Magnitude Accumulation Production Diffusive Convective flux flux Mass 0 = +0 (9) balance (global) Mass 0 = + balance (10) (volatile species) Energy 0 = + balance (11) where the enthalpy reference has been chosen for the vapour, at the liquid temperature (that is h=0 i, T0 why a hLV,0 input at the origin is accounted for in (11). Notice that the thermal capacity in the convective flux must be the vapour one, because the sum reduces to just the vapour term ivicpiA (because dry air cannot move in the steady state), and ivicpiA iviA=vA=. In (9), stands for the mass-flow-rate of liquid consumed (the parameter sought), and one concludes that the global mass-flow-rate of across the spherical surface, , is independent of and, from , the bulk r, radial velocity assuming constant gas density (pressure is constant and temperature does not vary too v,  much), and with finally yields: A=4r2, (12) Dividing (10) by and upon integration, yields: (13) i.e. the well-known Langmuir’s law (1918), or simply the stating that the droplet life-time, r2-law, tevap, is proportional to the square of the initial radius; often, the diameter, is used instead of radius (with our d, ). K, There is, however, an internal unknown in (13), which is controlled by the energy balance (11): the yi,0, heat for the liquid-to-vapour transition must come from the gas phase (droplets always attain a temperature below that of the environment, even if injected hotter); evaporation always implies a coupled heat and mass transfer.
Magnitude Accumulation Production Diffusive flux Convective flux Mass balance (global) 0 = +0 (9) Mass balance (volatile species) 0 = + (10) Energy balance 0 = + (11) where the enthalpy reference has been chosen h=0 for the vapour, i, at the liquid temperature T0 (that is why a hLV,0 input at the origin is accounted for in (11). Notice that the thermal capacity in the convective flux must be the vapour one, because the sum ivicpiA reduces to just the vapour term ivicpiA (because dry air cannot move in the steady state), and iviA=vA=. In (9), stands for the mass-flow-rate of liquid consumed (the parameter sought), and one concludes that the global mass-flow-rate of across the spherical surface, , is independent of r, and, from , the bulk radial velocity v, assuming constant gas density  (pressure is constant and temperature does not vary too much), and with A=4r2, finally yields: (12) Dividing (10) by and upon integration, yields: (13) i.e. the well-known Langmuir’s law (1918), or simply the r2-law, stating that the droplet life-time, tevap, is proportional to the square of the initial radius; often, the diameter, d, is used instead of radius (with our K, ). There is, however, an internal unknown in (13), yi,0, which is controlled by the energy balance (11): the heat for the liquid-to-vapour transition must come from the gas phase (droplets always attain a temperature below that of the environment, even if injected hotter); evaporation always implies a coupled heat and mass transfer.