A thin-film model for droplet spreading on soft solid substrates

Charitatos, Vasileios; Kumar, Satish

doi:10.1039/d0sm00643b

Cited by 30 publications

(53 citation statements)

References 69 publications

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“…the above expressions can be simplified (see Appendix A). Other dynamic long-wave models without considering the Shuttleworth effect or lateral displacements were developed for the dynamics of a liquid drop on a viscoelastic layer [41][42][43] and for the durotaxis of a liquid drop on a compliant Kirchhoff plate [44] while certain elasticity aspects also enter long-wave models for drops on polymer brushes [45] and on growing layers of ice [46]. These long-wave descriptions are further discussed in section 2.1 of Ref.…”

Section: B Mesoscopic Gradient Dynamics Modelmentioning

confidence: 99%

Soft wetting with (a)symmetric Shuttleworth effect

Henkel,

Essink,

Hoang

et al. 2022

Preprint

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The wetting of soft polymer substrates brings in multiple complexities as compared to the wetting on rigid substrates. The contact angle of the liquid is no longer governed by Young's law, but is affected by the substrate's bulk and surface deformations. On top of that, elastic interfaces exhibit a surface energy that depends on how much they are stretched -a feature known as the Shuttleworth effect (or as surface-elasticity). Here we present two models by which we explore the wetting of drops in the presence of a strong Shuttleworth effect. The first model is macroscopic in character and consistently accounts for large deformations via a neo-Hookean elasticity. The second model is based on a mesoscopic description of wetting, using a reduced description of the substrate's elasticity. While the second model is more empirical in terms of the elasticity, it enables a gradient dynamics formulation for soft wetting dynamics. We provide a detailed comparison between the equilibrium states predicted by the two models, from which we deduce robust features of soft wetting in the presence of a strong Shuttleworth effect. Specifically, we show that the (a)symmetry of the Shuttleworth effect between the "dry" and "wet" states governs horizontal deformations in the substrate. Our results are discussed in the light of recent experiments on the wettability of stretched substrates.

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Section: B Mesoscopic Gradient Dynamics Modelmentioning

confidence: 99%

Soft wetting with (a)symmetric Shuttleworth effect

Henkel,

Essink,

Hoang

et al. 2022

Preprint

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“…We now investigate the dynamical process of droplet spreading. Of particular interest is the effect of viscoelastic braking, i.e., the decrease of contact line speed during spreading with increasing substrate softness [4,13,14,44,54]. Any motion of the contact line will displace the wetting ridge, which induces a time-dependent deformation.…”

Section: Drop Spreadingmentioning

confidence: 99%

“…Ref. [14] uses method (iii) to predict certain subtle differences in the x C (t)-dependence of the spreading of partially and completely wetting liquids on softness. Here, we are only considering the dependence of dynamic contact angle on contact line speed dx C /dt and method (iii) gives robust results.…”

Section: A Partial Wettingmentioning

confidence: 99%

“…An effect that was already investigated by Carré and Shanahan [12,13] and Long, Ajdari & Leibler [54], followed up in recent years in Refs. [14,44,93]. New phenomena were discovered, such as intricate dependencies of sliding velocity on substrate thickness [102] and stretching [71], as well as effects of free polymer chains that can be present in the substrate [39].…”

Section: Introductionmentioning

confidence: 99%

“…This approach has now been extended to large deformations, including the possibility of the Shuttleworth effect [60,99]. Other studies employed an approach where the tractions are not imposed by hand, but computed via a Derjaguin (or disjoining) pressure [73]) -this is a hybrid approach coupling elasticity to a thin-film static equation [96] or dynamic evolution equation for the liquid layer [14,31,57]. Only recently, dynamic calculations coupling full hydrodynamic and elasticity models have become available [1,2,66,91].…”

Section: Introductionmentioning

confidence: 99%

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Gradient-dynamics model for liquid drops on elastic substrates

Henkel¹,

Snoeijer²,

Thiele³

2021

Preprint

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The wetting of soft elastic substrates exhibits many features that have no counterpart on rigid surfaces. Modelling the detailed elastocapillary interactions is challenging, and has so far been limited to single contact lines or single drops. Here we propose a reduced long-wave model that captures the main qualitative features of statics and dynamics of soft wetting, but which can be applied to ensembles of droplets. The model has the form of a gradient dynamics on an underlying free energy that reflects capillarity, wettability and compressional elasticity. With the model we first recover the double transition in the equilibrium contact angles that occurs when increasing substrate softness from ideally rigid towards very soft (i.e., liquid). Second, the spreading of single drops of partially and completely wetting liquids is considered showing that known dependencies of the dynamic contact angle on contact line velocity are well reproduced. Finally, we go beyond the single droplet picture and consider the coarsening for a two-drop system as well as for a large ensemble of drops. It is shown that the dominant coarsening mode changes with substrate softness in a nontrivial way.

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