Non-axisymmetric patterns in floating viscoplastic films

Experiments are presented to explore the non-axisymmetric instabilities of spreading films of aqueous suspensions of Carbopol and Xanthan gum floating on a bath of perfluoropolyether oil. The experimental observations are compared against theoretical predictions exploiting a shallow-film model in which the viscoplastic rheology is captured by the Herschel–Bulkley constitutive law. With this model, we construct axisymmetric base states that evolve from the moment that the film floats onto the bath, out towards long times at which spreading becomes self-similar, and then test their linear stability towards non-axisymmetric perturbations. In the geometry of a thinning expanding film, we find that shear thinning does not drive a loss of axisymmetry at early times (when the degree of expansion is small), but when the film has expanded in radius by a factor of two or so, shear-thinning hoop stresses drive non-axisymmetric instabilities. Unstable modes possess relatively low angular wavenumber, and the loss of symmetry is not particularly dramatic. When the oil in the bath is replaced by salty water, the experiments are completely different, with dramatic non-axisymmetric patterns emerging from interfacial effects.