The fingerprint of a flow: wrinkle patterns in nonuniform coatings on pre-stretched soft foundations

We study the wrinkle patterns obtained when applying a thin polymeric film on a uniaxially prestretched soft foundation. The film is coated onto a substrate where it drains under the action of gravity, thereby introducing a continuous variation in its thickness. We first study the fluid mechanics component of the problem and derive the coating profile as a function of the curing properties of the polymeric solution. Upon polymerization, the prestretch is released and yields the formation of wrinkles, which are arranged in organized patterns, including fractals. We study a variety of scenarios depending on the relative orientation of the gradient of film thickness and the stretching direction. In particular, we characterize and rationalize the distribution of singular events in our problem where wrinkles merge to allow a variation of the average value of the wrinkle wavelength across the sample.