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We investigate the dynamics of spreading in a regime where the shape of thedrop is close to a spherical cap. The latter simplification is applicable inthe late (viscous) stage of spreading for highly viscous drops with a diameterbelow the capillary length. Moreover, it applies to the spreading of a drop ona swellable polymer brush, where the complex interaction with the substrateleads to a very slow spreading dynamics. The spherical cap geometry allows toderive a closed ordinary differential equation (ODE) for the spreading if thecapillary number is a function of the contact angle as it is the case forempirical contact angle models. The latter approach has been introduced by deGennes (Reviews of Modern Physics, 1985) for small contact angles. In thepresent work, we generalize the method to arbitrary contact angles. The methodis applied to experimental data of spreading water-glycerol drops on a siliconwafer and spreading water drops on a PNIPAm coated silicon wafer. It is foundthat the ODE-model is able to describe the spreading kinetics in the case ofpartial wetting. Moreover, the model can predict the spreading dynamics ofspherical cap-shaped droplets if the relationship between the contact angle andthe capillary number is universal.

A geometry-based model for spreading drops applied to drops on a silicon wafer and a swellable polymer brush film