Boryan Radoev

Critical thickness of thin liquid films: Theory and experiment

Abstract A new theory of the critical state of the thin liquid film, at which it either ruptures or forms a black spot, is propounded. The concept of the spontaneous growth of the surface fluctuational waves at the critical state, proposed by A. Scheludko [ Proc. K. Ned. Akad. Wet. Ser. B 65 , 76 and 87 (1962)], is employed. The consistent application of the Brownian motion theory infers that the rate-determining process is that of attaining the state of instability and not, as assumed by A. Vrij [ Disc. Faraday Soc. 42 , 23 (1966)], the consequent evolution of the instability. The theory is confirmed by new experimental data on the critical thickness of formation of black spots in films from aqueous solutions of sodium dodecyl sulfate + NaCl. In contrast to the previous studies [E. Manev, A. Scheludko, and D. Exerowa, Colloid Polym. Soc. 252 , 586 (1974); A. Scheludko, loc cit. ] where the mean critical thickness of the films is determined, in the present study the thickness in the thinnest part of the critical film is measured. In the same manner the rate of thinning at the critical state is obtained. The agreement of experiment with theory confirms the estimate of the van der Waals-Hamaker function according to Lifshitzs theory.

EFFECT OF THICKNESS NON-HOMOGENEITY ON THE KINETIC BEHAVIOUR OF MICROSCOPIC FOAM FILM

Abstract The effect of thickness non-homogeneity on the drainage of microscopic horizontal foam films was studied experimentally and theoretically. Quasi-static and asymmetrical distribution of thickness irregularities over the film surface was established in the experiment. This type of dimpling was modelled theoretically and employed to derive a new equation for the film thinning. It differs from the theoretical expressions known from the literature and is in better agreement with the experimentally determined functional dependence of thinning rate on film size.

Investigations of the collision process between particles and gas bubbles in flotation — A theoretical analysis

Abstract The collision between a mineral particle and a gas bubble in froth flotations is studied theoretically. Special attention is paid to the bubble interface deformation resulting from the impact with the particle. Analytical formulas are obtained for the deformation depth and the frequency of oscillation as dependent on the kinetic energy of impact, particle size, surface tension, viscosity, etc. Theoretical calculations are compared with experimental data. A conclusion is drawn that collisions causing a pronounced deformation of the bubble surface are ineffective for the formation of a three-phase contact since the oscillation period is relatively short and there is no sufficient time left for the thinning and rupture of the film between the particle and the bubble and the establishment of strong contact between them. From this point of view one can assume that collisions occurring without considerable deformation, i.e. the slidings, are more favourable for the efficiency of flotation.

SOME NEW OBSERVATIONS ON LINE TENSION OF MICROSCOPIC DROPLETS

Abstract Line tension of micro-water droplets/lenses on the solid (glass, mica) and fluid (dodecane) interfaces is studied by means of the extended Young equation. The droplets or lenses respectively (μm-diameter) are prepared by condensation of atmospheric humidity. The contact angles are determined by restoring the three-phase contact (tpc) profile from the interference fringes, on the hydrophilic solid surface by fitting a spherical cap into the measured profile points, and in the case of fluid interfaces by interferometric determination of the one lens angle. In both investigated systems the determined line tension values lie in the nano-Newton scale. The results obtained are discussed (1) in the case of the solid/liquid system concerning the dependence on the contact angle according to the theoretical considerations given by Marmur (A. Marmur, J. Colloids Interface Sci. 186 (1997) 462), and (2) for the liquid/liquid system the results interpreted following a recent paper by Aveyard and Clint (R. Aveyard, J. Clint, J. Chem. Soc., Faraday Trans. 93(7) (1997) 1397).

On the kinetics of froth flotation

Abstract The problem of froth flotation kinetics is treated as a transport phenomenon. Two coupled equations of balance are formulated which concern the particles attached upon the bubbles and the free particles in the pulp. The combined equations are solved and an analytical expression for the recovery as a function of time is obtained. The correctness of the theoretical derivation is checked by way of laboratory flotation experiments with glass ballotini (160–200 μm) in a wide pH range (pH 3–13) and collector dodecylamine hydrochloride (C 12 H 25 NH 2 , HCL). The authors demonstrate that the recovery of glass possesses a well-defined maximum at pH 11.2. The cause of this maximum is sought for in the strong dependence of the three-phase contact (TPC) rate of expansion on pH. The role of the kinetic characteristics: time of TPC formation and TPC expansion rate are discussed with the help of the well-known criterion of floatability “attachment forces greater than the detachment forces” which is applied locally in any moment of the particle-bubble interaction.

Rupture of thin wetting films on hydrophobic surfaces: Part I: methylated glass surfaces

Abstract The dependence of hcrit on the macroscopic contact angle is discussed using measurements of the critical rupture thickness of wetting films on methylated glass surfaces. The rupture thickness increases with increasing contact angles on rather hydrophilic substrates but becomes, however, independent of ΘA on moderately hydrophobic surfaces once ΘA exceeds 45°. A qualitative estimation of the interaction forces reveals that hydrophobic interaction forces are the primary cause of the film rupture. The dimension of the first hole in the film lies in the range of 100 nm, indicating that macroscopic contact angles are not appropriate parameters in this context. A heterogeneous distribution of contact angles on microscopic length scales is demonstrated by means of droplet condensation. Earlier studies postulating a function hcrit=f(Θ) on various hydrophobic surfaces as well as on a wide range of contact angles could not be confirmed. Instead, the heterogeneity of the surface plays a more important role for thin film rupture.

Experiments on surface waves in thin wetting films

Abstract A new method for excitation and measurement of time stationary, free running waves on wetting films is described. The waves in the frequency range of 10–140 Hz are generated by an oscillating bubble against a quartz plate in a Derjaguin–Scheludko film balance. The results from the experimentally measured dispersion equation are compared with a theoretical model based on the lubrication approximation. It is shown that there are significant discrepancies between experiment and theory which cannot be explained by the classical DLVO-theory as well as by the assumption of a non-slip boundary condition.

On the energetics of new phase formation

Abstract For the purpose of applying the result of Gibbs onto heterogeneous phase formation as well as to incorporate the effect of line tension in that case and elucidate the problem of nuclei participation in Brownian motion, we shall consider in greater detail the work of formation of a new phase nucleus from supersaturated vapors.

DYNAMICS OF SURFACE WAVES IN WETTING FILMS

Abstract Acoustically excited linear waves in wetting films are described theoretically and their dispersion relation is derived. The analysis is based on the Reynolds lubrication theory, assuming interfacial mobility on the two film surfaces. The final result accounts for both the Marangoni effect on the liquid/gas surface and the slippage on the solid/liquid interface. New phenomena are pointed which are related to the thickness dependence of the surface tension and the adsorption dependence of the disjoining pressure. It is shown that these effects are important for the wave dynamics, and can even lead to film instability.

Mass transfer of surfactants and hydrodynamic interaction at small separations in emulsion systems 1. Scaling concepts

Abstract A model investigation of the coupling of the mass transfer of surfactants and the fluid flows in emulsion systems is presented. The case of close approach of two emulsion droplets, when a thin liquid layer is formed in the narrowest parts between the fluid interfaces, is analysed. New scaling parameters are proposed, based on the introduction of the surface Peclet number Pes. The increase in this surface analogue of the bulk Peclet number results in an increased mobility of the interfaces and in a reduced influence of the surfactant. The validity of the lubrication theory model for the drainage of the thin layers is outlined in terms of the tangential mobility and the Gibbs elasticity of the interfaces. The influence of surfactants on the tangential mobility and the velocity of coalescence is discussed.