Volatilization

Pesticide in the dissolved phase is available for volatilization. The amount of pesticide removed from the water via volatilization is:

$pst_{vol,wtr}=v_v*SA*\frac{F_d*pst_{lkwtr}}{V}$ 8:4.1.8

where $pst_{vol,wtr}$ is the amount of pesticide removed via volatilization (mg pst), $v_v$ is the volatilization mass-transfer coefficient (m/day), $SA$ is the surface area of the water body (m$^2$), $F_d$ is the fraction of total pesticide in the dissolved phase, $pst_{lkwtr}$ is the amount of pesticide in the water (mg pst), and V is the volume of water in the water body(m$^3$ H$_2$O).

The volatilization mass-transfer coefficient can be calculated based on Whitman’s two-film or two-resistance theory (Whitman, 1923; Lewis and Whitman, 1924 as described in Chapra, 1997). While the main body of the gas and liquid phases are assumed to be well-mixed and homogenous, the two-film theory assumes that a substance moving between the two phases encounters maximum resistance in two laminar boundary layers where transfer is a function of molecular diffusion. In this type of system the transfer coefficient or velocity is:

$v_v=K_l*\frac{H_e}{H_e+R*T_K*(K_l/K_g)}$ 8:4.1.9

where $v_v$ is the volatilization mass-transfer coefficient (m/day), $K_l$ is the mass-transfer velocity in the liquid laminar layer (m/day), $K_g$ is the mass-transfer velocity in the gaseous laminar layer (m/day), $H_{e}$ is Henry’s constant (atm m$^3$ mole$^{-1}$), $R$ is the universal gas constant (8.206 $*$ 10$^{-5}$ atm m$^3$ (K mole)$^{-1}$), and $T_K$ is the temperature ($K$).

For lakes, the transfer coefficients are estimated using a stagnant film approach:

$K_l=\frac{D_l}{z_l}$ $K_g=\frac{D_g}{z_g}$ 8:4.1.10

where $K_l$ is the mass-transfer velocity in the liquid laminar layer (m/day), $K_g$ is the mass-transfer velocity in the gaseous laminar layer (m/day), $D_l$ is the liquid molecular diffusion coefficient (m$^2$/day), $D_g$ is the gas molecular diffusion coefficient (m$^2$/day), $z_l$ is the thickness of the liquid film (m), and $z_g$ is the thickness of the gas film (m).

Alternatively, the transfer coefficients can be estimated with the equations:

$K_l=K_{l,O_2}*(\frac{32}{MW})^{0.25}$ 8:4.1.11

$K_g =168*\mu_w*(\frac{18}{MW})^{0.25}$ 8:4.1.12

where $K_l$ is the mass-transfer velocity in the liquid laminar layer (m/day), $K_g$ is the mass-transfer velocity in the gaseous laminar layer (m/day), $K_{l,O_2}$ is the oxygen transfer coefficient (m/day), $MW$ is the molecular weight of the compound, and $\mu_w$ is the wind speed (m/s). Chapra (1997) lists several different equations that can be used to calculate $K_{l,O_2}$.