Wetting flows of viscoelastic fluids
Minkush Kansal is a PhD student in the department Physics of Fluids. Promotors are prof.dr. J.H. Snoeijer and prof.dr. R.M. van der Meer from the Faculty of Science & Technology.
Wetting flows of viscoelastic fluids are encountered in various industrial and biological settings, e.g., dip-coating, deposition of pesticides on plant leaves or ink-jet printing. This thesis explored these viscoelastic wetting flows, specifically focusing on the normal stress effects which are expected to be significant in high shear rate regions in wetting flows. The existing Newtonian results in the literature were not easily generalized to include normal stress, since there was no established thin-film framework based on nonlinear viscoelastic constitutive relations. The goal of this thesis was to fill this gap, and to explore the consequences of viscoelastic normal stresses for classic wetting flows such as dip-coating and contact line motion.
We studied the wetting flows with normal stress using systematic expansions of the second-order fluid. We derived the corresponding thin-film equations using the lubrication approximation, which exploits the thinness of the film, to describe the interface profiles and to explore how normal stress changes the wetting behavior. In chapter 1, the long-wave analysis for the second-order fluid was performed using no approximation beyond the slenderness assumption. This resulted in a frame-invariant thin-film equation that contains normal stress, which, subsequently, we used to study the classical Landau-Levich dip-coating problem. We showed how viscoelasticity of the fluid affects the thickness of the deposited film, and resolved the film thinning versus thickening discrepancy present in the literature.
In chapter 2, we used the thin-film equation derived from a long-wave expansion of the second-order fluid in chapter 1 to systematically study how contact line motion is affected by the presence of normal stress. The classical Cox-Voinov theory of contact line motion provides a relation between the macroscopically observable contact angle, and the microscopic wetting angle as a function of contact line velocity. Here we investigated how the normal stress modifies wetting dynamics. We found that the normal stress effect is dominant at small scales and that the effect can be incorporated in the Cox-Voinov theory through an apparent microscopic angle, which differs from the true microscopic angle. The theory was applied to the classical problems of drop spreading and dip-coating, which shows how normal stress facilitates advancing and inhibits receding contact line motion. For rapid advancing motion, the apparent microscopic angle can tend to zero in which case the dynamics is described by a new regime that was already anticipated in the literature. The theory will be applicable to a broad range of wetting problems where the flow is (quasi) steady such as for the dewetting of a thin fluid film and drops sliding on a solid substrate.
In chapter 3, we extended our theory for viscoelastic contact line motion beyond the lubrication theory. The common approach using the lubrication approximation is intrinsically limited to small interface slopes and therefore only admits solutions at small contact angles. Using a perturbation expansion around corner flow solutions, a generalized lubrication theory can be derived that is valid for arbitrary contact angles. Here we extended this generalized lubrication theory to viscoelastic liquids that exhibit a normal stress effect. These normal stresses were included via the second-order fluid model as in previous chapters, for which we investigated corner flows and established the resulting generalized lubrication theory. Subsequently, we applied this model to advancing and receding contact lines in dip-coating where the plate angle with respect to the liquid bath was also varied along with the contact angle. This final chapter consolidated the results of chapter 2 while also highlighting the relevant dimensionless parameters for viscoelastic contact line motion.
