Spreading of viscoelastic drop on curved substrates*

The spreading behavior of drops of polymer solutions plays a critical role in various technologies such as 3D and inkjet printing, paint spraying, or coating. Recently, it has been shown that on flat surfaces the early phase of spreading follows a power law, where the exponent and pre-factor depend on the ratio between the internal relaxation time scale of the polymer solution and the spreading (elastocapillary) time scale.

In this work, we focus on the combined effects that the rheological behavior of the liquid and the curvature of the substrate have on the early dynamics of drop spreading, by studying the spreading of a drop on spherical beads (1mm to 40 mm in diameter). Varying the curvature of the substrate modifies the balance of forces at play – the influence of gravity becomes more important while the normal stresses (due to viscoelasticity), which apply to the three-phase contact line, also change. We show that as the bead diameter decreases, so does the pre-factor of the power law relative to flat surfaces, but the relationship with the elastocapillary time remains the same. Interestingly, for the smaller spheres the exponent depends on the radius of the bead (i.e., on the curvature of the substrate), as well as the elastocapillary time.