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

• Published in: Advances in colloid and interface science 2011-07, Vol.165 (2), p.70-90
• Main Authors: Chan, Derek Y.C., Klaseboer, Evert, Manica, Rogerio
• Format: Article
• Language: English
• Subjects: AFM force measurements; Atomic force microscopy; Bubbles; Coalescence; Deformable drops and bubbles; Deformation; Deformation effects; Dynamics; Film drainage; Force measurement; Formability; Impact tests; Stokes–Reynolds; Young–Laplace
• ISSN: 0001-8686; 1873-3727
• DOI: 10.1016/j.cis.2010.12.001

Over the past decade, direct force measurements using the Atomic Force Microscope (AFM) have been extended to study non-equilibrium interactions. Perhaps the more scientifically interesting and technically challenging of such studies involved deformable drops and bubbles in relative motion. The scientific interest stems from the rich complexity that arises from the combination of separation dependent surface forces such as Van der Waals, electrical double layer and steric interactions with velocity dependent forces from hydrodynamic interactions. Moreover the effects of these forces also depend on the deformations of the surfaces of the drops and bubbles that alter local conditions on the nanometer scale, with deformations that can extend over micrometers. Because of incompressibility, effects of such deformations are strongly influenced by small changes of the sizes of the drops and bubbles that may be in the millimeter range. Our focus is on interactions between emulsion drops and bubbles at around 100 μm size range. At the typical velocities in dynamic force measurements with the AFM which span the range of Brownian velocities of such emulsions, the ratio of hydrodynamic force to surface tension force, as characterized by the capillary number, is ~ 10 − 6 or smaller, which poses challenges to modeling using direct numerical simulations. However, the qualitative and quantitative features of the dynamic forces between interacting drops and bubbles are sensitive to the detailed space and time-dependent deformations. It is this dynamic coupling between forces and deformations that requires a detailed quantitative theoretical framework to help interpret experimental measurements. Theories that do not treat forces and deformations in a consistent way simply will not have much predictive power. The technical challenges of undertaking force measurements are substantial. These range from generating drop and bubble of the appropriate size range to controlling the physicochemical environment to finding the optimal and quantifiable way to place and secure the drops and bubbles in the AFM to make reproducible measurements. It is perhaps no surprise that it is only recently that direct measurements of non-equilibrium forces between two drops or two bubbles colliding in a controlled manner have been possible. This review covers the development of a consistent theory to describe non-equilibrium force measurements involving deformable drops and bubbles. Predictions of t