Equilibrium force isotherms of a deformable bubble/drop interacting with a solid particle across a thin liquid film

Comparison of experimental force-distance isotherms obtained for a deformable drop/bubble and a solid particle interacting across a thin liquid film with colloidal theories, for example, the DLVO theory, currently relies on two incompatible and nonphysical assumptions. These are approximating the bubble/drop as a purely elastic solid and, contradictorily, as a nondeformable solid. To avoid these a physical assumptions, we have developed a more rigorous method for interpreting the experimental force-distance isotherms. Equilibrium shapes of the bubbles/drops are calculated from the augmented Young-Laplace equation pertinent to the relevant geometry of the experiments. The overall bubble/drop-solid interaction force is then calculated using a macroscopic force balance. We find that the nondeformable and the elastic-deformation models for the bubble/drop are rather inaccurate. The developed methodology is of particular relevance to interparticle force measurements using an atomic force microscope (AFM). To this end, the theoretical method developed here is applied to several actual AFM experiments. It is seen that inaccurate deductions can be made regarding the range and form of thin-film forces if the analysis is done using the elastic and nondeformable assumptions. In particular, jump distances, that form the basis for estimating the range of thin-film forces, are grossly overestimated because of the above-mentioned assumptions. Finally, we provide an alternate method to compare experiments with theory that evaluates self-consistently the bubble/drop shapes and the macroscopic interaction force.