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My goal is to design a process that, with no automated machinery (I'm using a mechanical pipette), would allow for extremely uniform coverage (that is, with minimal area of multilayers or empty spaces) of a hydrophilic surface with a thin film of polymer solution.

I would also like some pointers on where to get help on writing a mathematical model for this.

I am using a stock polymer suspension in water. The concentration of this suspension can be varied widely. Currently I'm taking a small microliter size portion of this stock suspension and dripping it onto the surface of a substrate cut into exactly 1 cm2 squares. Then I let it dry. This seems too crude. I'm thinking of adding additives such as detergents or other polymers, changing temperature, or changing humidity, but would like a mathematical model to help guide my experiment.

how do I define the conditions such that the sample is dry and only the polymer remains?

how do I calculate the distribution of the polymers on the surface? Is there an analytical model? It is NOT uniform because the polymers are concentrated along the drying front; as water evaporates, the polymers do not, and get concentrated, yet diffusion of the polymers in water is much slower than evaporation (by my observations), and they get 'stuck' on the edges.

I keep looking at the diffusion equation and I have no idea how to use it, but there's no other equation to use.

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# Designing a polymer coating process

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