Stick-slip dynamics in the forced wetting of polymer brushes

Abstract

We study the static and dynamic wetting of adaptive substrates using a mesoscopic hydrodynamic model for a liquid droplet on a solid substrate covered by a polymer brush. First, we...

Drops on Polymer Brushes: Advances in Thin-Film Modeling of Adaptive Substrates

“…Furthermore, models in gradient dynamics form can be systematically extended by amending the energy functionals (e.g., by incorporating surfactant phase transitions or considering full-curvature instead of long-wave variants , ). Recently, the approach has been applied for drops on soft elastic , and adaptive − substrates. The latter case is reviewed next.…”

“…Next, we apply the introduced general approach and present a model for drops of volatile liquids on an adaptive substrate, namely, a solid covered by a polymer brush. It corresponds to the model employed in ref and further builds on models in refs , , and (that result as limiting cases). In particular, we consider a confined geometry as sketched in Figure .…”

“…They are defined by ξ ζ = 1 + false| normal∇ ζ false| 2 and ξ h + ζ = 1 + false| normal∇ ( h + ζ ) false| 2 (i.e., in general, the full-curvature formulation is used). Employing this exact parametrization of the interface instead of the long-wave approximation allows for a recovery of the precise mesoscopic equivalent of the macroscopic Neumann condition valid at the three-phase contact where the adaptive substrate and the liquid–vapor interface meet (for details, see section 3.2 of ref ).…”

“…Technically, one eliminates the third column and third row from the mobility matrices (eq ) and (eq ), removes f liq , f vap and f air from eq , thereby eliminating the dynamic equation for the vapor phase. The resulting model is developed and analyzed in ref . Here, we will employ it to study the natural and forced spreading of a drop on a brush-covered substrate. A further simplification, assuming brush state-independent interface and wetting energies, results in the more restricted two-field model of ref . Obviously, by eliminating columns and rows two and three in the mobility matrices as well as all terms related to vapor and brush in the energy, one obtains (the full-curvature version of) the basic thin-film model in eq . Assuming a laterally uniform system eliminates all terms with spatial derivatives.…”

“…Here, we review how the gradient dynamics form of mesoscopic hydrodynamics is employed to extend the reach of thin-film models toward brush-covered substrates − and, in passing, as well show how for volatile liquids the vapor dynamics can be covered . In particular, the next section introduces the gradient dynamics approach for films/drops of nonvolatile simple liquids on rigid, smooth solid substrates, and then expands it to an arbitrary number of coupled scalar degrees of freedom.…”