An adaptive isogeometric analysis approach to elasto‐capillary fluid‐solid interaction

The wetting of deformable elastic structures has been recently shown to comprise a rich variety of new physical phenomena (stick-slip motion, durotaxis, Shuttleworth effect, etc.) whose fundamental understanding demands for numerical simulation tools. In this article, we develop a novel unified model and numerical method for this problem. As special features, the method includes exact incompressibility and a linear monolithic assembly of the Navier-Stokes and Cahn-Hilliard equations which stabilizes dominant surface tension at small interface lengths. Also, solid viscosity is included which offers the opportunity to simulate the surfing behavior of droplets on viscoelastic substrates for the first time. We show that the method is highly accurate and more robust than most previous approaches and illustrate its potential by numerical simulation examples. K E Y W O R D S binary fluid structure interaction, elasto-capillarity, moving contact line, phase field method, soft wetting This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

“…Compared to the previous literature on soft wetting, 15 we omit the term

I false(\tilde{σ} ϵ / 2 | \nabla ϕ |^{2} + \tilde{σ} / ϵ W (ϕ) - μ ϕ false)

in the definition of the capillary stress S ca , as it only rescales the interfacial pressure. That is, the pressure p f used here is related to the real physical pressure p phys by

p_{f} = p_{phys} - \tilde{σ} ϵ / 2 | \nabla ϕ |^{2} + \tilde{σ} / ϵ W (ϕ) - μ ϕ

.…”

Section: Mathematical Modelmentioning

confidence: 99%

Section: Mathematical Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A ternary phase‐field model for wetting of soft elastic structures

Aland

Auerbach

2021

Soft wetting, that is, the interaction of liquid-fluid interfaces with deformable elastic structures, provides a rich variety of physical phenomena (stick-slip motion, durotaxis, Shuttleworth effect, etc.) which are not yet understood. We propose a novel phase-field approach to study such problems. The method uses two phase-fields to describe the three domains (solid, liquid, ambient fluid) by the ternary Navier-Stokes Cahn-Hilliard equations. We use a recent phase-field approach for fluid-structure interaction to equip one phase with elastic properties. The resulting method is significantly simpler than all previous approaches for soft wetting, since no grids are used to represent the geometries. Accordingly, the method avoids grid-based computation of interface curvature, mappings between different grids, complicated mesh generation, and retriangulation, while the elastic object can move freely through the computational domain. As a special feature, the elastic structure is for the first time represented as a neo-Hookean Kelvin-Voigt-Maxwell material which makes it very versatile. The accuracy of the method is shown in a benchmark simulation of a droplet on an elastic substrate. The geometrical flexibility is illustrated by simulating a rotating solid object within a fluidic interface. Finally, we provide the first 3D simulations of soft wetting including solid surface tensions. K E Y W O R D Sbinary fluid structure interaction, elastocapillarity, moving contact line, phase-field method, soft wetting INTRODUCTIONWetting of soft elastic structures (also: soft wetting, or elastocapillarity) describes the interaction of two fluids with one soft elastic object, typically dominated by capillary effects which originate from the surface tension of the involved three surfaces. Such scenarios play a major role in a broad variety of phenomena. In biology, capillary interactions with soft materials crucially influence the self-organization of cell tissues, 1 cell motility, 2 and cancer cell migration. 3 Driven by miniaturization, more and more technical applications involve significant soft wetting effects, for example, the patterning of cells 4 or droplets 5 onto soft surfaces, the optimization of condensation processes 6 or the deposition of droplets in ink-jetThis is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Vanguard developments in computational methods for fluid‐structure interaction

Brummelen

Farhat

2021

The analytical approach, which lies at the basis of the exact and natural sciences, rests on the notion that complex systems can be reduced to simple components. This divide-and-conquer approach has shaped contemporary science and technology, and has formed the foundation for virtually all scientific breakthroughs in the 19th and 20th century. It is also the origin of the separation of mechanics into fluid and solid mechanics, so much so that these branches of mechanics are commonly considered as distinct scientific disciplines. Notably, the disconnection between fluid and solid mechanics is evidenced by the tremendous advancements in computational methods and commercial simulation codes for fluid-and solid-mechanical systems separately, as compared to the relative underdevelopment of commercial codes for fluid-structure-interaction analyses.With the advancement of analysis capabilities for fluid-and structure-mechanics systems separately, emerged the realization that many problems in science and engineering cannot be appropriately categorized as either a fluid or structure problem, but are fundamentally determined by the interaction of a fluid and a solid. Examples are flutter and buffet instabilities in aerospace and civil engineering, the functioning of heart valves in biomechanics, sloshing and vibrations in flexible fluid containers and fluid conduits, deployment of inflatable structures such as airbeams and airbags, and deformation of soft substrates due to capillary forces, for example, in microfluidic applications and biomechanics. The development of computational methods for fluid-structure-interaction problems commenced in the early 1980s and many important foundations were laid in the 1990s. Despite the significant progress that has been made since then in computational models and methods for Fluid-Structure Interaction (FSI), many open challenges still remain, and computational FSI continues to be an active area of investigation and development.This special issue presents an overview of vanguard developments in computational methods for fluid-structure interaction. The 12 manuscripts in this special issue cover a variety of contemporary topics in computational FSI.The development of efficient and robust partitioned solution methods continues to be an important branch of research in computational FSI. Such partitioned solution methods allow to retain the modularity of the fluid and structure subsystems, thus enabling the reuse of the complete gamut of advanced commercial and open-source simulation software for fluid-dynamics and solid-dynamics problems separately. In this special issue, Cao et al. present a spatially-varying Robin coupling condition to mitigate the added-mass effect of incompressible flows in FSI in partitioned solution procedures. 1 In a similar vein, Dettmer et al. present a new combined two-field relaxation strategy to enhance the stability of the standard Dirichlet-Neumann FSI coupling strategy in the presence of strong added-mass effects. 2 The work by Rüth et al. is concerned wit...