Significance of electrically induced shear stress in drainage of thin aqueous films

We develop a novel model of drainage of microscale thin aqueous film separating a gas bubble and a solid wall. In contrast to previous studies, the electrostatic effects are accounted for not only in the normal but also in the shear stress balance at the liquid-gas interface. We show that the action of the tangential component of the electric field leads to potentially strong spatially variable shear stress at the deforming charged interface. This previously overlooked effect turns out to be essential for correctly estimating the long-time drainage rates. Comparison of time-dependent fluid interface shapes predicted by our model with the experimental data is discussed.

Figure 1

Sketch of an axisymmetric bubble pressed against a solid wall, also showing nondimensional cylindrical coordinates.

Figure 2

Comparison of interface shapes obtained with the shear stress variations included in the model (black solid lines) and neglected (blue dashed lines) for two parameter sets based on experimental studies of drainage [2]: (a) 0.25 mM salt solution, $\kappa =4.29, \widehat{\psi }=-5.06, t^{*}=250$ s; (b) pure water, $\kappa =0.384, \widehat{\psi }=-5.76, t^{*}=50$ s.

Figure 3

Film thickness at $r=0$ as a function of time for the same parameter values as in Fig. 2 (b), with electrically induced shear stress included in the model (black solid line) and neglected (dashed blue line).

Figure 4

Experimental data (triangles) and predicted interface shapes from the numerical solution of Eq. (13) (solid lines) for (a) NaCl solution, $\kappa =4.29, \widehat{\psi }=-5.06, \mathrm{\Delta }t=0.221$, at $t^{*}=200$ s; (b) pure water, $\kappa =0.384, \widehat{\psi }=-5.76, \mathrm{\Delta }t=0.3133$, at $t^{*}=50$ s. Predictions of models neglecting the electrically induced shear stress are shown by dashed lines (with perfect slip at the deforming interface) and dot-dashed lines (with the no-slip condition at the deforming interface).

Figure 5

Time-dependent interface shapes for $\kappa =4.29, \widehat{\psi }=-5.06$, predicted by our model and compared with the experimental data of Ref. [2].

Figure 6

(a) Fluid interface shapes for $\widehat{\psi }=-0.5, \tilde{q}=-0.5, \kappa =1, t={10}^4$ obtained with the shear stress variations included into the model (black solid line) and neglected (blue dashed line); (b) the absolute value of the interfacial electrostatic potential plotted versus the radial coordinate at the same parameter values.

Figure 7

Comparison of predicted interface shapes with and without charge transport for $\widehat{\psi }=-0.5, \kappa =1$, with fixed $\tilde{q}=-0.5$ (solid line) and $\tilde{q}$ found from the numerical solution of (16) (dashed line).