In sintering of materials, we can have mass flow in the absence of a concentration gradient via surface diffusion. In this process, surface molecules redistribute themselves driven by a gradient in...

In sintering of materials, we can have mass flow in the absence of a concentration gradient via surface diffusion. In this process, surface molecules redistribute themselves driven by a gradient in surface curvature. This phenomenon causes metals to bead-up on surfaces when heated and other materials to redistribute themselves over time. It is of fundamental importance to the semiconductor industry. If we express the mass flux as:

where γ is a surface energy parameter and κ is the curvature, what are the two possible equilibrium surface shapes?