Elastic Cheerios effect: Self-assembly of cylinders on a soft solid

¹ Department of Chemical and Biomolecular Engineering, Lehigh University - Bethlehem, PA 18015, USA
² Paulson School of Engineering and Applied Sciences, Harvard University - Cambridge, MA 02138, USA
³ Department of Physics, Harvard University - Cambridge, MA 02138, USA

^(a) mkc4@lehigh.edu
^(b) lm@seas.harvard.edu

Received: 11 July 2015
Accepted: 30 November 2015

Abstract

A rigid cylinder placed on a soft gel deforms its surface. When multiple cylinders are placed on the surface, they interact with each other via the topography of the deformed gel which serves as an energy landscape; as they move, the landscape changes which in turn changes their interaction. We use a combination of experiments, simple scaling estimates and numerical simulations to study the self-assembly of cylinders in this elastic analog of the “Cheerios Effect”, which describes capillary interactions on a fluid interface. Our results show that the effective two-body interaction can be well described by an exponential attraction potential as a result of which the dynamics also show an exponential behavior with respect to the separation distance. When many cylinders are placed on the gel, the cylinders cluster together if they are not too far apart; otherwise their motion gets elastically arrested.