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Digital twin of a droplet microarray platform:Evaporation behavior for multiple droplets on patterned chips for cell culture

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Droplet 2024年第1期3卷 113-124页

作者： Yanchen Wu Joaquin E.Urrutia Gomez Hongmin Zhang Fei Wang Pavel A.Levkin Anna A.Popova Britta Nestler Institute for Applied Materials–Microstructure Modeling and Simulation Karlsruhe Institute of TechnologyKarlsruheGermany Institute of Nanotechnology Karlsruhe Institute of TechnologyEggenstein‐LeopoldshafenGermany Institute of Biological and Chemical Systems(IBCS‐FMS) Karlsruhe Institute of TechnologyEggenstein‐LeopoldshafenGermany Institute of Organic Chemistry Karlsruhe Institute of TechnologyKarlsruheGermany Institute of Digital Materials Science Karlsruhe University of Applied SciencesKarlsruheGermany

Precise control of the evaporation of multiple droplets on patterned surfaces is crucial in many technological applications,such as anti‐icing,coating,and high‐throughput ***,the complex evaporation process of multiple droplets on well‐defined patterned surfaces is still poorly ***,we develop a digital twin system for real‐time monitoring of key processes on a droplet microarray(DMA),which is essential for parallelization and automation of the operations for cell ***,we investigate the evaporation of multiple nanoliter droplets under different conditions via experiments and numerical *** demonstrate that the evaporation rate is not only affected by the environmental humidity and temperature but is also strongly linked to the droplet distribution on the patterned surfaces,being significantly reduced when the droplets are densely ***,we propose a theoretical method to aid in the experimental detection of volumes and pH variation of evaporating droplets on patterned *** versatile and practical strategy allows us to achieve active maneuvering of the collective evaporation of droplets on a DMA,which provides essential implications for a wide range of applications including cell culture,heat management,microreactors,biochips,and so on.

关键词： coating culture collective

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Phase-field based shape optimization of uni- and multiaxially loaded nature-inspired porous structures while maintaining characteristic properties

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Discover Mechanical Engineering 2024年第1期3卷 1-19页

作者： Selzer, Michael Wallat, Leonie Kersch, Nils Reder, Martin Seiler, Marcus Poehler, Frank Nestler, Britta Institute of Digital Materials Science Karlsruhe University of Applied Sciences Moltkestraße 30 Baden-Wuerttemberg Karlsruhe 76133 Germany Institute of Materials and Processes Karlsruhe University of Applied Sciences Moltkestraße 30 Baden-Wuerttemberg Karlsruhe 76133 Germany Institute for Applied Materials - Microstructure Modelling and Simulation Karlsruhe Institute of Technology (KIT) Strasse am Forum 7 Baden-Wuerttemberg Karlsruhe 76131 Germany Institute of Nanotechnology Karlsruhe Institute of Technology (KIT) Hermann-von-Helmholtz-Platz 1 Baden-Wuerttemberg Eggenstein-Leopoldshafe 76344 Germany ReOss GmbH Echterdinger Str. 57 Baden-Wuerttemberg Filderstadt 70794 Germany

Triply periodic minimal surfaces (TPMS) are highly versatile porous formations that can be defined by formulas. Computationally based, load-specific shape optimization enables tailoring these structures for their respective application areas and thereby enhance their potential. In this investigation, individual sheet-based gyroid structures with varying porosities are specifically optimized with respect to their stiffness. A modified phase-field method is employed to establish a simulation framework for the shape optimization process. Despite constant volume and the preservation of the periodicity of the unit cells, volume redistribution occurs through displacement of the interfaces. The phase-field-based optimization process is detailed using unidirectional loading on three gyroidal unit cells with porosities of 75 %, 80 %, and 85 %. Subsequently, the gyroidal unit cell with a porosity of 85 % is shape-optimized under multidirectional loading. A subsequent experimental validation of the unidirectionally loaded cells confirms that the shape-optimized structures exhibit, on average, higher stiffness than the non-optimized structures. The highest increase of 40 % in effective modulus is achieved with the gyroid structure having a porosity of 75 %, while maintaining minimal alteration to the surface-to-volume ratio and preserving periodicity. Additionally, the experimental data show that the optimization process resulted in a shift in the linear elasticity and plasticity range. In summary, the phase-field method proves to be a valid optimization technique for complex porous structures, allowing the preservation of characteristic properties. © The Author(s) 2024.

关键词： Gyroid Phase-field Shape optimization TPMS-structures

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Wetting Phenomena: Line Tension and Gravitational Effect

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Physical Review Letters 2024年第24期133卷 246201-246201页

作者： Fei Wang (王飞) Haodong Zhang Britta Nestler Institute for Applied Materials - Microstructure Modelling and Simulation (IAM-MMS) Karlsruhe Institute of Technology (KIT) Strasse am Forum 7 76131 Karlsruhe Germany and Institute of Nanotechnology (INT) Karlsruhe Institute of Technology (KIT) Hermann-von-Helmholtz-Platz 1 76344 Eggenstein-Leopoldshafen Germany

An apparent contact angle is formed when a droplet is deposited on a solid substrate. Young’s law has been employed to describe the equilibrium contact angle. Often in experiments, the equilibrium contact angle deviates from Young’s law and depends on the volume of the droplet, known as the line tension effect. However, the physical origin of the line tension is quite controversial. Especially, the sign and the quantity of the line tension spanning 6 orders of magnitude are unsolved problems. Here, we quantify the line energy in terms of physical parameters and demonstrate that both positive and negative line tensions exist. The results are quantitatively compared with existing experiments as well as with previous theories.

关键词： Gravitational effects

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Wetting and Contact-Angle Hysteresis: Density Asymmetry and van der Waals Force

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Physical Review Letters 2024年第12期132卷 126202-126202页

作者： Fei Wang (王飞) Britta Nestler Institute for Applied Materials-Microstructure Modelling and Simulation (IAM-MMS) Karlsruhe Institute of Technology (KIT) Strasse am Forum 7 76131 Karlsruhe Germany Institute of Nanotechnology (INT) Karlsruhe Institute of Technology (KIT) Hermann-von-Helmholtz-Platz 1 76344 Eggenstein-Leopoldshafen Germany and Institute of Digital Materials Science Karlsruhe University of Applied Sciences Moltkestrasse 30 76133 Karlsruhe Germany

A droplet depositing on a solid substrate leads to the wetting phenomenon, such as dew on plant leaves. On an ideally smooth substrate, the classic Young’s law has been employed to describe the wetting effect. However, no real substrate is ideally smooth at the microscale. Given this fact, we introduce a surface composition concept to scrutinize the wetting mechanism via considering the liquid-gas density asymmetry and the fluid-solid van der Waals interaction. The current concept enables one to comprehend counterintuitive phenomenon of contact-angle hysteresis on a smooth substrate and increase of contact angle with temperature as well as gas bubble wetting.

关键词： Wetting Liquid-solid interfaces Solid-gas interfaces Phase-field modeling

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Solidification of quaternary X5CrNi18-10 alloy after laser beam welding: A phase-field approach

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Procedia CIRP 2024年 124卷 460-463页

作者： Muhammad Umar Daniel Schneider Britta Nestler Institute for Digital Materials Science (IDM) Karlsruhe University of Applied Sciences Moltkestraße 30 76133 Karlsruhe Germany Institute for Applied Materials - Microstructure Modelling and Simulation (IAM-MMS) Karlsruhe Institute of Technology (KIT) Straße am Forum 7 76131 Karlsruhe Germany Institute of Nanotechnology – Microstructure Simulations (INT) Karlsruhe Institute of Technology (KIT) Hermann-von-Helmholtz-Platz 1 76344 Eggenstein-Leopoldshafen Germany

The austenitic stainless steel (X5CrNi18-10) is the most commonly used chrome-nickel steel, due to its high corrosion resistance. However, it faces the challenge of cracking events during post-laser-beam-welding dendritic solidification. These microstructural changes significantly impact the final mechanical properties. To contribute to a more precise understanding of the physical mechanisms of the appearance of cracking, the goal of this research is to investigate various aspects at the microscale influenced by process-specific extreme thermal conditions. A thermodynamic model of quaternary alloy configuration is used to study the micro-segregation behavior of alloying elements and resulting morphology based on the local thermal conditions. For this purpose, a multi-component and multiphase-field-based grand chemical potential model is used. It is observed that in addition to global processing conditions, local conditions are also important to consider and classify the morphology changes from columnar-dendritic to cellular along the liquidus isotherm of the weld pool.

关键词： dendritic solidification phase-field simulations austenitic stainless steel thermochemical modelling CALPHAD database

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Brownian motion of droplets induced by thermal noise

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Physical Review E 2024年第2期109卷 024208-024208页

作者： Haodong Zhang Fei Wang Lorenz Ratke Britta Nestler Institute of Applied Materials-Microstructure Modelling and Simulation Karlsruhe Institute of Technology (KIT) Strasse am Forum 7 76131 Karlsruhe Germany Institute of Nanotechnology Karlsruhe Institute of Technology (KIT) Hermann-von-Helmholtz-Platz 1 76344 Eggenstein-Leopoldshafen Germany Institute of Materials Research German Aerospace Center Linder Hoehe 51147 Cologne Germany Institute of Digital Materials Science Karlsruhe University of Applied Sciences Moltkestrasse 30 76133 Karlsruhe Germany

Brownian motion (BM) is pivotal in natural science for the stochastic motion of microscopic droplets. In this study, we investigate BM driven by thermal composition noise at submicro scales, where intermolecular diffusion and surface tension both are significant. To address BM of microscopic droplets, we develop two stochastic multiphase-field models coupled with the full Navier-Stokes equation, namely, Allen-Cahn-Navier-Stokes and Cahn-Hilliard-Navier-Stokes. Both models are validated against capillary-wave theory; the Einstein's relation for the Brownian coefficient D*∼kBT/r at thermodynamic equilibrium is recovered. Moreover, by adjusting the co-action of the diffusion, Marangoni effect, and viscous friction, two nonequilibrium phenomena are observed. (I) The droplet motion transits from the Brownian to Ballistic with increasing Marangoni effect which is emanated from the energy dissipation mechanism distinct from the conventional fluctuation-dissipation theorem. (II) The deterministic droplet motion is triggered by the noise induced nonuniform velocity field which leads to a novel droplet coalescence mechanism associated with the thermal noise.

关键词： Brownian motion Noise Stochastic processes Stochastic thermodynamics

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Line tension of sessile droplets: Thermodynamic considerations

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Physical Review E 2023年第5期108卷 054121-054121页

作者： Haodong Zhang Fei Wang Britta Nestler Institute of Applied Materials-Microstructure Modelling and Simulation Karlsruhe Institute of Technology (KIT) Strasse am Forum 7 Karlsruhe 76131 Germany Institute of Nanotechnology Karlsruhe Institute of Technology (KIT) Hermann-von-Helmholtz-Platz 1 Eggenstein-Leopoldshafen 76344 Germany Institute of Digital Materials Science Karlsruhe University of Applied Sciences Moltkestrasse 30 Karlsruhe 76133 Germany

We deduce a thermodynamically consistent diffuse interface model to study the line tension phenomenon of sessile droplets. By extending the standard Cahn-Hilliard model via modifying the free energy functional due to the spatial reflection asymmetry at the substrate, we provide an alternative interpretation for the wall energy. In particular, we find the connection of the line tension effect with the droplet-matrix-substrate triple interactions. This finding reveals that the apparent contact angle deviating from Young's law is contributed by the wall energy reduction as well as the line energy minimization. Besides, the intrinsic negative line tension resulting from the curvature effect is observed in our simulations and shows good accordance with recent experiments [Tan et al. Phys. Rev. Lett. 130, 064003 (2023)]. Moreover, our model sheds light upon the understanding of the wetting edge formation which results from the vying effect of wall energy and line tension.

关键词： Surface tension effects Thermodynamics Wetting

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Capillary adsorption of droplets into a funnel-like structure

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Physical Review Fluids 2022年第5期7卷 054004-054004页

作者： Yanchen Wu Fei Wang Weidong Huang Michael Selzer Britta Nestler Institute for Applied Materials–Microstructure Modelling and Simulation (IAM-MMS) Karlsruhe Institute of Technology (KIT) Straße am Forum 7 Karlsruhe 76131 Germany and Institute of Digital Materials Science Karlsruhe University of Applied Sciences Moltkestraße 30 Karlsruhe 76133 Germany

Penetration of liquid with distinct volumes into a funnel-like pore structure is widely observed in nature and technical applications. However, when the droplet size is comparable with the pore size, the penetration criterion, i.e., under which condition the droplet can penetrate into the pore, remains an open question. In this work, we present theoretical models to address the penetration criteria in terms of the droplet size, the intrinsic wettability, and the opening angle of the funnel-shaped structure. The proposed theoretical models are well corroborated by phase-field simulations. Our findings demonstrate a critical contact angle below which a finite-volume droplet can penetrate into a hydrophobic pore. This critical contact angle is intimately related to the opening angle and the droplet size, which provides a complement to previous literature. Note that for a certain-sized droplet, the critical contact angle becomes invariant when the opening angle is greater than a certain threshold. Moreover, we find that for a constant opening angle, the critical contact angle decreases with the increase of the droplet size. As the droplet volume tends to be infinite, the opening angle has almost no influence on the penetration, and the critical contact angle asymptotically approaches 90∘, being consistent with previous works. Our observations illuminate a special mechanism for a precise maneuver of droplets in pore structures with potential applications in filter systems and microfluidic platforms.

关键词： Capillary interactions Coatings Contact line dynamics Drops & bubbles Flow-structure interactions Hydrophilic interactions Hydrophobic interactions Liquid bridges Surface tension effects Wetting Water

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A Phase-Field Model for the Wetting Phenomenon of Miscible and Immmiscible Ternary Fluids

SSRN

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SSRN 2022年

作者： Wang, Fei Zhang, Haodong Wu, Yanchen Nestler, Britta Institute of Applied Materials-Microstructure Modelling and Simulation Karlsruhe Institute of Technology Straße am Forum 7 Karlsruhe76131 Germany Institute of Digital Materials Science Karlsruhe University of Applied Sciences Moltkestraße 30 Karlsruhe76133 Germany

Wetting effect has arisen great scientific interest because of its natural significance as well as technical applications. Previous models mostly focus on pure substrate fluids or binary immiscible liquid mixtures. Modeling of the wetting phenomenon for multicomponent and multiphase fluids is a knotty issue. In this work, we present a phase-field model to describe the wetting effect for ternary fluids. In particular, we consider both immiscible and miscible ternary fluids, in contrast to previous immiscible ternary fluids in literature. For the miscible fluids, we vary the droplet composition and validate the present model both with Young’s law and Young-Laplace equation. For the immiscible ternary fluids, we manipulate the wettability of two contact droplets deposited on a solid substrate according to three scenarios: (I) both droplets are hydrophilic;(II) a hydrophilic droplet in contact with a hydrophobic one;(III) both droplets are hydrophobic. The contact angles at each triple junction from the simulations are compared with Young’s contact angle as well as with Neumann’s triangle rule. simulations for the validation of our work are performed in 2D and 3D. In addition, we model the evaporation process of a ternary droplet and obtain the same power law of previous experiments. Our model allows to relate the interfacial energies with surface composition, enabling to model coffee ring phenomenon in further perspective. © 2022, The Authors. All rights reserved.

关键词： Wetting

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Efficient thermomechanically coupled FE-FFT-based multiscale simulation of polycrystals

Efficient thermomechanically coupled FE-FFT-based multiscale...

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93rd Annual Meeting of the International Association of applied Mathematics and Mechanics, GAMM 2023

作者： Gierden, Christian Schmidt, Annika Waimann, Johanna Svendsen, Bob Reese, Stefanie Institute of Applied Mechanics RWTH Aachen University Aachen Germany Modeling and Simulation Techniques for Systems of Polycrystalline Materials RWTH Aachen University Aachen Germany Material Mechanics RWTH Aachen University Aachen Germany Microstructure Physics and Alloy Design Max-Planck-Institut für Eisenforschung GmbH Düsseldorf Germany

In general, the overall macroscopic material behavior of any structural component is directly dependent on its underlying microstructure. For metal components, the associated microstructure is given in terms of a polycrystal. To enable the simulation of the related microstructural and overall elasto-viscoplastic material behavior, a two-scale simulation approach can be used. In this context, we use a FE-FFT-based two-scale method, which is an efficient alternative to the classical FE2 method for the simulation of periodic microstructures. In addition, we consider a thermomechanically coupled framework to account for both thermal and mechanical loads. Finally, we incorporate a model order reduction technique based on a coarsely discretized microstructure to develop an efficient two-scale simulation technique. As a demonstration of the feasibility of the proposed simulation framework, a numerical example will be investigated. © 2023 The Authors. Proceedings in applied Mathematics and Mechanics published by Wiley-VCH GmbH.

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