Influence of interfacial elasticity on liquid entrainment in thin foam films

The influence of interfacial elasticity on the rate of liquid drainage from gas-liquid interfaces is a subject that has encouraged prolific scientific work on coalescence and film stability. Elucidating this relationship is important for the design of surfactant mixtures where the amount of liquid content of the foam is critical for the aesthetics and/or effectiveness of the product. However, contradictory theoretical predictions exist with regard to how surface elasticity may influence thin-film dynamics. In this work, interferometric studies are performed to measure the liquid film entrainment between a bubble and an air-liquid interface in response to systematic variations of the surface elasticity. The surface elasticity is varied by adjusting the age of the interface or by adjusting the bulk concentration of a surface-active molecule known to form highly elastic surface layers. Surprisingly, the results indicate the absence of a strong relationship between the surface shear elasticity and the entrainment of liquid in foam films. In addition, qualitative differences are observed between the shapes of foam films with differences in interfacial shear viscosity, with no net effect on liquid entrainment under the conditions studied.

Figure 1

(a) Overview of the DFI used for thin-film measurements: two cameras, a light source, a syringe pump, a pressure transducer (labeled as P), and a chamber capable of vertical translational motion. (b) Diagram of the process for a typical thin-film experiment. (I) Initially, the bubble and bulk air-solution interface are stationary and separated. (II) The interfaces are brought into contact, resulting in deformation of the two interfaces that traps a thin film of liquid. The term $a$ denotes the film radius, $R$ the bubble radius, and $h$ the film thickness (on the order of $0.1–1\mu \mathrm{m}$). (c) Top view of the interferometry patterns that arise from liquid entrainment in the thin film. The term $d$ denotes the capillary outer diameter.

Figure 2

Representative dynamic air-solution surface pressure behavior as a function of time for a range of bulk BSA concentrations ($1.5\times {10}^{-3}$ mM [0.1 mg/mL], $1.5\times {10}^{-2}$ mM [1 mg/mL], 0.60 mM [40 mg/mL], and 0.96 mM [64 mg/mL]).

Figure 3

Time $t$ sweep of the interfacial shear elastic modulus [(a) elastic modulus $G_s^{\prime }$ and (b) viscous modulus $G_s^{\prime \prime }]$ for several bulk concentrations of BSA. Subsequent figures will compare the trends in interfacial shear rheology at either a surface aging time of 40 min for concentration-dependent studies or at a bulk BSA concentration of 0.96 mM for surface aging-dependent studies.

Figure 4

Effect of aging on the film drainage for 0.96 mM BSA films. From left to right, the interferometry patterns are shown at three representative drainage time points: 1.46 s before the chamber stops moving, the time at which the chamber stops moving (corresponding to maximum film volume), and 59.9 s after the chamber stops. The bottom row corresponds to air-solution surfaces aged for 10 min, whereas the top row corresponds to surfaces aged for 240 min. Note the axisymmetry in film shape.

Figure 5

(a) Mean film thickness $h_m$ as a function of bulk BSA concentration $c$ at a surface aging time of $t=40$ min, with a lower concentration limit of $1.5\times {10}^{-3}$ mM, scientific notation. (b) Mean film thickness $h_m$ as a function of surface aging time $t$ at a bulk BSA concentration $c$ of 0.96 mM.

Figure 6

Concentration dependence of interfacial and bulk properties in BSA solutions normalized by initial values at $1.5\times {10}^{-3}$ mM. The circles and diamonds correspond to the normalized surface shear elastic $G_s^{\prime }$ and shear viscous modulus $G_s^{\prime \prime }$, respectively. Squares, right-facing triangles, and upward-facing triangles correspond to normalized surface pressure $\pi$, normalized bulk viscosity $\eta$, and normalized mean thickness $h_m$, respectively.

Figure 7

Temporal behavior for several interfacial parameters and the mean film thickness in a solution of 0.96 mM [64 mg/mL] BSA, with the data normalized by initial values at a 10-min aging time. The circles and diamonds denote the normalized surface shear elastic $G_s^{\prime }$ and shear viscous modulus $G_s^{\prime \prime }$, respectively. Squares correspond to the normalized surface pressure $\pi$ and the upward-facing triangles correspond to the normalized mean thickness $h_m$.

Figure 8

Film volume $V$ as a function of thin-film drainage time $t_d$ for 0.96 mM BSA surfaces aged for 10 min ($G_s^{\prime }=14$ mN/m, black circles) and for 240 min ($G_s^{\prime }=33$ mN/m, gray circles) prior to film formation. Note that the time axis is shifted such that $t_d=0$ corresponds to the occurrence of the maximum film volume, which in this case also corresponds to the time at which the chamber stops moving. Accompanying the volume curves are three pairs of interferometry patterns corresponding to approximately $t_d=-1.46$, 0, and 59.9 s. Each pair compares the interferometry patterns for a film aged briefly, 10 min, (left of the pair) and for a prolonged period, 240 min (right of the pair).

Figure 9

(a) Maximum film thickness $h_{\max }$, (b) mean film thickness $h_m$, and (c) minimum film thickness $h_{\min }$ as a function of thin-film drainage time $t_d$ for BSA surfaces aged for short (10 min, red circles) and long (240 min, black circles) times before film formation. Note that the time axis is shifted such that $t_d=0$ corresponds to the occurrence of the maximum film volume.

Figure 10

(a) Comparison of the surface shear elastic modulus $G_s^{\prime }$ and the surface shear viscous modulus $G_s^{\prime \prime }$ (left $y$ axis) with the mean film thickness $h_m$ (right $y$ axis) for 4.4 mM escin. (b) Comparison of dynamic surface pressure $\pi$ (left $y$ axis) with mean film thickness $h_m$ (right $y$ axis) for 4.4 mM escin.

Figure 11

Comparison of film contours arising from 5-min (black) and 90-min (gray) aged surfaces for (a) 0.96 mM BSA and (b) 4.4 mM escin. The outermost points in the figures demarcate the edge of the film as observed in the interference patterns. The circles represent user-selected points, connected by lines of interpolated points.