The left hand side term of Eq. (6) represents the mass accumulation rate in the control volume. While the first, second, and third term of the right hand side represent mass influx through left boundary, mass flux through the wall ($\Delta m\xb7wall$), and the mass outflux through right boundary, respectively. Mass flux across the wall can be divided into two terms: mass added due to sugar influx ($\varpi JSw\Delta s$) and due to cell membrane water flow ($\rho wvwf\Delta s$), where *v*_{w} is the wall flow velocity, $JSw$ is the sucrose influx, *f* is a geometrical factor accounting for the sieve plate, and *ϖ* is the molecular mass of sucrose. Assuming constant sap (fluid) properties across the channel, the continuity equation becomes
Display Formula

(7)$\u2202\u2202t\rho h+\u2202\u2202s(\rho u\xaf)h-\rho wvwf-\varpi JSw=0$