Pressure-dependent surface viscosity and its surprising consequences in interfacial lubrication flows

Manikantan, Harishankar; Squires, Todd M.

doi:10.1103/physrevfluids.2.023301

Cited by 18 publications

(40 citation statements)

References 49 publications

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“…The effect of Π -dependent rheology is, therefore, more prominent as the fluid film between surface layers becomes thinner. Within this thin layer, a Π -dependent lubrication analysis [29] is possible, which, as we show in §3c, retrieves the same limiting behaviour as equation (3.9). The complementary case of a disc approaching (or departing) a wall along the y-direction is amenable to a simple symmetry argument.…”

Section: Cylinder Next To a Plane Wall (A) Translationsupporting

confidence: 53%

“…We have previously established the surprising consequences of Π -dependent viscosity in small fluid gaps [29], for any form of η s (Π ) and arbitrary velocities. The current work, on the other hand, focuses on 'small' velocities in a perturbative sense, without restrictions on the thickness of the fluid gap.…”

Section: Resultsmentioning

confidence: 97%

“…Let h(x) be the profile of the thin fluid layer between a disc and a wall ( figure 4a) such that the characteristic thickness of this gap, h 0 , is much smaller that the size of the disc (h 0 a). With the same assumptions as before (incompressible 2D flow; high Bo), the momentum equation equation (2.2) can be shown to simplify in thin gaps to [29]:…”

Section: (C) the Lubrication Limitmentioning

confidence: 99%

“…The 2D journal bearing is a well-studied limit of this geometry when the fluid is Newtonian and the characteristic thickness of the fluid gap is small. Although our analysis is not restricted to thin fluid gaps, we shall again use results from lubrication theory [6,29] to compare our solutions in the appropriate limits. Notably, translation and rotation are now coupled, unlike in the case of a plane wall.…”

Section: Cylinder Within a Cylinder (A) The Two-dimensional Journal Bmentioning

confidence: 99%

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Irreversible particle motion in surfactant-laden interfaces due to pressure-dependent surface viscosity

Manikantan¹,

Squires²

2017

Proc. R. Soc. A.

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The surface shear viscosity of an insoluble surfactant monolayer often depends strongly on its surface pressure. Here, we show that a particle moving within a bounded monolayer breaks the kinematic reversibility of low-Reynolds-number flows. The Lorentz reciprocal theorem allows such irreversibilities to be computed without solving the full nonlinear equations, giving the leading-order contribution of surface pressure-dependent surface viscosity. In particular, we show that a disc translating or rotating near an interfacial boundary experiences a force in the direction perpendicular to that boundary. In unbounded monolayers, coupled modes of motion can also lead to non-intuitive trajectories, which we illustrate using an interfacial analogue of the Magnus effect. This perturbative approach can be extended to more complex geometries, and to two-dimensional suspensions more generally.

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Section: Cylinder Next To a Plane Wall (A) Translationsupporting

confidence: 53%

Section: Resultsmentioning

confidence: 97%

Section: (C) the Lubrication Limitmentioning

confidence: 99%

Section: Cylinder Within a Cylinder (A) The Two-dimensional Journal Bmentioning

confidence: 99%

See 2 more Smart Citations

Irreversible particle motion in surfactant-laden interfaces due to pressure-dependent surface viscosity

Manikantan¹,

Squires²

2017

Proc. R. Soc. A.

Self Cite

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“…For Manifold B and C we use r(θ, φ) = 1 + r 0 sin(3φ) cos(θ) (Manifold B), r(θ, φ) = 1 + r 0 sin(7φ) cos(θ) (Manifold C). (60) Additional details concerning the differential geometry of these radial manifolds can be found in our prior work [35] and in Appendix B and C. Figure 9: Radial Manifold Shapes. We consider hydrodynamic flows on manifolds with shapes ranging from the sphere to the more complicated geometries generated by equation 60.…”

Section: Hydrodynamic Flows On Curved Fluid Interfacesmentioning

confidence: 99%

Hydrodynamic flows on curved surfaces: Spectral numerical methods for radial manifold shapes

Gross

Atzberger

2018

Journal of Computational Physics

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W e formulate hydrodynamic equations and spectrally accurate numerical methods for investigating the role of geometry in flows within two-dimensional fluid interfaces. To achieve numerical approximations having high precision and level of symmetry for radial manifold shapes, we develop spectral Galerkin methods based on hyperinterpolation with Lebedev quadratures for L 2 -projection to spherical harmonics. We demonstrate our methods by investigating hydrodynamic responses as the surface geometry is varied. Relative to the case of a sphere, we find significant changes can occur in the observed hydrodynamic flow responses as exhibited by quantitative and topological transitions in the structure of the flow. We present numerical results based on the Rayleigh-Dissipation principle to gain further insights into these flow responses. We investigate the roles played by the geometry especially concerning the positive and negative Gaussian curvature of the interface. We provide general approaches for taking geometric effects into account for investigations of hydrodynamic phenomena within curved fluid interfaces.presents some significant challenges in the manifold setting [61]. For instance in a two-dimensional curved fluid sheet the equations must account for the distinct components of linear momentum correctly. The concept of momentum is not an intrinsic field of the manifold and must be interpreted with respect to the ambient physical space [61]. For instance, when considering non-relativistic mechanics in an inertial reference frame with coordinates x, y, z, the x-component of momentum is a conserved quantity distinct from the y and z-components of momentum. An early derivation using coordinate-based tensor calculus in the ambient space was given for hydrodynamics within a curved two-dimensional fluid interface in Scriven [88]. This was based on the more general shell theories developed in [28,110]. Many subsequent derivations have been performed using tensor calculus for related fluid-elastic interfaces motivated by applications. This includes derivation of equations for surface rheology [25,63,64], investigation of red-blood cells [89], surface transport in capsules and surfactants on bubbles [30,75], and investigations of the mechanics, diffusion, and fluctuations associated with curved lipid bilayer membranes [18,23,39,79,80,84,92,95,101]. Recent works by Marsden et al. [45,61,109] develop the continuum mechanics in the more general setting when both the reference body and ambient space are treated as general manifolds as the basis for rigorous foundations for elasticity [45,61]. In this work, some of the challenges associated with momentum and stress with reference to ambient space can be further abstracted in calculations by the use of covector-valued differential forms and a generalized mixed type of divergence operator [45,109]. A particularly appealing way to derive the conservation laws for manifolds is through the use of variational principles based on the balance of energy and symmetries [61]. This has rec...

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Meshfree methods on manifolds for hydrodynamic flows on curved surfaces: A Generalized Moving Least-Squares (GMLS) approach

Gross

Trask²,

Kuberry³

et al. 2020

Journal of Computational Physics

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Pressure-dependent surface viscosity and its surprising consequences in interfacial lubrication flows

Cited by 18 publications

References 49 publications

Irreversible particle motion in surfactant-laden interfaces due to pressure-dependent surface viscosity

Irreversible particle motion in surfactant-laden interfaces due to pressure-dependent surface viscosity

Hydrodynamic flows on curved surfaces: Spectral numerical methods for radial manifold shapes

Meshfree methods on manifolds for hydrodynamic flows on curved surfaces: A Generalized Moving Least-Squares (GMLS) approach

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