Abstract
A model is developed to describe the dynamic forces acting between two deformable drops, or between one drop and a solid surface, when they are in relative axisymmetric motion at separations of ≲100nm in a Newtonian liquid. Forces arise from hydrodynamic pressure in the draining liquid film that separates the interfaces and from disjoining pressure due to repulsive or attractive surface forces. Predictions of the model are successfully compared with recent experimental measurements of the force between two micrometer-scale surfactant stabilized decane drops in water in an atomic force microscope [S. L. Carnie, D. Y. C. Chan, C. Lewis, R. Manica, and R. R. Dagastine, Langmuir 21, 2912 (2005); R. R. Dagastine, R. Manica, S. L. Carnie, D. Y. C. Chan, G. W. Stevens, and F. Grieser, Science 313, 210 (2006)] and with subnanometer resolution measurements of time-dependent deformations of a millimeter-scale mercury drop approaching a flat mica surface in a modified surface force apparatus [J. N. Connor and R. G. Horn, Faraday Discuss. 123, 193 (2003); R. G. Horn, M. Asadullah, and J. N. Connor, Langmuir 22, 2610 (2006)]. Special limits of the model applicable to small and moderate deformation regimes are also studied to elucidate the key physical ingredients that contribute to the characteristic behavior of dynamic collisions involving fluid interfaces.
Highlights
Inmanymultiphase processes ranging from ore otation in the mineral industry to controlling emulsion stability in the manufacture of pharmaceutical and health care products, an important objective is to quantify and control the interaction involving deformable interfaces
Ments between decane emulsion drops of radii in the range 40–500 m stabilized by anionic surfactants sodium dodecyl sulfate the dynamic forces as a function of displacement can bemeasuredwith a precisionwithin 0.1 nN over a range of attractive and repulsive forces that span over 10 nN.18,19
These experiments are relevant to the study of emulsion stability because the range of relative velocities that can be achieved in the AFM experiments span the average thermal velocity of emulsion drops in the same size range in solution
Summary
Inmanymultiphase processes ranging from ore otation in the mineral industry to controlling emulsion stability in the manufacture of pharmaceutical and health care products, an important objective is to quantify and control the interaction involving deformable interfaces. The surface force apparatus SFA has recently been adapted to visualize deformations of a mercury/ electrolyte interface that arise from interactions with an approaching mica plate Fig. 2 This technique provides real timemeasurements of the hydrodynamic drainage process of the intervening aqueous lm for thicknesses down to 50 nm with subnanometer resolution, but currently does not yield direct information about the forces or pressure distributions that give rise to the observed interfacial deformations. The theory performs well for interacting decane drops of 40–500 m radius in the AFM experiments and formercury interfaces of 2 mm radius in the SFA experiments where in addition, the surface forces between the mica plate and the mercury drop arising from electrical double layer interactions can be made to be repulsive or attractive by adjusting the bias voltage between the mercury and the bulk electrolyte solution.. The paper closes with a discussion that considers reasons why the no-slip or immobile hydrodynamic boundary condition at the liquid/liquid interface provides the best agreement between experiments and theory and other assumptions of the model
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