A mathematical model of the transport and deposition of charged spray drops

Abstract

This paper seeks to clarify the mechanisms by which charged spray is transported to and deposited within a crop canopy by using a mathematical modelling approach. The spraying area is divided into two regions, one between the atomizer and the top of the crop and the other within the crop canopy. The conditions at the boundary between the two regions (velocity and volume of spray) can be regarded as the output of the above-canopy model. These can then be used as inputs to the within-canopy model to predict deposit patterns. The way in which the model is used can also be reversed, in that the atomizer parameters (e.g. drop size, velocity, flow rate) which are required to give a specified deposit pattern can be calculated. The spray is produced from spinning disc atomizers mounted on a boom travelling at a constant forward speed. The crop is represented as an array of vertical plates. For a fixed crop geometry, the deposit pattern within the canopy is determined by two dimensionless groups of variables. One group is proportional to the velocity of the spray drops entering the crop canopy and the other includes the charge-to-mass ratio and mass flow rate of the spray. Above the crop canopy three dimensionless groups are found to affect the spray behaviour. The first is proportional to initial drop velocity, the second includes the charge-to-mass ratio and the application rate of the spray, and the third is proportional to an electrode voltage. Of these, the second group is found to be most important in determining the spray behaviour. An example of the use of the model is given. To improve canopy penetration the velocity of the spray on entry to the canopy must be increased. To achieve this, one can increase the mass flow rate, the charge-to-mass ratio or the drop size.