Polymer Coating on a Disk

From this description we should be able to predict the thickness of the polymer coating as a function of the delivery rate and substrate velocity. The monomer and activator are taken to have equal densities. The total material balance around the spray nozzle is  

There should be no net accumulation in the spray nozzle, meaning that it will nearly always operate at a steady state. (In fact a design criterion for a sprayer like this is that it have nearly 

The rate of mass flow into the spray gun is given as the sum of the mass flows of the monomer and the activator. The densities of the two liquids are nearly identical and the volumetric flow rate of the monomer is five times the flow rate of the activator. Therefore the mass out of the orifice is  

The mass flux from the orifice is the mass flow rate out divided by the orifice area. Since the spray spreads in the form of a right cone, the mass flux at the substrate is smaller than the flux from the orifice. To solve our problem we must know this. It is obvious then that the product of the flux and the area is the mass flow rate. By the conservation of mass the mass flow to the substrate must be the same as the mass flow from the orifice. Therefore we can proceed as follows  

We will review what we know. We know the mass flow out of the spray nozzle and we can calculate the area of impingement knowing the area of the orifice Ao, the distance to the substrate L, and the angle, alpha, made by the spray leaving the nozzle. Thus the next step must be to find the area of impingement in terms of alpha, L, and Aq. 

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