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Guzowski J, Gim B. Particle clusters at fluid-fluid interfaces: equilibrium profiles, structural mechanics and stability against detachment. SOFT MATTER 2019; 15:4921-4938. [PMID: 31169851 DOI: 10.1039/c9sm00425d] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
We investigate clustering of particles at an initially flat fluid-fluid interface of surface tension γ under an external force f directed perpendicular to the interface. We employ analytical theory, numerical energy minimization (Surface Evolver) and computational fluid dynamics (the Lattice-Boltzmann method) to study the equilibrium deformation of the interface and structural mechanics of the clusters, in particular at the onset of instability. In the case of incompressible clusters, we find that the equilibrium 3D interface profiles are uniquely determined by the length scale γ/(fn0), where n0 is the particle surface number density, and a non-dimensional shape parameter f2Nn0/γ2. The scaling remains valid in the whole regime of forces f, i.e., even close to the stability limit fcrit. In the cases with an initial hexagonal arrangement of the particles, upon f approaching fcrit, our simulations additionally reveal the emergence of curvature-induced defects and 2D stress anisotropy. We develop stability diagrams in terms of f, N (we study 7 ≤ N ≤ 61), and the contact angle θp at the particles and identify three unstable regimes corresponding to (i) collective detachment of the whole cluster from the interface, (ii) ejection of individual particles, and (iii) both detachment and ejection. We also discuss possible metastable states. Altogether, our results may help in better understanding and controlling the particle interfacial instabilities with potential uses in synthesis of new materials, environmental sciences and microfluidics.
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Affiliation(s)
- Jan Guzowski
- Institute of Physical Chemistry, Polish Academy of Sciences, ul. Kasprzaka 44/52, 01-224, Warsaw, Poland.
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Löwen H. Dynamical Density Functional Theory for Brownian Dynamics of Colloidal Particles. VARIATIONAL METHODS IN MOLECULAR MODELING 2017. [DOI: 10.1007/978-981-10-2502-0_9] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
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Lee DG, Cicuta P, Vella D. Self-assembly of repulsive interfacial particles via collective sinking. SOFT MATTER 2016; 13:212-221. [PMID: 27357475 DOI: 10.1039/c6sm00901h] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Charged colloidal particles trapped at an air-water interface are well known to form an ordered crystal, stabilized by a long ranged repulsion; the details of this repulsion remain something of a mystery, but all experiments performed to date have confirmed a dipolar-repulsion, at least at dilute concentrations. More complex arrangements are often observed, especially at higher concentration, and these seem to be incompatible with a purely repulsive potential. In addition to electrostatic repulsion, interfacial particles may also interact via deformation of the surface: so-called capillary effects. Pair-wise capillary interactions are well understood, and are known to be too small (for these colloidal particles) to overcome thermal effects. Here we show that collective effects may significantly modify the simple pair-wise interactions and become important at higher density, though we remain well below close packing throughout. In particular, we show that the interaction of many interfacial particles can cause much larger interfacial deformations than do isolated particles, and show that the energy of interaction per particle due to this "collective sinking" grows as the number of interacting particles grows. Though some of the parameters in our simple model are unknown, the scaling behaviour is entirely consistent with experimental data, strongly indicating that estimating interaction energy based solely on pair-wise potentials may be too simplistic for surface particle layers.
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Affiliation(s)
- Duck-Gyu Lee
- Mathematical Institute, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK.
| | | | - Dominic Vella
- Mathematical Institute, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK.
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Domínguez A, Malgaretti P, Popescu MN, Dietrich S. Collective dynamics of chemically active particles trapped at a fluid interface. SOFT MATTER 2016; 12:8398-8406. [PMID: 27714377 DOI: 10.1039/c6sm01468b] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Chemically active colloids generate changes in the chemical composition of their surrounding solution and thereby induce flows in the ambient fluid which affect their dynamical evolution. Here we study the many-body dynamics of a monolayer of spherically symmetric active particles trapped at a fluid-fluid interface. To this end we consider a model for the large-scale spatial distribution of particles which incorporates the direct pair interaction (including also the capillary interaction which is caused specifically by the interfacial trapping) as well as the effect of hydrodynamic interactions (including the Marangoni flow induced by the response of the interface to the chemical activity). The values of the relevant physical parameters for typical experimental realizations of such systems are estimated and various scenarios, which are predicted by our approach for the dynamics of the monolayer, are discussed. In particular, we show that the chemically-induced Marangoni flow can prevent the clustering instability driven by the capillary attraction.
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Affiliation(s)
- Alvaro Domínguez
- Física Teórica, Universidad de Sevilla, Apdo. 1065, 41080 Sevilla, Spain.
| | - P Malgaretti
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstr. 3, 70569 Stuttgart, Germany and IV. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
| | - M N Popescu
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstr. 3, 70569 Stuttgart, Germany and IV. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
| | - S Dietrich
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstr. 3, 70569 Stuttgart, Germany and IV. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
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Zimmermann U, Smallenburg F, Löwen H. Flow of colloidal solids and fluids through constrictions: dynamical density functional theory versus simulation. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:244019. [PMID: 27116706 DOI: 10.1088/0953-8984/28/24/244019] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Using both dynamical density functional theory and particle-resolved Brownian dynamics simulations, we explore the flow of two-dimensional colloidal solids and fluids driven through a linear channel with a constriction. The flow is generated by a constant external force acting on all colloids. The initial configuration is equilibrated in the absence of flow and then the external force is switched on instantaneously. Upon starting the flow, we observe four different scenarios: a complete blockade, a monotonic decay to a constant particle flux (typical for a fluid), a damped oscillatory behaviour in the particle flux, and a long-lived stop-and-go behaviour in the flow (typical for a solid). The dynamical density functional theory describes all four situations but predicts infinitely long undamped oscillations in the flow which are always damped in the simulations. We attribute the mechanisms of the underlying stop-and-go flow to symmetry conditions on the flowing solid. Our predictions are verifiable in real-space experiments on magnetic colloidal monolayers which are driven through structured microchannels and can be exploited to steer the flow throughput in microfluidics.
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Affiliation(s)
- Urs Zimmermann
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
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Bleibel J, Domínguez A, Oettel M. A dynamic DFT approach to generalized diffusion equations in a system with long-ranged and hydrodynamic interactions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:244021. [PMID: 27115236 DOI: 10.1088/0953-8984/28/24/244021] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We build on an existing approximation scheme to the Smoluchowski equation in order to derive a dynamic density functional theory (DDFT) including two-body hydrodynamic interactions. A generalized diffusion equation and a wavenumber-dependent diffusion coefficient D(k) are derived by linearization in the density fluctuations. The result is applied to a colloidal monolayer at a fluid interface, having bulk-like hydrodynamic interactions and/or interacting via long-ranged capillary forces. In these cases, D(k) shows characteristic singularities as [Formula: see text]. The consequences of these singularities are studied by means of analytical perturbation theory, numerical solution of DDFT and simulations for an explicit example: the capillary collapse of a finite, disk-like distribution of particles. There is in general a good agreement between DDFT and simulations if the initial density distributions for the theoretical prediction correspond to the actual initial configurations of simulations, rather than to an average over them. Otherwise, discrepancies arise that are discussed in detail.
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Affiliation(s)
- Johannes Bleibel
- Institut für Angewandte Physik, Auf der Morgenstelle 10, Eberhard Karls Universität, 72076 Tübingen, Germany. Max-Planck-Institut für Intelligente Systeme, Heisenbergstr. 3, 70569 Stuttgart, Germany
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McNamee CE, Kappl M. Forces and physical properties of the Langmuir monolayers of TiO2 particles at air/water interfaces after collisions by a particle in water. RSC Adv 2016. [DOI: 10.1039/c6ra09499f] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022] Open
Abstract
Vary diameter (D) of TiO2 particles in monolayer and measure surface pressure–area/particle isotherms and force curves.
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Affiliation(s)
- Cathy E. McNamee
- Department of Chemistry and Materials
- Faculty of Textile Science and Technology
- Shinshu University
- Ueda
- Japan
| | - Michael Kappl
- Max Planck Institute for Polymer Research
- 55128 Mainz
- Germany
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Yatsyshin P, Savva N, Kalliadasis S. Wetting of prototypical one- and two-dimensional systems: Thermodynamics and density functional theory. J Chem Phys 2015; 142:034708. [DOI: 10.1063/1.4905605] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
Affiliation(s)
- Petr Yatsyshin
- Department of Chemical Engineering, Imperial College London, London SW7 2AZ, United Kingdom
| | - Nikos Savva
- Department of Chemical Engineering, Imperial College London, London SW7 2AZ, United Kingdom
- School of Mathematics, Cardiff University, Cardiff CF24 4AG, United Kingdom
| | - Serafim Kalliadasis
- Department of Chemical Engineering, Imperial College London, London SW7 2AZ, United Kingdom
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Soligno G, Dijkstra M, van Roij R. The equilibrium shape of fluid-fluid interfaces: Derivation and a new numerical method for Young’s and Young-Laplace equations. J Chem Phys 2014; 141:244702. [DOI: 10.1063/1.4904391] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Domínguez A. Signature of time-dependent hydrodynamic interactions on collective diffusion in colloidal monolayers. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:062314. [PMID: 25615100 DOI: 10.1103/physreve.90.062314] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/09/2014] [Indexed: 06/04/2023]
Abstract
It has been shown recently that the coefficient of collective diffusion in a colloidal monolayer is divergent due to the hydrodynamic interactions mediated by the ambient fluid in bulk. The analysis is extended to allow for time-dependent hydrodynamic interactions. Observational features specific to this time dependency are predicted. The possible experimental detection in the dynamics of the monolayer is discussed.
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Affiliation(s)
- Alvaro Domínguez
- Física Teórica, Universidad de Sevilla, Apdo. 1065, 41080 Sevilla, Spain
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