Detachment force of particles from fluid droplets

We calculate the deformation of a spherical droplet, resulting from the application of a pair of opposite forces to particles located diametrically opposite at the two ends of the droplet. The free-energy analysis is used to calculate the force–distance curves for the generated restoring forces, arising from the displacement of the particles relative to each other. While the logarithmic dependence of the “de Gennes–Hooke” constant on the particle to droplet size ratio, ν, is rather well known in the limit of very small ν, we find that for more realistic particle to droplet size ratios, i.e. ν = 0.001 to 0.01, the additional constant terms of O(1) constitute a significant correction to previously reported results. We derive the restoring force constant to be 2πγ[0.5 − ln(ν/2)]−1, in perfect agreement with the exact semi-numerical analysis of the same problem. The deviation from the linear force–displacement behaviour, occurring close to the point of detachment, is also investigated. A study of the energy dissipated shows it to be an increasingly dominant component of the work done during the detachment of the particles, as ν decreases. This indicates the existence of a significantly higher energy barrier to desorption of very small particles, compared to the one suggested by their adsorption energy alone. The influence of the line tension on the detachment force is also considered. It is shown that where line tension is important, the contact angle is no longer a constant but instead alters with the displacement of the particles from their equilibrium positions

Direct Observation of the Dynamics of Latex Particles Confined inside Thinning Water-Air Films

The dynamics of micrometer-size polystyrene latex particles confined in thinning foam films was investigated by microscopic interferometric observation. The behavior of the entrapped particles depends on the mobility of the film surfaces, the particle concentration, hydrophobicity, and rate of film formation. When the films were stabilized by sodium dodecyl sulfate, no entrapment of particles between the surfaces was possible. When protein was used as a stabilizer, a limited number of particles were caught inside the film area due to the decreased mobility of the interfaces. In this case, extraordinary long-ranged (>100 Ìm) capillary attraction leads to two-dimensional (2D) particle aggregation. A major change occurs when the microspheres are partially hydrophobized by the presence of cationic surfactant. After the foam films are opened and closed a few times, a layer of particles simultaneously adsorbed to the two interfaces is formed, which sterically inhibits any further film opening and thinning. The particles within this layer show an excellent 2D hexagonal ordering. The experimental data are relevant to the dynamics of defects in coating films, Pickering emulsions, and particle assembly into 2D arrays

Wetting film dynamics and stability

Although the wetting films are similar in many aspects to other thin liquid films, there are some differences in their behavior, too. In contrast to soap and emulsion films, whose surfaces are homogeneous, solid substrates of wetting films are heterogeneous as a rule, unless special measures for their homogenization are taken. Here we mean primarily heterogeneous distribution of surface energy leading to existence of hydrophobic domains on hydrophilic surfaces and vice versa. As is known, such hydrophobic domains could play the role of gas-phase nucleation centers and it is widely accepted nowadays that nano-bubbles can be formed there. The present paper reviews the effect of nano-bubbles adhered at solid surface on stability of wetting films. It is shown that the existence of nano-bubbles is crucial for the lifetime of wetting films. Another peculiarity typical for hydrophobic solid surface, the so-called slippage effect, is also investigated and its contribution to the dispersion equation of capillary waves on wetting films is accounted for

An Algorithm for Emulsion Stability Simulations: Account of Flocculation, Coalescence, Surfactant Adsorption and the Process of Ostwald Ripening

The first algorithm for Emulsion Stability Simulations (ESS) was presented at the V Conferencia Iberoamericana sobre Equilibrio de Fases y Diseño de Procesos [Luis, J.; García-Sucre, M.; Urbina-Villalba, G. Brownian Dynamics Simulation of Emulsion Stability In: Equifase 99. Libro de Actas, 1st Ed., Tojo J., Arce, A., Eds.; Solucion’s: Vigo, Spain, 1999; Volume 2, pp. 364–369]. The former version of the program consisted on a minor modification of the Brownian Dynamics algorithm to account for the coalescence of drops. The present version of the program contains elaborate routines for time-dependent surfactant adsorption, average diffusion constants, and Ostwald ripening

Bounding the stability and rupture condition of emulsion and foam films

[Abstract]: A scaling law is presented that provides a complete solution to the equations bounding the stability and rupture of thin films. The scaling law depends on the fundamental physicochemical properties of the film and interface to calculate bounds for the critical thickness and other key film thicknesses, the relevant waveforms associated with instability and rupture, and film lifetimes. Critical thicknesses calculated from the scaling law are shown to bound the values reported in the literature for numerous emulsion and foam films. The majority of critical thickness values are between 15 to 40 percent lower than the upper bound critical thickness provided by the scaling law

Scaling laws for the critical rupture thickness of common thin films

[Abstract]: Despite decades of experimental and theoretical investigation on thin films, considerable uncertainty exists in the prediction of their critical rupture thickness. According to the spontaneous rupture mechanism, common thin films become unstable when capillary waves at the interfaces begin to grow. In a horizontal film with symmetry at the midplane, unstable waves from adjacent interfaces grow towards the center of the film. As the film drains and becomes thinner, unstable waves osculate and cause the film to rupture. Uncertainty stems from a number of sources including the theories used to predict film drainage and corrugation growth dynamics. In the early studies, the linear stability of small amplitude waves was investigated in the context of the quasi-static approximation in which the dynamics of wave growth and film thinning are separated. The zeroth order wave growth equation of Vrij predicts faster wave growth rates than the first order equation derived by Sharma and Ruckenstein. It has been demonstrated in an accompanying paper that film drainage rates and times measured by numerous investigations are bounded by the predictions of the Reynolds equation and the more recent theory of Manev, Tsekov, and Radoev. Solutions to combinations of these equations yield simple scaling laws which should bound the critical rupture thickness of foam and emulsion films. In this paper, critical thickness measurements reported in the literature are compared to predictions from the bounding scaling equations and it is shown that the retarded Hamaker constants derived from approximate Lifshitz theory underestimate the critical thickness of foam and emulsion films. The non-retarded Hamaker constant more adequately bounds the critical thickness measurements over the entire range of film radii reported in the literature. This result reinforces observations made by other independent researchers that interfacial interactions in flexible liquid films are not adequately represented by the retarded Hamaker constant obtained from Lifshitz theory and that the interactions become significant at much greater separations than previously thought