Nanoscale Transport during Liquid Film Thinning Inhibits Bubble Coalescing Behavior in Electrolyte Solutions

The long-standing puzzle of why two colliding bubbles in an electrolyte solution do not coalesce immediately upon contact is resolved. The water film between the bubbles needs to be drained out first before its rupture, i.e., coalescence. Experiments reveal clearly that the film thinning exhibits a rather sudden slowdown (around 30–50 nm), which is orders of magnitude smaller than similar experiments involving surfactants. A critical step in explaining this phenomenon is to realize that the solute concentration is different in bulk and at the surface. During thinning, this will generate an electrolyte concentration difference in film solution along the interacting region, which in turn causes a Marangoni stress to resist film thinning. We develop a film drainage model that explains the experimentally observed phenomena well. The underlying physical mechanism, that confused the scientific community for decades, is now finally revealed.

Figure 1

(a) A sketch of the experimental setup. A bubble of radius $R_b=1.00\mathrm{mm}$ was held at the glass capillary orifice, whereas another bubble of radius $R_s$ was immobilized on a hydrophobic silica surface. The capillary was driven downward with velocity $V$ by a speaker diaphragm to allow bubble collision. A high-speed camera connected to an inverted microscope was used to record the interference fringes. Snapshots of the fringes in a time sequence obtained between two colliding bubbles in (b) pure water ($R_s=0.41\mathrm{mm}$) and (c) 100 mM NaCl solutions ($R_s=0.42\mathrm{mm}$). By analyzing the interferometric images, (d) the film thickness evolution was obtained; NaCl curves were shifted by 1 ms for clarity. The difference in film thinning behavior between pure water and water with electrolytes is clearly visible.

Figure 2

(a) Coalescence time as a function of harmonic mean radius $R_H=2R_s{R}_b/(R_s+R_b)$, in NaCl solutions at different concentrations. (b) Two-stage film thinning behavior until bubble coalescence is observed in different electrolyte solutions; each curve has been shifted by a time $t_i$ for clarity. (c) Variation of coalescence time with $R_H$ in different electrolyte solutions.

Figure 3

Schematics for the electrolyte transportation process within the thin liquid film for surface depleted electrolytes (e.g., NaCl). With (i) the mobile surfaces and (ii) the surface depletion behavior, (iii) electrolyte concentration inside the film region starts to rise, enabling a radial electrolyte concentration gradient, hence a surface tension gradient that reduces the surface mobility.

Figure 4

(a) Comparison between theory (lines) and experimental observations (symbols) of the center film thickness evolution. Three concentrations are included: $C_0=50\mathrm{mM}$, $R_s=0.19\mathrm{mm}$, $C_0=75\mathrm{mM}$, $R_s=0.42\mathrm{mm}$, $C_0=100\mathrm{mM}$, $R_s=0.42\mathrm{mm}$; curves are shifted for clarity. (b) The lateral film thickness at three times ($t_1=-0.01\mathrm{ms}$, $t_2=1.13\mathrm{ms}$, $t_3=4.59\mathrm{ms}$) in 100 mM NaCl solution, $R_s=0.47\mathrm{mm}$. (c) The NaCl concentration distribution within the thin liquid film. At time $t_2$, (d) the fluid shear stress and Marangoni stress distribution and (e) the surface velocity distribution within the thin liquid film. (f) The film thinning behavior until bubble coalescence in sucrose solution with $R_s=0.43\mathrm{mm}$, and in ${\mathrm{HClO}}_4$ solution with $R_s=0.49\mathrm{mm}$; curves are shifted for clarity. The inset shows a linear relationship between the measured $h_s$ and $\sqrt{(d\sigma /dC{)}^2(C_o{R}_H/\sigma RT)}$, with varying $C_0$ and $R_H$ in experiment.