Motion of a sphere in the presence of a plane interface. Part 2. An exact solution in bipolar co-ordinates

Lee, S. H.; Leal, L. Gary

doi:10.1017/s0022112080000109

Cited by 118 publications

(115 citation statements)

References 11 publications

Supporting

Mentioning

111

Contrasting

Order By: Relevance

“…where Γ z is the L-dependent mobility of a (chemically passive) rigid spherical particle moving normal to the planar fluid interface [35]. The boundary-value problems given by Eqs.…”

mentioning

confidence: 99%

Effective Interaction between Active Colloids and Fluid Interfaces Induced by Marangoni Flows

et al. 2016

View full text Add to dashboard Cite

We show theoretically that near a fluid-fluid interface a single active colloidal particle generating, e.g., chemicals or a temperature gradient experiences an effective force of hydrodynamic origin. This force is due to the fluid flow driven by Marangoni stresses induced by the activity of the particle; it decays very slowly with the distance from the interface, and can be attractive or repulsive depending on how the activity modifies the surface tension. We show that, for typical systems, this interaction can dominate the dynamics of the particle as compared to Brownian motion, dispersion forces, or self-phoretic effects. In the attractive case, the interaction promotes the self-assembly of particles into a crystal-like monolayer at the interface. DOI: 10.1103/PhysRevLett.116.078301 Significant attention has been paid lately to micrometer sized particles capable of self-induced motility [1][2][3]. They are seen as promising candidates for novel techniques in chemical sensing [4] or water treatment [5]. The motion of active colloidal particles has been the subject of numerous experimental [1][2][3]6,7] and theoretical [8][9][10][11][12] studies. One realization is a particle with a catalytic surface promoting a chemical reaction in the surrounding solution [13]. For an axisymmetric particle lacking fore-and-aft symmetry, the distributions of reactant and product molecules may become nonuniform along its surface and the particle could move due to self-induced phoresis [14]. If the particle is spherically symmetric, it will remain immobile in bulk solution but can be set into motion by the vicinity of walls or other particles (not necessarily active) which break the spherical symmetry [10,[13][14][15][16].A relevant case corresponds to the movement of active particles bounded by a fluid-fluid interface. This situation raises new issues, in particular if the reactants or the products have a significant effect on the properties of the fluid interface implying tensioactivity. For example, it has been recently predicted that catalytically active, spherical particles which are trapped at the interface may be set into motion along the interface by Marangoni flows, selfinduced via the spatially nonuniform distribution of tensioactive molecules [17][18][19]. (A similar motility mechanism can originate from thermally induced Marangoni flows if, e.g., the particle contains a metal cap which is heated by a laser beam [20].) Furthermore, self-induced Marangoni flows, combined with a mechanism of triggering spontaneous symmetry breaking, have also been used to develop self-propelled droplets [21][22][23].However, another category of experimental situations occurs if the particles are not trapped at the interface but may reside in the vicinity of the interface or get near it during their motion. In this study we provide theoretical evidence that such catalytically active or locally heated spherical particles, although immobile in bulk, experience a very strong, long-ranged effective force field due to the Marangoni stresses...

show abstract

“…where Γ z is the L-dependent mobility of a (chemically passive) rigid spherical particle moving normal to the planar fluid interface [35]. The boundary-value problems given by Eqs.…”

mentioning

confidence: 99%

Effective Interaction between Active Colloids and Fluid Interfaces Induced by Marangoni Flows

et al. 2016

View full text Add to dashboard Cite

show abstract

“…(5) and (6) represent the natural continuity of the flow field across the membrane, whereas Eqs. (7) and (8) are the discontinuity of the normal-tangential and normal-normal components of the fluid stress tensor at the membrane. Here ∆f θ and ∆f r are the meridional and radial traction where the superscripts S and B stand for the shearing and bending related parts, respectively.…”

Section: Singularity Solutionmentioning

confidence: 99%

Hydrodynamic mobility of a solid particle near a spherical elastic membrane: Axisymmetric motion

2017

View full text Add to dashboard Cite

We use the image solution technique to compute the leading order frequency-dependent self-mobility function of a small solid particle moving perpendicular to the surface of a spherical capsule whose membrane possesses shearing and bending rigidities. Comparing our results with those obtained earlier for an infinitely extended planar elastic membrane, we find that membrane curvature leads to the appearance of a prominent additional peak in the mobility. This peak is attributed to the fact that the shear resistance of the curved membrane involves a contribution from surface-normal displacements which is not the case for planar membranes. In the vanishing frequency limit, the particle self-mobility near a no-slip hard sphere is recovered only when the membrane possesses a non-vanishing resistance towards shearing. We further investigate capsule motion, finding that the pair-mobility function is solely determined by membrane shearing properties. Our analytical predictions are validated by fully resolved boundary integral simulations where a very good agreement is obtained.

show abstract

“…Jeffery (1912), Brenner (1961) and Lee & Leal (1980) for motion in a quiescent flow. Goren & O'Neill (1971) used the same approach to consider the motion of a sphere in simple shear flow near a solid, plane wall, and, more recently, Dukhin & Rulev (1977) considered a sphere on the axis of symmetry of a pure straining flow near a gas-liquid interface.…”

Section: Introductionmentioning

confidence: 99%

Particle motion in Stokes flow near a plane fluid–fluid interface. Part 2. Linear shear and axisymmetric straining flows

Yang

Leal

1984

J. Fluid Mech.

View full text Add to dashboard Cite

275We consider the motion of a sphere or a slender body in the presence of a plane fluid-fluid interface with an arbitrary viscosity ratio, when the fluids undergo a linear undisturbed flow. First, the hydrodynamic relationships for the force and torque on the particle at rest in the undisturbed flow field are determined, using the method of reflections, from the spatial distribution of Stokeslets, rotlets and higher-order singularities in Stokes flow. These fundamental relationships are then applied, in combination with the corresponding solutions obtained in earlier publications for the translation and rotation through a quiescent fluid, to determine the motion of a neutrally buoyant particle freely suspended in the flow. The theory yields general trajectory equations for an arbitrary viscosity ratio which are in good agreement with both exact-solution results and experimental data for sphere motions near a rigid plane wall. Among the most interesting results for motion of slender bodies is the generalization of the Jeffrey orbit equations for linear simple shear flow.

show abstract

Motion of a sphere in the presence of a plane interface. Part 2. An exact solution in bipolar co-ordinates

Cited by 118 publications

References 11 publications

Effective Interaction between Active Colloids and Fluid Interfaces Induced by Marangoni Flows

Effective Interaction between Active Colloids and Fluid Interfaces Induced by Marangoni Flows

Hydrodynamic mobility of a solid particle near a spherical elastic membrane: Axisymmetric motion

Particle motion in Stokes flow near a plane fluid–fluid interface. Part 2. Linear shear and axisymmetric straining flows

Contact Info

Product

Resources

About