Films, layers, and droplets: The effect of near-wall fluid structure on spreading dynamics

Abstract

We present a study of the spreading of liquid droplets on a solid substrate at very small scales. We focus on the regime where effective wetting energy (binding potential) and surface tension effects significantly influence steady and spreading droplets. In particular, we focus on strong packing and layering effects in the liquid near the substrate due to underlying density oscillations in the fluid caused by attractive substrate-liquid interactions. We show that such phenomena can be described by a thin-film (or long-wave or lubrication) model including an oscillatory Derjaguin (or disjoining or conjoining) pressure and explore the effects it has on steady droplet shapes and the spreading dynamics of droplets on both an adsorption (or precursor) layer and completely dry substrates. At the molecular scale, commonly used two-term binding potentials with a single preferred minimum controlling the adsorption layer height are inadequate to capture the rich behavior caused by the near-wall layered molecular packing. The adsorption layer is often submonolayer in thickness, i.e., the dynamics along the layer consists of single-particle hopping, leading to a diffusive dynamics, rather than the collective hydrodynamic motion implicit in standard thin-film models. We therefore modify the model in such a way that for thicker films the standard hydrodynamic theory is realized, but for very thin layers a diffusion equation is recovered.

Recent advances in and future challenges for mesoscopic hydrodynamic modelling of complex wetting

“…The continuous DFT used in [53] is based on fundamental measure theory [47] and therefore includes the influence of the layering of molecules close to interfaces and the resulting oscillatory density profiles. The extracted wetting potentials are represented by well defined fit functions that can easily be incorporated in mesoscale hydrodynamic models [136]. The calculated static drop shapes are shown to be in quite good agreement with drop profiles determined directly from the microscopic DFT [53].…”

“…The direct combination of the different transport channels into the same mobility function proposed in Ref. [136] should also be seen in the context of the ongoing discussion of the mechanisms of contact line motion [14,15,84,87,88,94,98,135].…”

“…Beside changing the energies, one can also amend the mobilities, e.g., by incorporating slip at the substrate as done for two-layer systems in [78] or by allowing for solvent diffusion along the substrate as discussed for single layers in Refs. [51,136] and section IV. Another important question relevant, e.g., for particle suspensions, is the dependence of the liquid viscosity on solute concentration.…”

Equilibrium Contact Angle and Adsorption Layer Properties with Surfactants

“…often used in gradient dynamics models on the interface Hamiltonian (aka thin-film or lubrication models) [19][20][21]. The liquid volume V = dxh is controlled via the Lagrange multiplier P .…”

Controlling breath figure patterns on PDMS by concentration variation of ethanol-methanol binary vapors

“…At equilibrium, the total free energy is minimized and the droplet shape stops varying. It is well known that the droplet shape is determined by the inter-facial tension between the polymer and the droplet and the intermolecular interactions within the droplet [35]. And the spreading co-efficient in terms of these two factors is given by,…”