Mason Equation
From Wikipedia, the free encyclopedia
The Mason Equation is an approximate analytical expression for the growth (due to condensation) or evaporation of a water droplet - it is due to the meteorologist B. J. Mason and given by him in ref. 1.
The expression is found by recognising that mass diffusion towards the water drop in a supersaturated environment transports energy as latent heat, and this has to be balanced by the diffusion of sensible heat back across the boundary layer.
In Mason's formulation the changes in temperature acros the boundary layer can be related to the changes in saturated vapour pressure by the Clausius-Clapeyron relation; the two energy transport terms must be nearly equal but opposite in sign and so this sets the interface temperature of the drop.
The resulting expression for the growth rate is significantly lower than that expected if the drop were not warmed by the latent heat.
Thus
If the drop has a size r, the inward mass flow rate is given by
Mdot = 4πrD(ρ0 − ρw)
and the sensible heat flux by
Qdot = 4πrK(T0 − Tw)
and the final expression for the growth rate is
![r (dr/dt) = \frac {(S-1)} { [(L/RT-1). L \rho_l /K T_0 + (\rho_l R T_0)/ (D \rho_v) ]}](../../../math/5/9/2/592058835b8e2635a9b18ebbbb8a3f8d.png)
where
- S is the supersaturation far from the drop
- L is the Latent heat
- K is the vapour thermal conductivity
- D is the binary diffusion coefficient
- R is the gas constant
[edit] Reference
1. B. J. Mason The Physics of Clouds (1957) Oxford Univ. Press.
 |
This physics-related article is a stub. You can help Wikipedia by expanding it. |
