Gradient dynamics model for drops spreading on polymer brushes
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part of Springer Nature, 2020 https://doi.org/ 10.1140/epjst/e2020-900231-2
THE EUROPEAN PHYSICAL JOURNAL SPECIAL TOPICS
Regular Article
Gradient dynamics model for drops spreading on polymer brushes Uwe Thiele1,2,3,a and Simon Hartmann1,b 1
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Institut f¨ ur Theoretische Physik, Westf¨ alische Wilhelms-Universit¨ at M¨ unster, Wilhelm Klemm Str. 9, 48149 M¨ unster, Germany Center of Nonlinear Science (CeNoS), Westf¨ alische Wilhelms-Universit¨ at M¨ unster, Corrensstr. 2, 48149 M¨ unster, Germany Center for Multiscale Theory and Computation (CMTC), Westf¨ alische Wilhelms-Universit¨ at, Corrensstr. 40, 48149 M¨ unster, Germany Received 24 October 2019 / Accepted 6 July 2020 Published online 14 September 2020 Abstract. When a liquid drop spreads on an adaptive substrate the latter changes its properties what may result in an intricate coupled dynamics of drop and substrate. Here we present a generic mesoscale hydrodynamic model for such processes that is written as a gradient dynamics on an underlying energy functional. We specify the model details for the example of a drop spreading on a dry polymer brush. There, liquid absorption into the brush results in swelling of the brush causing changes in the brush topography and wettability. The liquid may also advance within the brush via diffusion (or wicking) resulting in coupled drop and brush dynamics. The specific model accounts for coupled spreading, absorption and wicking dynamics when the underlying energy functional incorporates capillarity, wettability and brush energy. After employing a simple version of such a model to numerically simulate a droplet spreading on a swelling brush we conclude with a discussion of possible model extensions.
1 Introduction In spreading processes simple or complex liquids advance onto various substrates. Such dynamic wetting processes are common in daily life and are also of large importance for many technological processes [1–4]. Most experimental and theoretical work of the past decades considers these processes on smooth homogeneous solid substrates or studies the influence of static substrate heterogeneities like wettability and topography patterns and defects [5–8]. However, recent developments in areas like microelectronics or 3D printing increasingly involve cases where (de)wetting hydrodynamics and substrate dynamics are coupled. This is particularly important on microscopic and mesoscopic length scales, where (non-)equilibrium interface phenomena dominate. For instance, viscous and soft elastic substrates reversibly change their profile when one deposits a liquid drop [9–13]. In this case, nearly no transport of a b
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The European Physical Journal Special Topics
material takes place across the liquid–solid interface and the substrate mainly changes its topography. In contrast, adaptive substrates change their physico-chemical properties like wettability and possibly additionally their topography due to the presence of a liquid or through external con
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