Figure 1

Effects of confinement on surface energy increase required for deformation. (a) A finite volume of liquid metal (or any liquid) minimizes its surface energy by contracting into a sphere with radius r. Flattening this sphere leads to a cylinder with facial radius R and perimeter P. (b) Elongating the liquid sphere can be approximated as transforming it into a prolate spheroid whose semi-major axis a is longer than both the original radius r and the semi-minor axis b. This action necessarily involves increasing its surface area, and thus its free surface energy. Similarly distorting the cylinder will transform it into an ellipse, but its semi-major axis will lengthen by a much larger amount for the same change in overall surface energy. (c) Calculated maximum deformation of a liquid-metal spherical droplet with a 1-mm radius as it is compressed into a cylinder of varying heights. As the liquid metal is flattened it is capable of much greater deformation for a given increase in its surface energy.