Volatilization

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

$pst_{vol,wtr}=\frac{v_v}{depth}*F_d*pst_{rchwtr}*TT$ 7:4.1.8

where $pst_{vol,wtr}$ is the amount of pesticide removed via volatilization (mg pst), $v_v$ is the volatilization mass-transfer coefficient (m/day), $depth$ is the flow depth (m), $F_d$ is the fraction of total pesticide in the dissolved phase, $pst_{rchwtr}$ is the amount of pesticide in the water (mg pst), and $TT$ is the flow travel time (days).

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:

$v_v=K_l*\frac{H_e}{H_e+R*T_K*(K_l/K_g)}$ 7:4.1.9

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 rivers where liquid flow is turbulent, the transfer coefficients are estimated using the surface renewal theory (Higbie, 1935; Danckwerts, 1951; as described by Chapra, 1997). The surface renewal model visualizes the system as consisting of parcels of water that are brought to the surface for a period of time. The fluid elements are assumed to reach and leave the air/water interface randomly, i.e. the exposure of the fluid elements to air is described by a statistical distribution. The transfer velocities for the liquid and gaseous phases are calculated:

$K_l=\sqrt{r_l*D_l}$ $K_g=\sqrt{r_g*D_g}$ 7:4.1.10

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), $r_l$ is the liquid surface renewal rate (1/day), and $r_g$ is the gaseous surface renewal rate (1/day).

O’Connor and Dobbins (1958) defined the surface renewal rate as the ratio of the average stream velocity to depth.

$r_l=\frac{86400*v_c}{depth}$ 7:4.1.11

where $r_l$ is the liquid surface renewal rate (1/day), $v_c$ is the average stream velocity (m/s) and $depth$ is the depth of flow (m).