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However, the following calculations show that convection of PS and Zn in this way will not be important. We consider the relevant equations in dimensionless form (Roose & Kirk 2009). The flux, FY(t), of PS across the root is given by Eqn?(12). The dimensionless form of this equation is (19) where R?=?r/a, Y?=?[Y]/YL?=?and Pe?=?av/DY. The dimensionless variable Pe is the Peclet number. The relevant scale for the PS concentration is [Y]?=?FYmaxa/DY, where FYmax is the maximum flux of PS from the root. Hence the dimensionless Pexidartinib order boundary condition is (20) where F(t) is the dimensionless flux, whose value is between 0 and 1. It follows that if Pe?FKBP diffusion coefficients are relatively large and therefore Peclet numbers are small. Figure?2 shows the calculated profiles of PS in the soil solution near the root over time with a diurnally varying secretion, and the corresponding profiles of Zn in the soil solution and changes in Zn in the whole soil. It shows that the concentration of PS in solution is greatest close to the root surface in the secretion zone and decreases with distance away. A trace of the previous day's secretion is evident in the region behind the secretion zone. However, as a result of decomposition by microbes, little PS persists longer than a day. Because the length of the secretion zone (2?cm) is comparable with the distance the root grows in a day, secretion buy SRT1720 is largely into fresh soil at all times, and lateral diffusion from the previous day's secretion makes little difference to this. By contrast, the calculated profiles of Zn in the soil solution (middle panels in Fig.?2) show depletion of Zn close to the root surface and a peak some distance away where Zn has been solubilized by PS. The PS-Zn complex diffuses away from this region, both towards the root and away from it. After 3?d, some of the Zn solubilized has spread as far as the edge of the zone of root influence (r?=?x). It then influences the concentration profile around the neighbouring root, and therefore increases the net recovery of solubilized Zn by the root system. This effect will increase as x decreases (i.e. greater rooting density). The bottom panels in Fig.?2 give the calculated changes in Zn concentration in the whole soil (i.e.