> For the complete documentation index, see [llms.txt](https://swatplus.gitbook.io/io-docs/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://swatplus.gitbook.io/io-docs/theoretical-documentation/section-7-main-channel-processes/in-stream-pesticide-transformations/pesticide-in-the-water/volatilization.md).

# 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).