Hydrodynamic forces involving deformable interfaces at nanometer separations

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 Շ100 nm 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. 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 ͑2003͒; R. G. Horn, M. Asadullah, and J. N. Connor, Langmuir 22, 2610 ͑2006͔͒. 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.

Theory of non-equilibrium force measurements involving deformable drops and bubbles

“…This is a generalization of a similar result given earlier for drops with the same interfacial tension [93]. Unfortunately that result contained a typographical error.…”

Dynamic interactions between microbubbles in water

“…The quantity α is a known function of the radii ðR c ;R s Þ and contact angles ðθ c ;θ s Þ of the bubbles (16). This boundary condition follows from a constant volume constraint on the bubbles and is a key and crucial difference between our model for AFM experiments (16) and previous work.…”

“…In fact, we observed that our experimental results were consistent with bubble surfaces that are immobile as described by the no-slip hydrodynamic boundary condition. To facilitate comparisons with our collision experiments on the AFM, an appropriate description of the collision protocol between two incompressible but deformable bubbles also had to be developed to provide the correct boundary condition to augment the governing equations (16,40).…”

“…Otherwise, the expected physical forces that can control bubble coalescence are as follows: (i) A surface tension force that minimizes the surface area of the bubbles and the way this affects bubble deformations is well described by the Young-Laplace theory (13); (ii) an attractive van der Waals-Lifshitz force between the bubbles for which accurate methods of calculating its magnitude from dielectric data, including effects due to electromagnetic retardation, is well known (13,14); and (iii) a hydrodynamic force generated by relative bubble motion and the associated flow of water; where Reynolds lubrication theory (15) for flow in thin films gives a good description. A theoretical model (16) that encompasses all these features, (i-iii), was used to analyze our measurements.…”

Dynamic deformations and forces in soft matter

“…given results for the interaction between two identical drops, it is straightforward to generalize to the case of interacting dissimilar drops or to describe how drops interact with solids 17 .…”