What determines drying rates at the onset of diffusion controlled stage‐2 evaporation from porous media?

Abstract

Early stages of evaporation from porous media are marked by relatively high evaporation rates supplied by capillary liquid flow from a receding drying front to vaporization surface. At a characteristic drying front depth, hydraulic continuity to the surface is disrupted marking the onset of stage‐2 evaporation where a lower evaporative flux is supported by vapor diffusion. Observations suggest that in some cases the transition is accompanied by a jump in the vaporization plane from the surface to a certain depth below. The resulting range of evaporation rates at the onset of stage‐2 is relatively narrow (0.5–2.5 mm d−1). The objective is to estimate the depth of the vaporization plane that defines vapor diffusion length at the onset of stage‐2. The working hypothesis is that the jump length is determined by a characteristic length of connected clusters at the secondary drying front that obeys a power law with the system's Bond number. We conducted evaporation experiments using sands and glass beads of different particle size distributions and extracted experimental data from the literature for model comparison. Results indicate the jump length at the end of stage‐1 was affected primarily by porous media properties and less so by boundary conditions. Results show power law relationships between the length of the vaporization plane jump and Bond number with an exponent of −0.48 in good agreement with the percolation theory theoretical exponent of −0.47. The results explain the origins of a relatively narrow range of evaporation rates at the onset of stage‐2, and provide a means for estimating these rates.