Estimation of Forces between Objects in the Cheerios Effect

We develop an analysis and method to estimate the attractive forces due to the capillary interactions between nearby interfacial objects, often dubbed as the Cheerios effect. The method involve mapping the 3-dimensional surface deformation surrounding a floating object and estimating the force directly from the gradient field. The surface deformation is obtained by correlating the image of a random dot background with its refraction from the liquid surface. The scaling of attractive force as a function of distance for objects of arbitrary shape is directly obtainable from a series of gradient fields. We specialize to the case of objects with sharp corners and observe that force scales exponentially with distance on the order of a capillary length. Furthermore, this optical method is potentially instrumental in studying colloidal self-assembly because it can be implemented in real time in a dynamically changing array of floating objects.