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Hartmann S, Diekmann J, Greve D, Thiele U. Drops on Polymer Brushes: Advances in Thin-Film Modeling of Adaptive Substrates. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2024; 40:4001-4021. [PMID: 38358424 DOI: 10.1021/acs.langmuir.3c03313] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/16/2024]
Abstract
We briefly review recent advances in the hydrodynamic modeling of the dynamics of droplets on adaptive substrates, in particular, solids that are covered by polymer brushes. Thereby, the focus is on long-wave and full-curvature variants of mesoscopic hydrodynamic models in gradient dynamics form. After introducing the approach for films/drops of nonvolatile simple liquids on a rigid smooth solid substrate, it is first expanded to an arbitrary number of coupled degrees of freedom before considering the specific case of drops of volatile liquids on brush-covered solids. After presenting the model, its usage is illustrated by briefly considering the natural and forced spreading of drops of nonvolatile liquids on a horizontal brush-covered substrate, stick-slip motion of advancing contact lines as well as drops sliding down a brush-covered incline. Finally, volatile liquids are also considered.
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Affiliation(s)
- Simon Hartmann
- Institut für Theoretische Physik, Universität Münster, Wilhelm Klemm Str. 9, D-48149 Münster, Germany
| | - Jan Diekmann
- Institut für Theoretische Physik, Universität Münster, Wilhelm Klemm Str. 9, D-48149 Münster, Germany
| | - Daniel Greve
- Institut für Theoretische Physik, Universität Münster, Wilhelm Klemm Str. 9, D-48149 Münster, Germany
| | - Uwe Thiele
- Institut für Theoretische Physik, Universität Münster, Wilhelm Klemm Str. 9, D-48149 Münster, Germany
- Center of Nonlinear Science (CeNoS), Universität Münster, Corrensstr. 2, 48149 Münster, Germany
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2
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Weyer H, Brauns F, Frey E. Coarsening and wavelength selection far from equilibrium: A unifying framework based on singular perturbation theory. Phys Rev E 2023; 108:064202. [PMID: 38243507 DOI: 10.1103/physreve.108.064202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2023] [Accepted: 08/29/2023] [Indexed: 01/21/2024]
Abstract
Intracellular protein patterns are described by (nearly) mass-conserving reaction-diffusion systems. While these patterns initially form out of a homogeneous steady state due to the well-understood Turing instability, no general theory exists for the dynamics of fully nonlinear patterns. We develop a unifying theory for nonlinear wavelength-selection dynamics in (nearly) mass-conserving two-component reaction-diffusion systems independent of the specific mathematical model chosen. Previous work has shown that these systems support an extremely broad band of stable wavelengths, but the mechanism by which a specific wavelength is selected has remained unclear. We show that an interrupted coarsening process selects the wavelength at the threshold to stability. Based on the physical intuition that coarsening is driven by competition for mass and interrupted by weak source terms that break strict mass conservation, we develop a singular perturbation theory for the stability of stationary patterns. The resulting closed-form analytical expressions enable us to quantitatively predict the coarsening dynamics and the final pattern wavelength. We find excellent agreement with numerical results throughout the diffusion- and reaction-limited regimes of the dynamics, including the crossover region. Further, we show how, in these limits, the two-component reaction-diffusion systems map to generalized Cahn-Hilliard and conserved Allen-Cahn dynamics, therefore providing a link to these two fundamental scalar field theories. The systematic understanding of the length-scale dynamics of fully nonlinear patterns in two-component systems provided here builds the basis to reveal the mechanisms underlying wavelength selection in multicomponent systems with potentially several conservation laws.
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Affiliation(s)
- Henrik Weyer
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, Theresienstraße 37, D-80333 München, Germany
| | - Fridtjof Brauns
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, Theresienstraße 37, D-80333 München, Germany
| | - Erwin Frey
- Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, Theresienstraße 37, D-80333 München, Germany
- Max Planck School Matter to Life, Hofgartenstraße 8, D-80539 Munich, Germany
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3
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Kap Ö, Hartmann S, Hoek H, de Beer S, Siretanu I, Thiele U, Mugele F. Nonequilibrium configurations of swelling polymer brush layers induced by spreading drops of weakly volatile oil. J Chem Phys 2023; 158:2888849. [PMID: 37144718 DOI: 10.1063/5.0146779] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2023] [Accepted: 04/18/2023] [Indexed: 05/06/2023] Open
Abstract
Polymer brush layers are responsive materials that swell in contact with good solvents and their vapors. We deposit drops of an almost completely wetting volatile oil onto an oleophilic polymer brush layer and follow the response of the system upon simultaneous exposure to both liquid and vapor. Interferometric imaging shows that a halo of partly swollen polymer brush layer forms ahead of the moving contact line. The swelling dynamics of this halo is controlled by a subtle balance of direct imbibition from the drop into the brush layer and vapor phase transport and can lead to very long-lived transient swelling profiles as well as nonequilibrium configurations involving thickness gradients in a stationary state. A gradient dynamics model based on a free energy functional with three coupled fields is developed and numerically solved. It describes experimental observations and reveals how local evaporation and condensation conspire to stabilize the inhomogeneous nonequilibrium stationary swelling profiles. A quantitative comparison of experiments and calculations provides access to the solvent diffusion coefficient within the brush layer. Overall, the results highlight the-presumably generally applicable-crucial role of vapor phase transport in dynamic wetting phenomena involving volatile liquids on swelling functional surfaces.
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Affiliation(s)
- Özlem Kap
- Physics of Complex Fluids Group and MESA+ Institute, Faculty of Science and Technology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
| | - Simon Hartmann
- Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Str. 9, 48149 Münster, Germany
- Center for Nonlinear Science (CeNoS), Westfälische Wilhelms-Universität Münster, Corrensstr. 2, 48149 Münster, Germany
| | - Harmen Hoek
- Physics of Complex Fluids Group and MESA+ Institute, Faculty of Science and Technology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
| | - Sissi de Beer
- Sustainable Polymer Chemistry Group, Department of Molecules & Materials MESA+ Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
| | - Igor Siretanu
- Physics of Complex Fluids Group and MESA+ Institute, Faculty of Science and Technology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
| | - Uwe Thiele
- Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Str. 9, 48149 Münster, Germany
- Center for Nonlinear Science (CeNoS), Westfälische Wilhelms-Universität Münster, Corrensstr. 2, 48149 Münster, Germany
| | - Frieder Mugele
- Physics of Complex Fluids Group and MESA+ Institute, Faculty of Science and Technology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
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4
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Kumar S, Charitatos V. Influence of Surface Roughness on Droplet Evaporation and Absorption: Insights into Experiments from Lubrication-Theory-Based Models. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2022; 38:15889-15904. [PMID: 36519694 DOI: 10.1021/acs.langmuir.2c01930] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
While solid substrates are often idealized as being perfectly smooth, all real surfaces possess some level of topographical and chemical heterogeneity. This heterogeneity can greatly influence droplet dynamics. Mathematical models based on lubrication theory that account for surface roughness reveal how topographical defects induce contact-line pinning and affect the deposition patterns of colloidal particles suspended in the droplet. Contact-line pinning profoundly changes the behavior of droplet evaporation on horizontal and inclined impermeable substrates and droplet absorption on horizontal permeable substrates. Models accounting for surface roughness yield predictions that are qualitatively consistent with experimental observations and also provide insight into the underlying physical mechanisms. These models are a foundation for the exploration of a rich array of problems concerning droplet dynamics which are of both fundamental and practical interest.
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Affiliation(s)
- Satish Kumar
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, United States
| | - Vasileios Charitatos
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, United States
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5
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Schott M, Repetto L, Savio RL, Firpo G, Angeli E, Valbusa U. Identification of the seeding mechanism in the spinodal instability of dewetting liquids. J Colloid Interface Sci 2022; 632:65-73. [DOI: 10.1016/j.jcis.2022.11.028] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2022] [Revised: 11/03/2022] [Accepted: 11/06/2022] [Indexed: 11/13/2022]
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Henkel C, Essink MH, Hoang T, van Zwieten GJ, van Brummelen EH, Thiele U, Snoeijer JH. Soft wetting with (a)symmetric Shuttleworth effect. Proc Math Phys Eng Sci 2022; 478:20220132. [PMID: 35937429 PMCID: PMC9347665 DOI: 10.1098/rspa.2022.0132] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2022] [Accepted: 07/04/2022] [Indexed: 11/12/2022] Open
Abstract
The wetting of soft polymer substrates brings in multiple complexities when compared with 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 through 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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Affiliation(s)
- C. Henkel
- Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Str. 9, Münster 48149, Germany
| | - M. H. Essink
- Physics of Fluids Group, Faculty of Science and Technology, Mesa+ Institute, University of Twente, Enschede 7500 AE, The Netherlands
| | - T. Hoang
- Physics of Fluids Group, Faculty of Science and Technology, Mesa+ Institute, University of Twente, Enschede 7500 AE, The Netherlands
| | | | - E. H. van Brummelen
- Multiscale Engineering Fluid Dynamics Group, Department of Mechanical Engineering, Eindhoven University of Technology, PO Box 513, Eindhoven 5600 MB, The Netherlands
| | - U. Thiele
- Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Str. 9, Münster 48149, Germany
- Center for Nonlinear Science (CeNoS), Westfälische Wilhelms-Universität Münster, Corrensstr. 2, Münster 48149, Germany
| | - J. H. Snoeijer
- Physics of Fluids Group, Faculty of Science and Technology, Mesa+ Institute, University of Twente, Enschede 7500 AE, The Netherlands
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Kamis NI, Jiann LY, Shafie S, Khairuddin TKA, Md Basir MF. Magnetohydrodynamics Boundary Layer Flow of Hybrid Nanofluid in a Thin-Film Over an Unsteady Stretching Permeable Sheet. JOURNAL OF NANOFLUIDS 2022. [DOI: 10.1166/jon.2022.1821] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
Abstract
This analysis explored the computational process of heat transfer analysis in a thin-film MHD flow embedded in the hybrid nanoparticles, which combine the spherical copper and alumina dispersed in ethylene glycol as the conventional heat transfer Newtonian fluid model over a stretching
sheet. The nonlinear ordinary differential equations (ODEs) was attained by transforming partial differential equation (PDEs) as governing equations when implementing the similarity transformations technique. The resulting nonlinear ODEs have been utilized by using the Keller box method. The
natures of the thin-film flow and heat transfer through the various values of the pertinent parameters: unsteadiness, nanoparticle volume fraction, thin-film thickness, magnetic interaction and intensity suction/injection are deliberated. The approximate results for velocity and temperature
distributions and physical quantities in terms of local skin friction and Nusselt number have been obtained and analyzed via graphs and tables. As a consequence, the suction expresses a more prodigious effect on the hybrid nanofluid rather than injection fluid for all the investigation parameters.
It is worth acknowledging that the existence of the nanoparticles and MHD in the viscous hybrid nanofluid tends to enhance the temperature profile but decay the particle movement in the thin-film flow. It is perceived that the velocity and temperature profiles decline for the growth of the
unsteadiness, thin-film thickness and suction/injection parameters.
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Affiliation(s)
- Nur Ilyana Kamis
- Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia
| | - Lim Yeou Jiann
- Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia
| | - Sharidan Shafie
- Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia
| | - Taufiq Khairi Ahmad Khairuddin
- Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia
| | - Md Faisal Md Basir
- Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia
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8
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Henkel C, Snoeijer JH, Thiele U. Gradient-dynamics model for liquid drops on elastic substrates. SOFT MATTER 2021; 17:10359-10375. [PMID: 34747426 DOI: 10.1039/d1sm01032h] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
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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Affiliation(s)
- Christopher Henkel
- Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Str. 9, 48149 Münster, Germany.
| | - Jacco H Snoeijer
- Physics of Fluids Group and J. M. Burgers Centre for Fluid Dynamics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
| | - Uwe Thiele
- Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Str. 9, 48149 Münster, Germany.
- Center for Nonlinear Science (CeNoS), Westfälische Wilhelms-Universität Münster, Corrensstr. 2, 48149 Münster, Germany
- Center for Multiscale Theory and Computation (CMTC), Westfälische Wilhelms-Universität, Corrensstr. 40, 48149 Münster, Germany
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9
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Straub BB, Schmidt H, Rostami P, Henrich F, Rossi M, Kähler CJ, Butt HJ, Auernhammer GK. Flow profiles near receding three-phase contact lines: influence of surfactants. SOFT MATTER 2021; 17:10090-10100. [PMID: 34714897 PMCID: PMC8597584 DOI: 10.1039/d1sm01145f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/06/2021] [Accepted: 10/18/2021] [Indexed: 06/13/2023]
Abstract
The dynamics of wetting and dewetting is largely determined by the velocity field near the contact lines. For water drops it has been observed that adding surfactant decreases the dynamic receding contact angle even at a concentration much lower than the critical micelle concentration (CMC). To better understand why surfactants have such a drastic effect on drop dynamics, we constructed a dedicated setup on an inverted microscope, in which an aqueous drop is held stationary while the transparent substrate is moved horizontally. Using astigmatism particle tracking velocimetry, we track the 3D displacement of the tracer particles in the flow. We study how surfactants alter the flow dynamics near the receding contact line of a moving drop for capillary numbers in the order of 10-6. Even for surfactant concentrations c far below the critical micelle concentration (c ≪ CMC) Marangoni stresses change the flow drastically. We discuss our results first in a 2D model that considers advective and diffusive surfactant transport and deduce estimates of the magnitude and scaling of the Marangoni stress from this. Modeling and experiment agree that a tiny gradient in surface tension of a few μN m-1 is enough to alter the flow profile significantly. The variation of the Marangoni stress with the distance from the contact line suggests that the 2D advection-diffusion model has to be extended to a full 3D model. The effect is ubiquitous, since surfactant is present in many technical and natural dewetting processes either deliberately or as contamination.
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Affiliation(s)
- Benedikt B Straub
- Max Planck Institute for Polymer Research, Ackermannweg 10, D-55128 Mainz, Germany
| | - Henrik Schmidt
- Max Planck Institute for Polymer Research, Ackermannweg 10, D-55128 Mainz, Germany
| | - Peyman Rostami
- Max Planck Institute for Polymer Research, Ackermannweg 10, D-55128 Mainz, Germany
- Leibniz-Institut für Polymerforschung, Hohe Straße 6, D-01069 Dresden, Germany.
| | - Franziska Henrich
- Max Planck Institute for Polymer Research, Ackermannweg 10, D-55128 Mainz, Germany
| | - Massimiliano Rossi
- Department of Physics, Technical University of Denmark, DTU Physics Building 309, DK-2800 Kongens Lyngby, Denmark
- Institute of Fluid Mechanics and Aerodynamics, Bundeswehr University Munich, D-85577 Neubiberg, Germany
| | - Christian J Kähler
- Institute of Fluid Mechanics and Aerodynamics, Bundeswehr University Munich, D-85577 Neubiberg, Germany
| | - Hans-Jürgen Butt
- Max Planck Institute for Polymer Research, Ackermannweg 10, D-55128 Mainz, Germany
| | - Günter K Auernhammer
- Max Planck Institute for Polymer Research, Ackermannweg 10, D-55128 Mainz, Germany
- Leibniz-Institut für Polymerforschung, Hohe Straße 6, D-01069 Dresden, Germany.
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10
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Grawitter J, Stark H. Droplets on substrates with oscillating wettability. SOFT MATTER 2021; 17:9469-9479. [PMID: 34614053 DOI: 10.1039/d1sm01113h] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
In recent decades novel solid substrates have been designed which change their wettability in response to light or an electrostatic field. Here, we investigate a droplet on substrates with oscillating uniform wettability by varying minimum and maximum contact angles and frequency. To simulate this situation, we use our previous work [Grawitter and Stark, Soft Matter, 2021, 17, 2454], where we implemented the boundary element method in combination with the Cox-Voinov law for the contact-line velocity, to determine the fluid flow inside a droplet. After a transient regime the droplet performs steady oscillations, the amplitude of which decreases with increasing frequency. For slow oscillations our numerical results agree well with the linearized spherical-cap model. They collapse on a master curve when we rescale frequency by a characteristic relaxation time. In contrast, for fast oscillations we observe significant deviations from the master curve. The decay of the susceptibility is weaker and the phase shift between oscillations in wettability and contact angle stays below the predicted π/2. The reason becomes obvious when studying the combined dynamics of droplet height and contact angle. It reveals non-reciprocal shape changes during one oscillation period even at low frequencies due to the induced fluid flow inside the droplet, which are not captured by the spherical-cap model. Similar periodic non-reciprocal shape changes occur at low frequencies when the droplet is placed on an oscillating nonuniform wettability profile with six-fold symmetry. Such profiles are inspired by the light intensity pattern of Laguerre-Gauss laser modes. Since the non-reciprocal shape changes induce fluid circulation, which is controllable from the outside, our findings envisage the design of targeted microfluidic transport of solutes inside the droplet.
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Affiliation(s)
- Josua Grawitter
- Technische Universität Berlin, Institut für Theoretische Physik, Straße des 17. Juni 135, 10623 Berlin, Germany.
| | - Holger Stark
- Technische Universität Berlin, Institut für Theoretische Physik, Straße des 17. Juni 135, 10623 Berlin, Germany.
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11
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Frohoff-Hülsmann T, Wrembel J, Thiele U. Suppression of coarsening and emergence of oscillatory behavior in a Cahn-Hilliard model with nonvariational coupling. Phys Rev E 2021; 103:042602. [PMID: 34006003 DOI: 10.1103/physreve.103.042602] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/02/2020] [Accepted: 03/04/2021] [Indexed: 12/27/2022]
Abstract
We investigate a generic two-field Cahn-Hilliard model with variational and nonvariational coupling. It describes, for instance, passive and active ternary mixtures, respectively. Already a linear stability analysis of the homogeneous mixed state shows that activity not only allows for the usual large-scale stationary (Cahn-Hilliard) instability of the well-known passive case but also for small-scale stationary (Turing) and large-scale oscillatory (Hopf) instabilities. In consequence of the Turing instability, activity may completely suppress the usual coarsening dynamics. In a fully nonlinear analysis, we first briefly discuss the passive case before focusing on the active case. Bifurcation diagrams and selected direct time simulations are presented that allow us to establish that nonvariational coupling (i) can partially or completely suppress coarsening and (ii) may lead to the emergence of drifting and oscillatory states. Throughout, we emphasize the relevance of conservation laws and related symmetries for the encountered intricate bifurcation behavior.
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Affiliation(s)
- Tobias Frohoff-Hülsmann
- Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Str. 9, 48149 Münster, Germany
| | - Jana Wrembel
- Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Str. 9, 48149 Münster, Germany
| | - Uwe Thiele
- Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Str. 9, 48149 Münster, Germany.,Center for Nonlinear Science (CeNoS), Westfälische Wilhelms-Universität Münster, Corrensstr. 2, 48149 Münster, Germany.,Center for Multiscale Theory and Computation (CMTC), Westfälische Wilhelms-Universität, Corrensstr. 40, 48149 Münster, Germany
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12
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Vlasko-Vlasov VK, Sulwer M, Shevchenko EV, Parker J, Kwok WK. Ring patterns generated by an expanding colloidal meniscus. Phys Rev E 2020; 102:052608. [PMID: 33327138 DOI: 10.1103/physreve.102.052608] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/25/2020] [Accepted: 11/06/2020] [Indexed: 11/07/2022]
Abstract
The drop-and-dry is a common technique allowing for creation of periodic nanoparticle (NP) structures for sensing, photonics, catalysis, etc. However, the reproducibility and scalability of this approach for fabrication of NP-based structures faces serious challenges due to the complexity of the simple, at first glance, evaporation process. In this work we study the effect of the spatial confinement on the NP self-assembly under slow solvent evaporation, when the air-liquid-substrate contact line (CL) expands from the center towards the walls of a cylindrical cell, forming a toroid. Using in situ video monitoring of the stick-slip CL motion, we find regular hydrodynamic perturbations in the meniscus, and reveal fine details of the formation of quasiperiodic rings of close packed NP layers. We report that drying of the toroidal NP droplet has a number of important differences from drying of the classical hemispherical colloidal drops. In toroidal drops we observe linear-in-time average meniscus motion, in contrast to the hemispherical drops where the meniscus moves as a square root of time. While both droplet geometries produce NP ring patterns, the ring width for the toroidal drop decreases with increasing ring radius, while it decreases with decreasing the radius of the hemispherical drop. We suggest that free ligands are the main cause of the Marangoni instabilities driving the periodic vorticity in the meniscus. In addition, we show that the usually ignored contact line tension may yield a considerable contribution to the CL pinning causing the CL slip-stick motion and the ring formation.
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Affiliation(s)
- V K Vlasko-Vlasov
- Materials Sciences Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - M Sulwer
- Department of Physics, Lewis University, Romeoville, Illinois 60446, USA
| | - E V Shevchenko
- Argonne National Laboratory, Center for Nanoscale Materials, Argonne, Illinois 60439, USA
| | - J Parker
- Department of Physics, Lewis University, Romeoville, Illinois 60446, USA
| | - W K Kwok
- Materials Sciences Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
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13
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L'vov PE, Bulyarskiy SV, Gusarov GG, Molodenskiy MS, Pavlov AA, Ryazanov RM, Dudin AA, Svetukhin VV. Kinetics of nickel particle formation on silicon substrate with a buffer layer of niobium nitride. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:245001. [PMID: 32079003 DOI: 10.1088/1361-648x/ab7870] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
The size, form and distribution function of catalyst particles define the quality of synthesized arrays of carbon nanotubes. In this work, we study the kinetics of catalyst particle formation from the thin nickel film (9 nm) deposited on the silicon substrate (SiO2/Si) with a buffer layer of niobium nitride at the temperature of 880 °C. In the experiment, we have obtained the time dependences of the average radius, average height and concentration of nickel particles. The experimental data are satisfactorily described by simulations based on the wetting transition theory. Comparison of the simulation results and experimental data allows us to estimate the effective interaction potential between the nickel film and buffer layer of niobium nitride. Besides, we have estimated the viscosity of the nickel confirming an undercooled liquid state of the nanosized nickel film at the temperature of 880 °C.
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Affiliation(s)
- P E L'vov
- Ulyanovsk State University, Ulyanovsk, Russia. Institute of Nanotechnology of Microelectronics of the Russian Academy of Science, Moscow, Russia
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14
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Ly PMT, Thiele U, Chi L, Gurevich SV. Effects of time-periodic forcing in a Cahn-Hilliard model for Langmuir-Blodgett transfer. Phys Rev E 2019; 99:062212. [PMID: 31330734 DOI: 10.1103/physreve.99.062212] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2019] [Indexed: 06/10/2023]
Abstract
The influence of a temporal forcing on the pattern formation in Langmuir-Blodgett transfer is studied employing a generalized Cahn-Hilliard model. The occurring frequency-locking effects allow for controlling the pattern formation process. In the case of one-dimensional (i.e., stripe) patterns one finds various synchronization phenomena such as entrainment between the distance of deposited stripes and the forcing frequency. In two dimensions, the temporal forcing gives rise to the formation of intricate complex patterns such as vertical stripes, oblique stripes, and lattice structures. Remarkably, it is possible to influence the system in the spatial direction perpendicular to the forcing direction leading to synchronization in two spatial dimensions.
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Affiliation(s)
- Phong-Minh Timmy Ly
- Institute for Theoretical Physics, University of Münster, Wilhelm-Klemm-Str. 9, D-48149 Münster, Germany
| | - Uwe Thiele
- Institute for Theoretical Physics, University of Münster, Wilhelm-Klemm-Str. 9, D-48149 Münster, Germany
- Center for Nonlinear Science (CeNoS), University of Münster, Corrensstrasse 2, D-48149 Münster, Germany
| | - Lifeng Chi
- Institute of Functional Nano & Soft Materials (FUNSOM) and Jiangsu Key Laboratory for Carbon-based Functional Materials & Devices Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, 215123 Suzhou, People's Republic of China
| | - Svetlana V Gurevich
- Institute for Theoretical Physics, University of Münster, Wilhelm-Klemm-Str. 9, D-48149 Münster, Germany
- Center for Nonlinear Science (CeNoS), University of Münster, Corrensstrasse 2, D-48149 Münster, Germany
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Abo Jabal M, Egbaria A, Zigelman A, Thiele U, Manor O. Connecting Monotonic and Oscillatory Motions of the Meniscus of a Volatile Polymer Solution to the Transport of Polymer Coils and Deposit Morphology. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2018; 34:11784-11794. [PMID: 30179481 DOI: 10.1021/acs.langmuir.8b02268] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We study the deposition mechanisms of polymer from a confined meniscus of volatile liquid. In particular, we investigate the physical processes that are responsible for qualitative changes in the pattern deposition of polymer and the underlying interplay of the state of pattern deposition, motion of the meniscus, and the transport of polymer within the meniscus. As a model system we evaporate a solution of poly(methyl methacrylate) (PMMA) in toluene. Different deposition patterns are observed when varying the molecular mass, the initial concentration of the solute, and temperature; these are systematically presented in the form of morphological phase diagrams. The modi of deposition and meniscus motion are correlated. They vary with the ratio between the evaporation-driven convective flux and the diffusive flux of the polymer coils in the solution. In the case of a diffusion-dominated solute transport, the solution monotonically dewets the solid substrate by evaporation, supporting continuous contact line motion and continuous polymer deposition. However, a convection-dominated transport results in an oscillatory ratcheting dewetting-wetting motion of the contact line with more pronounced dewetting phases. The deposition process is then periodic and produces a stripe pattern. The oscillatory motion of the meniscus differs from the well documented stick-slip motion of the meniscus, observed as well, and is attributed to the opposing influences of evaporation and Marangoni stresses, which alternately dominate the deposition process.
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Affiliation(s)
- Mohammad Abo Jabal
- Wolfson Department of Chemical Engineering , Technion - Israel Institute of Technology , Haifa , Israel 32000
| | - Ala Egbaria
- Wolfson Department of Chemical Engineering , Technion - Israel Institute of Technology , Haifa , Israel 32000
| | - Anna Zigelman
- Wolfson Department of Chemical Engineering , Technion - Israel Institute of Technology , Haifa , Israel 32000
| | - Uwe Thiele
- Institut für Theoretische Physik , Westfälische Wilhelms-Universität Münster , Wilhelm Klemm Str. 9 , 48149 Münster , Germany
- Center of Nonlinear Science (CeNoS) , Westfälische Wilhelms Universität Münster , Corrensstr. 2 , 48149 Münster , Germany
| | - Ofer Manor
- Wolfson Department of Chemical Engineering , Technion - Israel Institute of Technology , Haifa , Israel 32000
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