Solid-state diffusion, surface evolution

A partial differential equation governing the evolution of the surface of a strained elastic solid due to surface diffusion appears in (9.9). Given the instantaneous elastic state of the deformed solid and the instantaneous shape of the evolving surface, this partial differential equation specifies the rate... 

In what has been presented so far, it has been made clear that in the example of the hydrogen evolution reaction (h.e.r.), the degree of occupancy of the surface with adsorbed H (i.e., the radical intermediate) builds up with time after the electric current is switched on. The steady state of a reaction is defined as that state at which this buildup of intermediate radicals in the reaction has come to an end. As long as electronic instrumentation is present to keep control of the electrode potential (and the ambient conditions remain the same), the current density—the rate of electrical reaction per unit area—should then be constant. (This assumes a plentiful supply of reactants, i.e., no diffusion control.) It is advisable to add should be, because— particularly for electrode reactions on solids that involve the presence of radicals and are therefore subject to the properties of the surface—the latter may change relatively slowly (seconds) and a corresponding (and unplanned) change in reaction rate (observable in seconds and even minutes) may occur (Section 7.5.10). 

---