Drag and diffusion coefficients of a spherical particle attached to a fluid–fluid interface

Dörr, Aaron; Hardt, Steffen; Masoud, Hassan; Stone, Howard A.

doi:10.1017/jfm.2016.41

Cited by 67 publications

(72 citation statements)

References 34 publications

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“…3b) and this restriction again does not lead to an anomalously large drag. The Stokes continuum drag of a nonrotating smooth particle moving along a gas/liquid interface [3][4][5][6] is shown in Fig. 3b as ξ c and is larger than the drag computed from the MD simulations.…”

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confidence: 76%

“…Alternatively, if an external force is applied to the particle to yield a steady velocity, ξ is calculated directly as their ratio. Using the latter method, continuum calculations of the surface drag exerted on a spherical, smooth, nonrotating particle in the limit of zero inertia and a flat, zero-thickness interface separating two immiscible liquids have been undertaken [3][4][5][6]. The continuum drag increases with immersion into the more viscous phase, and approaches the Stokes bulk drag coefficient 6πµR, where µ is the fluid viscosity far from the surface.…”

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confidence: 99%

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Diffusivity and hydrodynamic drag of nanoparticles at a vapor-liquid interface

Koplik

Maldarelli

2017

Phys. Rev. Fluids

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Measurements of the surface diffusivity of colloidal spheres translating along a vapor/liquid interface show an unexpected decrease in diffusivity, or increase in surface drag (from the Stokes-Einstein relation) when the particles situate further into the vapor phase. However, direct measurements of the surface drag from the colloid velocity due to an external force find the expected decrease with deeper immersion into the vapor. The paradoxical drag increase observed in diffusion experiments has been attributed to the attachment of the fluid interface to heterogeneities on the colloid surface, which causes the interface, in response to thermal fluctuations, to either jump or remain pinned, creating added drag. We have performed molecular dynamics simulations of the diffusivity and force experiments for a nanoparticle with a rough surface at a vapor/liquid interface to examine the effect of contact line fluctuations. The drag calculated from both experiments agree and decrease as the particle positions further into the vapor. The surface drag is smaller than the bulk liquid drag due to the partial submersion into the liquid, and the finite thickness of the interfacial zone relative to the nanoparticle size. Contact line fluctuations do not give rise to an anomalous increase in drag.When a colloid particle breaches the interfacial zone between two adjoining immiscible fluid phases the interfacial energy of the particle changes, because the area of the fluid interface decreases and the contact areas of the particle with the bounding fluid phases are altered. For a particle which only partially wets both adjoining fluids, the change in interfacial energy is at a minimum when the colloid partially straddles both adjoining phases. For example, for a spherical colloid of radius R at a vapor/liquid interface of interfacial tension γ (Fig. 1a), the minimum free energy relative to the vapor phase is [1] ∆F = −πγR 2 (1 + cos θ) 2 where the contact angle θ is measured through the liquid. For particles of large enough size, ∆F can overwhelm the typical thermal energy k B T and the particle becomes trapped, as thermal fluctuations cannot dislodge the particle from the interface. Monolayers of strongly adsorbed colloids at the fluid interfaces of foams and emulsions provide steric barriers to coalescence of the dispersed phase, and find applications as foam and emulsion stabilizers (e.g. Pickering emulsions). Particle stabilized foams and emulsions are also used for the fabrication of colloid-based solid foams, gels, and bijels, and crystalline monolayers find applications as superhydrophobic or antireflection coatings, and templates for micro and nanostructured materials [2]. Central to these applications is the surface organization of the colloids, which is a balance between interparticle attractive and repulsive forces, external forces applied parallel to the interface, and the viscous resistance or surface drag due to the hydrodynamic motion of the colloids along the fluid surface. As we explain, the surface drag is not w...

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confidence: 76%

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confidence: 99%

Diffusivity and hydrodynamic drag of nanoparticles at a vapor-liquid interface

Koplik

Maldarelli

2017

Phys. Rev. Fluids

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“…On other hand, small particles dynamically enter and detach from the aqueous–aqueous interface, which is driven by Brownian motion, resulting in reversible and unstable interfacial adsorption. Particularly, when the kinetic energy of Brownian motion is relative higher than the thermal energy to trap the surfactant at the aqueous–aqueous interface, surfactants cannot be irreversibly trapped at the interface, and the neighboring droplets will eventually coalesce . For instance, latex particles with a radius no less than 0.1 µm can be irreversibly trapped at the interfaces of the polyethylene oxide (PEO)/dextran ATPS with interfacial tensions down to 10 −6 N m −1 , as shown by the confocal laser scanning microscope (CLSM) images in a,b .…”

Section: All‐aqueous Interface Templated Biomaterials: Assembly Of Armentioning

confidence: 99%

Cell‐Inspired All‐Aqueous Microfluidics: From Intracellular Liquid–Liquid Phase Separation toward Advanced Biomaterials

et al. 2020

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Living cells have evolved over billions of years to develop structural and functional complexity with numerous intracellular compartments that are formed due to liquid–liquid phase separation (LLPS). Discovery of the amazing and vital roles of cells in life has sparked tremendous efforts to investigate and replicate the intracellular LLPS. Among them, all‐aqueous emulsions are a minimalistic liquid model that recapitulates the structural and functional features of membraneless organelles and protocells. Here, an emerging all‐aqueous microfluidic technology derived from micrometer‐scaled manipulation of LLPS is presented; the technology enables the state‐of‐art design of advanced biomaterials with exquisite structural proficiency and diversified biological functions. Moreover, a variety of emerging biomedical applications, including encapsulation and delivery of bioactive gradients, fabrication of artificial membraneless organelles, as well as printing and assembly of predesigned cell patterns and living tissues, are inspired by their cellular counterparts. Finally, the challenges and perspectives for further advancing the cell‐inspired all‐aqueous microfluidics toward a more powerful and versatile platform are discussed, particularly regarding new opportunities in multidisciplinary fundamental research and biomedical applications.

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“…Past studies using either boundary integral 15,16 , finite element 17,18 or integral transform methods 12,19 have focused on the translation, and have assumed that the colloid does not rotate due to the presence of surface roughness or chemical heterogeneities that pin the three-phase contact line (contact angle hysteresis). However recently, evaluating the drag exerted on non-smooth colloids 14 with heterogeneous surfaces as they diffuse along an interface while specifically examining the role of contact line pinning and de-pinning have been important given the extensive interest in particle-laden interfaces.…”

Section: Introductionmentioning

confidence: 99%

The Translational and Rotational Dynamics of a Colloid Moving Along the Air-Liquid Interface of a Thin Film

Das

Koplik

Farinato

et al. 2018

Sci Rep

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This study examines the translation and rotation of a spherical colloid straddling the (upper) air/liquid interface of a thin, planar, liquid film bounded from below by either a solid or a gas/liquid interface. The goal is to obtain numerical solutions for the hydrodynamic flow in order to understand the influence of the film thickness and the lower interface boundary condition. When the colloid translates on a film above a solid, the viscous resistance increases significantly as the film thickness decreases due to the fluid-solid interaction, while on a free lamella, the drag decreases due to the proximity to the free (gas/liquid) surface. When the colloid rotates, the contact line of the interface moves relative to the colloid surface. If no-slip is assumed, the stress becomes infinite and prevents the rotation. Here finite slip is used to resolve the singularity, and for small values of the slip coefficient, the rotational viscous resistance is dominated by the contact line stress and is surprisingly less dependent on the film thickness and the lower interface boundary condition. For a colloid rotating on a semi-infinite liquid layer, the rotational resistance is largest when the colloid just breaches the interface from the liquid side.

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Drag and diffusion coefficients of a spherical particle attached to a fluid–fluid interface

Cited by 67 publications

References 34 publications

Diffusivity and hydrodynamic drag of nanoparticles at a vapor-liquid interface

Diffusivity and hydrodynamic drag of nanoparticles at a vapor-liquid interface

Cell‐Inspired All‐Aqueous Microfluidics: From Intracellular Liquid–Liquid Phase Separation toward Advanced Biomaterials

The Translational and Rotational Dynamics of a Colloid Moving Along the Air-Liquid Interface of a Thin Film

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