretical prediction $T_r=3.92{[1+3.74{\kappa }^{10/7}]}^{-1}$ obtained by matching the two self-similar solutions from Fig. 2. The blue markers represent experimental data of rupture times of ethanol films deposited around long bubbles on a PDMS surface.

Figure 4

Map of observed topological regimes, for PDMS-ethanol-air, arising from the dynamics of film deposition and rupture: (I) no film deposition below a threshold $\mathcal{C}$, (II) simultaneous film deposition and dewetting (a speed-dependent unruptured length of film exists in all cases), and (III) completely lubricated bubbles encapsulated in intact thin films. Inset: Measured pressure drop across bubbles depends strongly on the topological regime.