Effective surface-shear viscosity of an incompressible particle-laden fluid interface

Lishchuk, Sergey V.

doi:10.1103/physreve.89.043003

Cited by 3 publications

(6 citation statements)

References 29 publications

(42 reference statements)

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“…This approach was pioneered by Einstein, who used it to determine the effective shear viscosity of dilute suspensions [28]. Similar approach can be used to define effective surface shear viscosity of particle-laden fluid interfaces [17,29]. The expression for the rate of energy dissipation in particle-laden flows can be cast in a form of an integral over the surface of the particles A p provided the integral (1) ∂r r + σ (1) dV (18) over the volume V occupied by fluid inside A s equals zero [30,31].…”

Section: Energy Dissipationmentioning

confidence: 99%

“…Nevertheless, it is straightforward to check that the integral (18) indeed equals zero in the case if identical particles are adsorbed at the interface between two fluids provided there is no extra dissipation of energy at the interface (for example, due to adsorbed surfactants). Then the expression for the rate of energy dissipation can be written as [17,29]…”

Section: Energy Dissipationmentioning

confidence: 99%

“…(25), is a sum of the base flow contribution ψ 0 , given by Eq. (29), and the disturbance contribution ψ, given by the integral (36) with the integrand defined by Eqs (45), (46), (54) and (55).…”

Section: Velocity Fieldmentioning

confidence: 99%

“…where the integrand is evaluated at the surface of the particle, and can be calculated numerically using velocity given by equations (24), (25), (29), (36), (45), (46), (54), (55), and pressure given by equations (60), (57), (58).…”

Section: Pressure On Particle Surfacementioning

confidence: 99%

“…It follows from the assumptions of the model that in order for the results to be valid the surface concentration of particles has to be small (φ ≪ 1), and the ratio of shear viscosities of both fluids has to be large (η 1 ≫ η 2 ). Additionally, shear rate has to be small enough [29] to reduce the inertial effects,…”

Section: Pressure On Particle Surfacementioning

confidence: 99%

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Dilatational viscosity of dilute particle-laden fluid interface at different contact angles

Lishchuk

2016

Phys. Rev. E

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We consider a solid spherical particle adsorbed at a flat interface between two immiscible fluids and having arbitrary contact angle at the triple contact line. We derive analytically the flow field corresponding to dilatational surface flow in the case of a large ratio of dynamic shear viscosities of two fluids. Considering a dilute assembly of such particles we calculate numerically the dependence on the contact angle of the effective surface dilatational viscosity particle-laden fluid interface. The effective surface dilatational viscosity is proportional to the size and surface concentration of particles and monotonically increases with the increase in protrusion of particles into the fluid with larger shear viscosity.

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Section: Energy Dissipationmentioning

confidence: 99%

Section: Energy Dissipationmentioning

confidence: 99%

Section: Velocity Fieldmentioning

confidence: 99%

Section: Pressure On Particle Surfacementioning

confidence: 99%

Section: Pressure On Particle Surfacementioning

confidence: 99%

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Dilatational viscosity of dilute particle-laden fluid interface at different contact angles

Lishchuk

2016

Phys. Rev. E

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Mobility of membrane-trapped particles

Stone

Masoud

2015

J. Fluid Mech.

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Rheological and transport studies of model thin films and membranes, often inspired by biological systems, make use of translational or rotational motion or diffusion of particles trapped in the surface film. Here, we consider the translational mobility of spherical and oblate spheroidal particles protruding into the surrounding subphase liquid. Both the subphase and surface film contribute to the resistance experienced by the particle, which is calculated as a function of the degree of protrusion as well as the viscosity contrast between the surface film and the surrounding fluid. The calculations are based on a combination of a perturbation expansion involving the particle shape and the Lorentz reciprocal theorem.

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Motion of a disk embedded in a nearly inviscid Langmuir film. Part 1. Translation

Yariv,

Brandão,

Siegel

et al. 2023

J. Fluid Mech.

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The motion of a disk in a Langmuir film bounding a liquid substrate is a classical hydrodynamic problem, dating back to Saffman (J. Fluid Mech., vol. 73, 1976, p. 593) who focused upon the singular problem of translation at large Boussinesq number, ${\textit {Bq}}\gg 1$ . A semianalytic solution of the dual integral equations governing the flow at arbitrary ${\textit {Bq}}$ was devised by Hughes et al. (J. Fluid Mech., vol. 110, 1981, p. 349). When degenerated to the inviscid-film limit ${\textit {Bq}}\to 0$ , it produces the value $8$ for the dimensionless translational drag, which is $50\,\%$ larger than the classical $16/3$ -value corresponding to a free surface. While that enhancement has been attributed to surface incompressibility, the mathematical reasoning underlying the anomaly has never been fully elucidated. Here we address the inviscid limit ${\textit {Bq}}\to 0$ from the outset, revealing a singular mechanism where half of the drag is contributed by the surface pressure. We proceed beyond that limit, considering a nearly inviscid film. A naïve attempt to calculate the drag correction using the reciprocal theorem fails due to an edge singularity of the leading-order flow. We identify the formation of a boundary layer about the edge of the disk, where the flow is primarily in the azimuthal direction with surface and substrate stresses being asymptotically comparable. Utilising the reciprocal theorem in a fluid domain tailored to the asymptotic topology of the problem produces the drag correction $(8\,{\textit {Bq}}/{\rm \pi} ) [ \ln (2/{\textit {Bq}}) + \gamma _E+1]$ , $\gamma _E$ being the Euler–Mascheroni constant.

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Effective surface-shear viscosity of an incompressible particle-laden fluid interface

Cited by 3 publications

References 29 publications

Dilatational viscosity of dilute particle-laden fluid interface at different contact angles

Dilatational viscosity of dilute particle-laden fluid interface at different contact angles

Mobility of membrane-trapped particles

Motion of a disk embedded in a nearly inviscid Langmuir film. Part 1. Translation

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