Understanding Frothing of Liquid Mixtures: A Surfactantlike Effect at the Origin of Enhanced Liquid Film Lifetimes

The formation of froth in mixtures of liquids is well documented, particularly in oil mixtures. However, in nonvolatile liquids and in the absence of surface-active molecules, the origin of increased liquid film lifetimes had not been identified. We suggest a stabilizing mechanism resulting from the nonlinear variations of the surface tension of a liquid mixture with its composition. We report on experimental lifetimes of froths in binary mixtures and show that their variations are well predicted by the suggested mechanism. We demonstrate that it prescribes the thickness reached by films before their slow drainage, a thickness which correlates well with froth lifetimes for both polar and nonpolar liquids.

Figure 1

Surface tensions of decane-toluene (red) and octane-decane (blue) mixtures as a function of the molar fraction of the species with the lowest surface tension (respectively, decane and octane). The full lines are guides for the eye.

Figure 2

Experimental foamability (squares) defined as the ratio of foam lifetimes and liquid viscosities (left axis) as a function of alkane molar fraction for mixtures of toluene with decane (red), nonane (blue), octane (green), and heptane (orange). Error bars correspond to uncertainties on measured foam heights. The length $\alpha$ characterizing the relative surface tension variation with film thickness [Eq. (5)] is shown as a solid line. The scale of right axis is for the decane-toluene mixture only; other $\alpha$ curves are in arbitrary units. Inset: molar fraction for which the foamability was measured to be maximum as a function of its value predicted by Eq. (4). Data for alkane-toluene (squares) and alcohol-cyclopentanol mixtures (circles, as in Fig. 4). Horizontal error bars are too small to be visible.

Figure 3

Schematic of a liquid film of thickness $h_f$ connected to a Plateau border in the foam and the forces (per unit length) it is submitted to.

Figure 4

Dimensionless foamabilities of alkane-toluene and alcohol-cyclopentanol mixtures as a function of the ratio of the predicted film thickness computed from Eq. (6) and the radius of curvature of the Plateau border,$\beta R_b$. The full line is a guide for the eye. Bubble radius $2R_b=(1.6\pm 0.3)\mathrm{mm}$ was measured to be independent of the nature and composition of the mixture, as well as $\beta =0.55$. Arrows indicate the thickness values predicted in mixtures in which no foam could be observed.