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Guzmán E, Ortega F, Rubio RG. Forces Controlling the Assembly of Particles at Fluid Interfaces. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2022; 38:13313-13321. [PMID: 36278952 PMCID: PMC9648339 DOI: 10.1021/acs.langmuir.2c02038] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/29/2022] [Indexed: 06/04/2023]
Abstract
The interaction of particles with fluid interfaces is ubiquitous in synthetic and natural work, involving two types of interactions: particle-interface interactions (trapping energy) and interparticle interactions. Therefore, it is urgent to gain a deep understanding of the main forces controlling the trapping of particles at fluid interfaces, and their assembly to generate a broad range of structures characterized by different degrees of order. This Perspective tries to provide an overview of the main contributions to the energetic landscape controlling the assembly of particles at fluid interfaces, which is essential for exploiting this type of interfacial systems as platforms for the fabrication of interface-based soft materials with technological interest.
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Affiliation(s)
- Eduardo Guzmán
- Departamento
de Química Física, Facultad de Ciencias Químicas, Universidad Complutense de Madrid, Ciudad Universitaria s/n, 28040Madrid, Spain
- Instituto
Pluridisciplinar, Universidad Complutense
de Madrid, Paseo Juan XXIII 1, 28040Madrid, Spain
| | - Francisco Ortega
- Departamento
de Química Física, Facultad de Ciencias Químicas, Universidad Complutense de Madrid, Ciudad Universitaria s/n, 28040Madrid, Spain
- Instituto
Pluridisciplinar, Universidad Complutense
de Madrid, Paseo Juan XXIII 1, 28040Madrid, Spain
| | - Ramón G. Rubio
- Departamento
de Química Física, Facultad de Ciencias Químicas, Universidad Complutense de Madrid, Ciudad Universitaria s/n, 28040Madrid, Spain
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2
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Zhang X, Zhang J, Liu H. How the presence of particles at the interface influences the droplet deformation in a simple shear flow? POWDER TECHNOL 2022. [DOI: 10.1016/j.powtec.2022.117920] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
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3
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Zhang X, Zhang J, Liu H, Jia P. Rayleigh-Plateau Instability of a Particle-Laden Liquid Column: A Lattice Boltzmann Study. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2022; 38:3453-3468. [PMID: 35274953 DOI: 10.1021/acs.langmuir.1c03262] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
Colloidal particles known to be capable of stabilizing fluid-fluid interfaces have been widely applied in emulsion preparation, but their precise role and underlying influencing mechanism remain poorly understood. In this study, a perturbed liquid column with particles evenly distributed on its surface is investigated using a three-dimensional lattice Boltzmann method, which is built upon the color-gradient two-phase flow model but with a new capillary force model and a momentum exchange method for particle dynamics. The developed method is first validated by simulating the wetting behavior of a particle on a fluid interface and the classic Rayleigh-Plateau instability and is then used to explore the effects of particle concentration and contact angle on the capillary instability of the particle-laden liquid column. It is found that increasing the particle concentration can enhance the stability of the liquid column and thus delay the breakup, and the liquid column is most stable under slightly hydrophobic conditions, which corresponds to the lowest initial liquid-gas interfacial free energy. Due to different pressure gradients inside and outside the liquid column and the capillary force being directed away from the neck, hydrophobic particles tend to assemble in a less compact manner near the neck of the deformed liquid column, while hydrophilic particles prefer to gather far away from the neck. For hydrophobic particles, in addition to the influence of the initial liquid-gas interfacial free energy, the self-assembly of particles in a direction opposite to the liquid flow also contributes to opposing the rupture of the liquid column.
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Affiliation(s)
- Xitong Zhang
- School of Energy and Power Engineering, Xi'an Jiaotong University, 28 West Xianning Road, Xi'an 710049, China
| | - Jiangang Zhang
- School of Energy and Power Engineering, Xi'an Jiaotong University, 28 West Xianning Road, Xi'an 710049, China
| | - Haihu Liu
- School of Energy and Power Engineering, Xi'an Jiaotong University, 28 West Xianning Road, Xi'an 710049, China
| | - Pan Jia
- School of Science, Harbin Institute of Technology, Shenzhen University Town, Xili, Nanshan District, Shenzhen 518055, China
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4
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Barakat JM, Squires TM. Capillary force on an 'inert' colloid: a physical analogy to dielectrophoresis. SOFT MATTER 2021; 17:3417-3442. [PMID: 33645603 PMCID: PMC8323820 DOI: 10.1039/d0sm02143a] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/02/2020] [Accepted: 02/09/2021] [Indexed: 06/08/2023]
Abstract
"Inert" colloids are μm-scale particles that create no distortion when trapped at a planar fluid-fluid interface. When placed in a curved interface, however, such colloids can create interfacial distortions of quadrupolar symmetry - so-called "induced capillary quadrupoles." The present work explores the analogy between capillary quadrupoles and electric dipoles, and the forces exerted on them by a symmetry-breaking gradient. In doing so, we weigh in on an outstanding debate as to whether a curvature gradient can induce a capillary force on an inert colloid. We argue that this force exists, for the opposite would imply that all dielectrophoretic forces vanish in two dimensions (2D). We justify our claim by solving 2D Laplace problems of electrostatics and capillary statics involving a single particle placed within a large circular shell with an imposed gradient. We show that the static boundary condition on the outer shell must be considered when applying the principle of virtual work to compute the force on the particle, as verified by a direct calculation of this force through integration of the particle stresses. Our investigation highlights some of the subtleties that emerge in virtual work calculations of capillary statics and electrostatics, thereby clarifying and extending previous results in the field. The broader implication of our results is that inert particles - including particles with planar, pinned contact lines and equilibrium contact angles - interact through interparticle capillary forces that scale quadratically with the deviatoric curvature of the host interface, contrary to recent claims made in the literature.
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Affiliation(s)
- Joseph M Barakat
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, USA.
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5
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Cenev Z, Würger A, Zhou Q. Motion and trapping of micro- and millimeter-sized particles on the air-paramagnetic-liquid interface. Phys Rev E 2021; 103:L010601. [PMID: 33601540 DOI: 10.1103/physreve.103.l010601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2020] [Accepted: 11/30/2020] [Indexed: 11/07/2022]
Abstract
Understanding the motion of particles on an air-liquid interface can impact a wide range of scientific fields and applications. Diamagnetic particles floating on an air-paramagnetic-liquid interface are previously known to have a repulsive motion from a magnet. Here, we show a motion mechanism where the diamagnetic particles floating on the air-paramagnetic-liquid interface are attracted and eventually trapped at an off-center distance from the magnet. The behavior of magnetic particles has been also studied and the motion mechanisms are theorized in a unified framework, revealing that the motion of particles on an air-paramagnetic-liquid interface is governed not only by magnetic energy, but as an interplay of the curvature of the interface deformation created by the nonuniform magnetic field, the gravitational potential, and the magnetic energy from the particle and the liquid. The attractive motion mechanism has been applied in directed self-assembly and robotic particle guiding.
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Affiliation(s)
- Zoran Cenev
- Department of Electrical Engineering and Automation, Aalto University, 02150 Espoo, Finland.,Department of Applied Physics, Aalto University, 02150 Espoo, Finland
| | - Alois Würger
- Laboratoire Ondes et Matière d'Aquitaine, Université de Bordeaux and CNRS, 33405 Talence, France
| | - Quan Zhou
- Department of Electrical Engineering and Automation, Aalto University, 02150 Espoo, Finland
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6
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Richard E, Dubois T, Allion-Maurer A, Jha PK, Faille C. Hydrophobicity of abiotic surfaces governs droplets deposition and evaporation patterns. Food Microbiol 2020; 91:103538. [PMID: 32539949 DOI: 10.1016/j.fm.2020.103538] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2020] [Revised: 04/16/2020] [Accepted: 04/25/2020] [Indexed: 11/18/2022]
Abstract
Surface contamination with droplets containing bacteria is of concern in the food industry and other environments where hygiene control is essential. Deposition patterns after the drying of contaminated droplets is affected by numerous parameters. The present study evaluated the rate of evaporation and the shape of deposition patterns after the drying of water droplets on a panel of materials with different surface properties (topography, hydrophobicity). The influence of the particle properties (in this study 1 μm-microspheres and two bacterial spores) was also investigated. Polystyrene microspheres were hydrophobic, while Bacillus spores were hydrophilic or hydrophobic, and surrounded by different surface features. In contrast to material topography, hydrophobicity was shown to deeply affect droplet evaporation, with the formation of small, thick deposits with microspheres or hydrophilic spores. Among the particle properties, the spore morphology (size and round/ovoid shape) did not clearly affect the deposition pattern. Conversely, hydrophobic spores aggregated to form clusters, which quickly settled on the materials and either failed to migrate, or only migrated to a slight extent on the surface, resulting in a steady distribution of spores or spore clusters over the whole contaminated area. Adherent bacteria or spores are known to be highly resistant to many stressful environmental conditions. In view of all the quite different patterns obtained following drying of spore-containing droplets, it seems likely that some of these would entail enhanced resistance to hygienic processes.
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Affiliation(s)
- Elodie Richard
- Univ. Lille, CNRS, INSERM, CHU Lille, Institut Pasteur de Lille, US 41 - UMS 2014 - PLBS, F-59000, Lille, France
| | - Thomas Dubois
- Univ. Lille, CNRS, INRAE, ENSCL, UMET, F-59650, Villeneuve d'Ascq, France
| | - Audrey Allion-Maurer
- Aperam Isbergues Research Center - Solutions Dept., BP 15, F-62330, Isbergues, France
| | - Piyush Kumar Jha
- Univ. Lille, CNRS, INRAE, ENSCL, UMET, F-59650, Villeneuve d'Ascq, France
| | - Christine Faille
- Univ. Lille, CNRS, INRAE, ENSCL, UMET, F-59650, Villeneuve d'Ascq, France.
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7
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Yoshida S, Trifkovic M. Unraveling the Effect of 3D Particle Localization on Coarsening Dynamics and Rheological Properties in Cocontinuous Polymer Blend Nanocomposites. Macromolecules 2019. [DOI: 10.1021/acs.macromol.9b01437] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Affiliation(s)
- Shohei Yoshida
- Department of Chemical and Petroleum Engineering, University of Calgary, 2500 University Dr. NW, Calgary, AB T2N 1N4, Canada
- Films & Film Products Research Laboratories, Toray Industries, Inc., 1-1, Sonoyama 1-chome, Otsu, Shiga 520-8558, Japan
| | - Milana Trifkovic
- Department of Chemical and Petroleum Engineering, University of Calgary, 2500 University Dr. NW, Calgary, AB T2N 1N4, Canada
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8
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Liu J, Li S. Capillarity-driven migration of small objects: A critical review. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2019; 42:1. [PMID: 30612222 DOI: 10.1140/epje/i2019-11759-1] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/28/2018] [Accepted: 11/30/2018] [Indexed: 06/09/2023]
Abstract
The phenomena on the capillarity-driven migration of small objects are full of interest for both scientific and engineering communities, and a critical review is thereby presented. The small objects mentioned here deal with the non-deformable objects, such as particles, rods, disks and metal sheets; and besides them, the soft objects are considered, such as droplets and bubbles. Two types of interfaces are analyzed, i.e., the solid-fluid interface and the fluid-fluid interface. Due to the easily deformable properties of the soft objects and distorted interfacial shapes induced by small objects, a more convenient way to obtain the driving force is through the potential energy of the system. The asymmetric factors causing the object migration include the asymmetric configuration of the interface, and the difference between the interfacial tensions. Finally, a simple outlook on the potential applications of small object migration is made. These behaviors may cast new light on the design of microfluidics and new devices, environment cleaning, oil and gas displacement and mineral industries.
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Affiliation(s)
- Jianlin Liu
- Department of Engineering Mechanics, College of Pipeline and Civil Engineering, China University of Petroleum (East China), 266580, Qingdao, China.
| | - Shanpeng Li
- Department of Engineering Mechanics, College of Pipeline and Civil Engineering, China University of Petroleum (East China), 266580, Qingdao, China
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9
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Kim PY, Dinsmore AD, Hoagland DA, Russell TP. Wetting, meniscus structure, and capillary interactions of microspheres bound to a cylindrical liquid interface. SOFT MATTER 2018; 14:2131-2141. [PMID: 29488991 DOI: 10.1039/c7sm02454a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Wetting, meniscus structure, and capillary interactions for polystyrene microspheres deposited on constant curvature cylindrical liquid interfaces, constructed from nonvolatile ionic or oligomeric liquids, were studied by optical interferometry and optical microscopy. The liquid interface curvature resulted from the preferential wetting of finite width lines patterned onto planar silicon substrates. Key variables included sphere diameter, nominal (or average) contact angle, and deviatoric interfacial curvature. Menisci adopted the quadrupolar symmetry anticipated by theory, with interfacial deformation closely following predicted dependences on sphere diameter and nominal contact angle. Unexpectedly, the contact angle was not constant locally around the contact line, the nominal contact angle varied among seemingly identical spheres, and the maximum interface deviation did not follow the predicted dependence on deviatoric interfacial curvature. Instead, this deviation was up to an order-of-magnitude larger than predicted. Trajectories of neighboring microspheres visually manifested quadrupole-quadrupole interactions, eventually producing square sphere packings that foreshadow interfacial assembly as a potential route to hierarchical 2D particle structures.
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Affiliation(s)
- Paul Y Kim
- Department of Polymer Science and Engineering, University of Massachusetts Amherst, Amherst, Massachusetts 01003, USA.
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10
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Mampallil D, Eral HB. A review on suppression and utilization of the coffee-ring effect. Adv Colloid Interface Sci 2018; 252:38-54. [PMID: 29310771 DOI: 10.1016/j.cis.2017.12.008] [Citation(s) in RCA: 250] [Impact Index Per Article: 41.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2017] [Revised: 11/29/2017] [Accepted: 12/14/2017] [Indexed: 01/22/2023]
Abstract
Evaporation of sessile droplets containing non-volatile solutes dispersed in a volatile solvent leaves behind ring-like solid stains. As the volatile species evaporates, pinning of the contact line gives rise to capillary flows that transport non-volatile solutes to the contact line. This phenomenon, called the coffee-ring effect, compromises the overall performance of industrially relevant manufacturing processes involving evaporation such as printing, biochemical analysis, manufacturing of nano-structured materials through colloidal and macromolecular patterning. Various approaches have been developed to suppress this phenomenon, which is otherwise difficult to avoid. The coffee-ring effect has also been leveraged to prepare new materials through convection induced assembly. This review underlines not only the strategies developed to suppress the coffee-ring effect but also sheds light on approaches to arrive at novel processes and materials. Working principles and applicability of these strategies are discussed together with a critical comparison.
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Affiliation(s)
- Dileep Mampallil
- Indian Institute of Science Education & Research Tirupati, Mangalam P. O., Tirupati-517507, India.
| | - Huseyin Burak Eral
- Process & Energy Department, 3ME Faculty, TU Delft, Leeghwaterstraat 39, 2628CB Delft, The Netherlands.
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11
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Thijssen JHJ, Vermant J. Interfacial rheology of model particles at liquid interfaces and its relation to (bicontinuous) Pickering emulsions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:023002. [PMID: 29165321 DOI: 10.1088/1361-648x/aa9c74] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Interface-dominated materials are commonly encountered in both science and technology, and typical examples include foams and emulsions. Conventionally stabilised by surfactants, emulsions can also be stabilised by micron-sized particles. These so-called Pickering-Ramsden (PR) emulsions have received substantial interest, as they are model arrested systems, rather ubiquitous in industry and promising templates for advanced materials. The mechanical properties of the particle-laden liquid-liquid interface, probed via interfacial rheology, have been shown to play an important role in the formation and stability of PR emulsions. However, the morphological processes which control the formation of emulsions and foams in mixing devices, such as deformation, break-up, and coalescence, are complex and diverse, making it difficult to identify the precise role of the interfacial rheological properties. Interestingly, the role of interfacial rheology in the stability of bicontinuous PR emulsions (bijels) has been virtually unexplored, even though the phase separation process which leads to the formation of these systems is relatively simple and the interfacial deformation processes can be better conceptualised. Hence, the aims of this topical review are twofold. First, we review the existing literature on the interfacial rheology of particle-laden liquid interfaces in rheometrical flows, focussing mainly on model latex suspensions consisting of polystyrene particles carrying sulfate groups, which have been most extensively studied to date. The goal of this part of the review is to identify the generic features of the rheology of such systems. Secondly, we will discuss the relevance of these results to the formation and stability of PR emulsions and bijels.
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Affiliation(s)
- J H J Thijssen
- SUPA School of Physics and Astronomy, The University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kindom
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12
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Şenbil N, Dinsmore AD. Deformation of the contact line around spherical particles bound at anisotropic fluid interfaces. SOFT MATTER 2017; 13:8234-8239. [PMID: 29067385 DOI: 10.1039/c7sm01548h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
When a particle adsorbs at a liquid interface, the 3-phase contact line geometry depends on the shape of the particle and of the liquid interface. The shape of the contact line is the key to controlling capillary forces among particles, and is therefore a useful means to direct assembly of interfacial particles. We measured the shape of the contact line around millimeter-sized PDMS-coated glass spheres at water/air interfaces with anisotropic shapes. We studied the advancing and receding conditions separately. We focused on interfaces with a cylindrical shape, where the predominant deformation of the meniscus and the contact line both have quadrupolar cos(2ϕ) symmetry. We related the measured magnitude of the quadrupolar deformation to the applied vertical force on the sphere and the interface's deviatoric curvature, D0. For modest curvature (D0 < 0.1 × sphere radius), our results agree with the theoretical prediction for free particles. At higher curvature, the measurements exceed the theory. The theory appears to apply even when there is contact-angle hysteresis, as long as the measured contact angle is used rather than the equilibrium (Young-Dupré) angle. The magnitude of the quadrupolar deformation depends on the applied force. Together, these results show the range of validity of the theory.
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Affiliation(s)
- Nesrin Şenbil
- Department of Physics, Univ. of Massachusetts, Amherst, MA 01003, USA.
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13
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Dasgupta S, Auth T, Gompper G. Nano- and microparticles at fluid and biological interfaces. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:373003. [PMID: 28608781 PMCID: PMC7104866 DOI: 10.1088/1361-648x/aa7933] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/30/2016] [Revised: 04/12/2017] [Accepted: 06/13/2017] [Indexed: 05/05/2023]
Abstract
Systems with interfaces are abundant in both technological applications and biology. While a fluid interface separates two fluids, membranes separate the inside of vesicles from the outside, the interior of biological cells from the environment, and compartmentalize cells into organelles. The physical properties of interfaces are characterized by interface tension, those of membranes are characterized by bending and stretching elasticity. Amphiphilic molecules like surfactants that are added to a system with two immiscible fluids decrease the interface tension and induce a bending rigidity. Lipid bilayer membranes of vesicles can be stretched or compressed by osmotic pressure; in biological cells, also the presence of a cytoskeleton can induce membrane tension. If the thickness of the interface or the membrane is small compared with its lateral extension, both can be described using two-dimensional mathematical surfaces embedded in three-dimensional space. We review recent work on the interaction of particles with interfaces and membranes. This can be micrometer-sized particles at interfaces that stabilise emulsions or form colloidosomes, as well as typically nanometer-sized particles at membranes, such as viruses, parasites, and engineered drug delivery systems. In both cases, we first discuss the interaction of single particles with interfaces and membranes, e.g. particles in external fields, non-spherical particles, and particles at curved interfaces, followed by interface-mediated interaction between two particles, many-particle interactions, interface and membrane curvature-induced phenomena, and applications.
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Affiliation(s)
- S Dasgupta
- Mechanobiology Institute, National University of Singapore, Singapore 117411, Singapore
- Institut Curie, CNRS, UMR 168, 75005 Paris, France
- Present address: Department of Physics, University of Toronto, Toronto, Ontario M5S1A7, Canada
| | - T Auth
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, 52425 Jülich, Germany
| | - G Gompper
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems and Institute for Advanced Simulation, Forschungszentrum Jülich, 52425 Jülich, Germany
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14
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Würger A. Comment on "Curvature capillary migration of microspheres" by N. Sharifi-Mood, I. B. Liu, K. J. Stebe, Soft Matter, 2015, 11, 6768. SOFT MATTER 2016; 12:331-336. [PMID: 26415717 DOI: 10.1039/c5sm01948f] [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
In a recent paper, Sharifi-Mood et al. studied colloidal particles trapped at a liquid interface with opposite principal curvatures c1 = -c2. In the theory part, they claim that the trapping energy vanishes at second order in Δc = c1 - c2, which would invalidate our previous result [Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2006, 74, 041402]. Here we show that this claim arises from an improper treatment of the outer boundary condition on the deformation field. For both pinned and moving contact lines, we find that the outer boundary is irrelevant, which confirms our previous work. More generally, we show that the trapping energy is determined by the deformation close to the particle and does not depend on the far-field.
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Affiliation(s)
- Alois Würger
- Laboratoire Ondes et Matière d'Aquitaine, Université de Bordeaux & CNRS, 33405 Talence, France
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15
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Sharifi-Mood N, Liu IB, Stebe KJ. Curvature capillary migration of microspheres. SOFT MATTER 2015; 11:6768-79. [PMID: 26154075 DOI: 10.1039/c5sm00310e] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/21/2023]
Abstract
We address the question: how does capillarity propel microspheres along curvature gradients? For a particle on a fluid interface, there are two conditions that can apply at the three phase contact line: either the contact line adopts an equilibrium contact angle, or it can be pinned by kinetic trapping, e.g. at chemical heterogeneities, asperities, or other pinning sites on the particle surface. We formulate the curvature capillary energy for both scenarios for particles smaller than the capillary length and far from any pinning boundaries. The scale and range of the distortion made by the particle are set by the particle radius; we use singular perturbation methods to find the distortions and to rigorously evaluate the associated capillary energies. For particles with equilibrium contact angles, contrary to the literature, we find that the capillary energy is negligible, with the first contribution bounded to fourth order in the product of the particle radius and the deviatoric curvature of the host interface. For pinned contact lines, we find curvature capillary energies that are finite, with a functional form investigated previously by us for disks and microcylinders on curved interfaces. In experiments, we show microspheres migrate along deterministic trajectories toward regions of maximum deviatoric curvature with curvature capillary energies ranging from 6 × 10(3)-5 × 10(4)kBT. These data agree with the curvature capillary energy for the case of pinned contact lines. The underlying physics of this migration is a coupling of the interface deviatoric curvature with the quadrupolar mode of nanometric disturbances in the interface owing to the particle's contact line undulations. This work is an example of the major implications of nanometric roughness and contact line pinning for colloidal dynamics.
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Affiliation(s)
- Nima Sharifi-Mood
- Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA.
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16
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McEnnis K, Dinsmore AD, Russell TP. Solid particles adsorbed on capillary-bridge-shaped fluid polystyrene surfaces. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2015; 31:5299-5305. [PMID: 25938879 DOI: 10.1021/acs.langmuir.5b00372] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Particles adsorbed on microscopic polystyrene (PS) capillary bridge surfaces were observed to investigate their motion under capillary forces arising from a nonuniform shape. Capillary bridges were created by placing thin PS films, heated above the glass transition temperature (Tg), between two electrodes with an air gap between the surface of the PS and the upper electrode. Silica particles, 100 nm in diameter, were placed on the surface of the PS capillary bridges, and the sample was heated above the Tg of PS to enable particle motion. Samples were cooled to below Tg, and the locations of the particles were observed using scanning electron microscopy. The particles did not preferentially locate around the center of the capillary bridge, as predicted by others, but instead segregated to the edges. These results indicate that the forces driving particles to the three-phase contact line (air/PS/electrode surface) are greater than those locating particles around the center.
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Affiliation(s)
- Kathleen McEnnis
- †Polymer Science and Engineering Department, and ‡Physics Department, University of Massachusetts Amherst, Massachusetts 01003, United States
| | - Anthony D Dinsmore
- †Polymer Science and Engineering Department, and ‡Physics Department, University of Massachusetts Amherst, Massachusetts 01003, United States
| | - Thomas P Russell
- †Polymer Science and Engineering Department, and ‡Physics Department, University of Massachusetts Amherst, Massachusetts 01003, United States
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17
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Yao L, Sharifi-Mood N, Liu IB, Stebe KJ. Capillary migration of microdisks on curved interfaces. J Colloid Interface Sci 2014; 449:436-42. [PMID: 25618486 DOI: 10.1016/j.jcis.2014.12.070] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/13/2014] [Revised: 12/18/2014] [Accepted: 12/20/2014] [Indexed: 10/24/2022]
Abstract
The capillary energy landscape for particles on curved fluid interfaces is strongly influenced by the particle wetting conditions. Contact line pinning has now been widely reported for colloidal particles, but its implications in capillary interactions have not been addressed. Here, we present experiment and analysis for disks with pinned contact lines on curved fluid interfaces. In experiment, we study microdisk migration on a host interface with zero mean curvature; the microdisks have contact lines pinned at their sharp edges and are sufficiently small that gravitational effects are negligible. The disks migrate away from planar regions toward regions of steep curvature with capillary energies inferred from the dissipation along particle trajectories which are linear in the deviatoric curvature. We derive the curvature capillary energy for an interface with arbitrary curvature, and discuss each contribution to the expression. By adsorbing to a curved interface, a particle eliminates a patch of fluid interface and perturbs the surrounding interface shape. Analysis predicts that perfectly smooth, circular disks do not migrate, and that nanometric deviations from a planar circular, contact line, like those around a weakly roughened planar disk, will drive migration with linear dependence on deviatoric curvature, in agreement with experiment.
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Affiliation(s)
- Lu Yao
- Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, PA 19104, United States
| | - Nima Sharifi-Mood
- Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, PA 19104, United States
| | - Iris B Liu
- Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, PA 19104, United States
| | - Kathleen J Stebe
- Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, PA 19104, United States.
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18
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Luu XC, Striolo A. Ellipsoidal Janus Nanoparticles Assembled at Spherical Oil/Water Interfaces. J Phys Chem B 2014; 118:13737-43. [DOI: 10.1021/jp5085422] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
Affiliation(s)
- Xuan-Cuong Luu
- School
of Chemical, Biological, and Materials Engineering, University of Oklahoma, Norman, Oklahoma 73019, United States
| | - Alberto Striolo
- Department
of Chemical Engineering, University College London, Torrington Place, London WC1E 7JE, United Kingdom
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19
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Galatola P, Fournier JB. Capillary force acting on a colloidal particle floating on a deformed interface. SOFT MATTER 2014; 10:2197-212. [PMID: 24652200 DOI: 10.1039/c3sm52622d] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/21/2023]
Abstract
We analytically determine the lateral capillary force acting on a spherical colloid trapped at an interface of arbitrary shape. Our calculations, which are valid for colloids that are small with respect to the capillary length, take into account surface tension, pressure and gravity. We relate the force acting on the colloid to the shape of the liquid interface prior to colloid deposition. Our approach is a generalization of a previous study of ours [Ch. Blanc et al., Phys. Rev. Lett., 2013, 111, 058302] to the case in which gravity is present. Our findings are in agreement with the so-called Nicolson superposition approximation [D. Y. C. Chan, J. D. J. Henry and L. R. White, J. Colloid Interface Sci., 1981, 79, 410] and with the curvature-dependent capillary force predicted by Würger [A. Würger, Phys. Rev. E, 2006, 74, 041402], and extend these results by including higher-order terms in the ratio between the size of the colloid and the capillary length. We thoroughly validate our theoretical expressions by means of an exact nonlinear numerical calculation.
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Affiliation(s)
- Paolo Galatola
- Université Paris Diderot, Sorbonne Paris Cité, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS, F-75205 Paris, France
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