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A shape sensitive, variational approach for the matching of surfaces considered as thin elastic shells is investigated. The elasticity functional to be minimized takes into account two different types of nonlinear energies: a membrane…

Optimization and Control · Mathematics 2021-06-09 José A. Iglesias , Martin Rumpf , Otmar Scherzer

A thin polymeric film in contact with a fluid body may leach low-molecular-weight compounds into the fluid. If this fluid is a small droplet, the compound concentration within the liquid increases due to ongoing leaching in combination with…

Soft Condensed Matter · Physics 2019-10-09 Thijs W. G. van der Heijden , Anton A. Darhuber , Paul van der Schoot

Fluid deformable surfaces show a solid-fluid duality which establishes a tight interplay between tangential flow and surface deformation. We derive the governing equations as a thin film limit and provide a general numerical approach for…

Computational Physics · Physics 2023-07-19 Sebastian Reuther , Ingo Nitschke , Axel Voigt

Recent experiments of thin films flowing down a vertical fiber with varying nozzle diameters present a wealth of new dynamics that illustrate the need for more advanced theory. We present a detailed analysis using a full lubrication model…

Fluid Dynamics · Physics 2019-01-03 H. Ji , C. Falcon , A. Sadeghpour , Z. Zeng , Y. S. Ju , A. L. Bertozzi

The spreading of a pure, volatile liquid on a wettable substrate has been studied in extensive detail. Here we show that the addition of a miscible, non-volatile liquid can strongly alter the contact line dynamics and the final liquid…

Soft Condensed Matter · Physics 2020-02-19 Asher P. Mouat , Clay E. Wood , Justin E. Pye , Justin C. Burton

Water vapor capture through free surface flows plays a crucial role in various industrial applications, such as liquid desiccant air conditioning systems, water harvesting, and dewatering. This paper studies the dynamics of a silicone…

Fluid Dynamics · Physics 2025-05-29 Souradip Chattopadhyay , Zihao Yu , Y. Sungtaek Ju , Hangjie Ji

We study the rheology of a suspension of soft deformable droplets subjected to a pressure-driven flow. Through computer simulations, we measure the apparent viscosity as a function of droplet concentration and pressure gradient, and provide…

Soft Condensed Matter · Physics 2017-11-22 M. Foglino , A. N. Morozov , O. Henrich , D. Marenduzzo

We present systematic wetting experiments and numerical simulations of gravity driven liquid drops sliding on a plane substrate decorated with a linear chemical step. Surprisingly, the optimal direction to observe crossing is not the one…

When a liquid droplet impacts a vibrated micro-structured surface with asymmetric topology, the liquids perform a horizontal motion during its bouncing. The moving effect is observed when the liquid is in contact with a low surface energy…

Fluid Dynamics · Physics 2020-09-10 Dinh-Tuan Phan , Hao Yu , Tuan Tran

The dynamics of the deformations of a moving contact line is studied assuming two different dissipation mechanisms. It is shown that the characteristic relaxation time for a deformation of wavelength $2\pi/|k|$ of a contact line moving with…

Soft Condensed Matter · Physics 2009-11-07 Ramin Golestanian , Elie Raphael

We report on the numerical implementation of thin film equations that describe the capillary-driven evolution of viscous films, in two-dimensional configurations. After recalling the general forms and features of these equations, we focus…

The fluid-mechanics community is currently divided in assessing the boundaries of applicability of the macroscopic approach to fluid mechanical problems. Can the dynamics of nano-droplets be described by the same macroscopic equations as…

Fluid Dynamics · Physics 2017-07-13 Alex V. Lukyanov , Tristan Pryer

We report an experimental investigation of the spontaneous motion of liquid droplets on soft gels with a crosslinking gradient. By systematically adjusting the spatial difference in crosslinking density, we observed that millimeter-sized…

Soft Condensed Matter · Physics 2025-01-29 Weiwei Zhao , Wenjie Qian , Chang Xu , Qin Xu

Switchable and adaptive substrates emerged as valuable tools for the control of wetting and actuation of droplet motion. Here we report a computational study of the dynamics of an unstable thin liquid film deposited on a switchable…

Fluid Dynamics · Physics 2024-01-03 Stefan Zitz , Andrea Scagliarini , Jens Harting

Droplet motion on surfaces influences phenomena as diverse as microfluidic liquid handling, printing technology and micro-organism migration. Typically, droplet motion is achieved by inducing energy gradients on a substrate or flow on the…

Soft Condensed Matter · Physics 2020-10-02 Robert Malinowski , Ivan P. Parkin , Giorgio Volpe

The dip-coating geometry, where a solid plate is withdrawn from or plunged into a liquid pool, offers a prototypical example of wetting flows involving contact-line motion. Such flows are commonly studied using the lubrication approximation…

Soft Condensed Matter · Physics 2024-11-20 Minkush Kansal , Charu Datt , Vincent Bertin , Jacco H. Snoeijer

A variational model for epitaxially-strained thin films on rigid substrates is derived both by {\Gamma}-convergence from a transition-layer setting, and by relaxation from a sharp-interface description available in the literature for…

Analysis of PDEs · Mathematics 2018-09-20 Elisa Davoli , Paolo Piovano

We study spreading of a droplet, with insoluble surfactant covering its capillary surface, on a textured substrate. In this process, the surfactant-dependent surface tension dominates the behaviors of the whole dynamics, particularly the…

Fluid Dynamics · Physics 2022-11-08 Yuan Gao , Jian-Guo Liu

The derivation of shallow water models from Navier-Stokes equations is revisited yielding a class of two-layer shallow water models.An improved velocity profile is proposed, based on the superposition of an ideal fluid and a viscous layer…

Analysis of PDEs · Mathematics 2018-06-11 François James , Pierre-Yves Lagrée , Hoang-Minh Le , Mathilde Legrand

In order to probe the dynamics of contact-line motion, we study the macroscopic properties of sessile drops deposited on and then aspirated from carefully prepared horizontal surfaces. By measuring the contact angle and drop width…

Soft Condensed Matter · Physics 2023-07-12 Chloe W. Lindeman , Sidney R. Nagel