Motion of a Colloidal Sphere Covered by a Layer of Adsorbed Polymers Normal to a Plane Surface

Kuo, Jimmy; Keh, Huan J.

doi:10.1006/jcis.1998.5979

Cited by 5 publications

(4 citation statements)

References 31 publications

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“…They also measured the settling velocity of a solid sphere with attached threads and found that theoretical predictions for the composite sphere are in excellent agreement with the experimental results. Employing a unit-cell model for the creeping flow relative to an assemblage of identical composite spheres, Kuo and Keh (1999) later obtained analytical solutions for the dependence of the average drag force of this assemblage on the volume fraction of the particles. Anderson and Solomentsev (1996) analyzed motions of a spherical particle covered by a thin layer of adsorbed polymer near an infinite plane wall on the creeping motions and along the centerline of a long cylindrical tube.…”

Section: Introductionmentioning

confidence: 99%

“…Using the concept of hydrodynamic thickness of the polymer layer and a method of reflections together with the technique of matched asymptotic expansions, they determined the boundary effects on the particle movement. On the other hand, the quasi steady motion of a sphere coated with a thin polymer layer normal to an infinite plane, which can be either a solid wall or a free surface, has been investigated (Kuo and Keh 1999). A combined analytical-numerical exact solution of the hydrodynamic effect exerted by the plane on the moving particle was also obtained using the method of matched asymptotic expansions and a boundary collocation technique.…”

Section: Introductionmentioning

confidence: 99%

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Drag and Separation Flow Past Solid Sphere with Porous Shell at Moderate Reynolds Number

Taamneh

Bataineh

2011

Transp Porous Med

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Axisymmetric viscous, two-dimensional steady and incompressible fluid flow past a solid sphere with porous shell at moderate Reynolds numbers is investigated numerically. There are two dimensionless parameters that govern the flow in this study: the Reynolds number based on the free stream fluid velocity and the diameter of the solid core, and the ratio of the porous shell thickness to the square root of its permeability. The flow in the free fluid region outside the shell is governed by the Navier-Stokes equation. The flow within the porous annulus region of the shell is governed by a Darcy model. Using a commercially available computational fluid dynamics (CFD) package, drag coefficient and separation angle have been computed for flow past a solid sphere with a porous shell for Reynolds numbers of 50, 100, and 200, and for porous parameter in the range of 0.025-2.5. In all simulation cases, the ratio of b/a was fixed at 1.5; i.e., the ratio of outer shell radius to the inner core radius. A parametric equation relating the drag coefficient and separation point with the Reynolds number and porosity parameter were obtained by multiple linear regression. In the limit of very high permeability, the computed drag coefficient as well as the separation angle approaches that for a solid sphere of radius a, as expected. In the limit of very low permeability, the computed total drag coefficient approaches that for a solid sphere of radius b, as expected. The simulation results are presented in terms of viscous drag coefficient, separation angles and total drag coefficient. It was found that the total drag coefficient around the solid sphere as well as the separation angle are strongly governed by the porous shell permeability as well as the Reynolds number. The separation point shifts toward the rear stagnation point as the shell permeability is increased. Separation angle and drag coefficient for the special case of a solid sphere of radius r = a was found to be in good agreement with previous experimental results and with the standard drag curve.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Drag and Separation Flow Past Solid Sphere with Porous Shell at Moderate Reynolds Number

Taamneh

Bataineh

2011

Transp Porous Med

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“…For example, surface layers are purposely formed by adsorbing long-chain polymers to make the suspended particles stable against flocculation . Even the surfaces of model colloids such as silica and polystyrene latex are “hairy” with a gel-like polymeric layer extending a substantial distance into the suspending medium from the bulk material inside the particle. , In particular, the surface of a biological cell is not a hard smooth wall, but rather is a permeable rough surface with various appendages ranging from protein molecules on the order of nanometers to cilia on the order of micrometers . Such particles can be modeled as a soft particle (or composite particle) having a central rigid core and an outer porous shell. − When the rigid core vanishes, the particle reduces to a permeable one, such as polymer coils or colloidal flocs.…”

Section: Introductionmentioning

confidence: 99%

Diffusiophoresis of a Spherical Soft Particle in Electrolyte Gradients

Huang

Keh

2012

J. Phys. Chem. B

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An analytical study of the diffusiophoresis (consisting of electrophoresis and chemiphoresis) of a charged soft particle (or composite particle) composed of a spherical rigid core and a surrounding porous shell in an electrolyte solution prescribed with a uniform concentration gradient is presented. In the solvent-permeable and ion-penetrable porous surface layer of the particle, idealized frictional segments with fixed charges are assumed to distribute at a constant density. The electrokinetic equations that govern the electric potential profile, ionic concentration distributions, and fluid flow field inside and outside the porous layer of the particle are linearized by assuming that the system is only slightly distorted from equilibrium. Using a regular perturbation method, these linearized equations are solved with the fixed charge densities on the rigid core surface and in the porous shell as the small perturbation parameters. An analytical expression for the diffusiophoretic mobility of the soft sphere in closed form is obtained from a balance between its electrostatic and hydrodynamic forces. This expression, which is correct to the second order of the fixed charge densities, is valid for arbitrary values of κa, λa, and r(0)/a, where κ is the reciprocal of the Debye screening length, λ is the reciprocal of the length characterizing the extent of flow penetration inside the porous layer, a is the radius of the soft sphere, and r(0) is the radius of the rigid core of the particle. It is shown that a soft particle bearing no net charge can undergo diffusiophoresis (electrophoresis and chemiphoresis), and the direction of its diffusiophoretic velocity is decided by the fixed charges in the porous surface layer of the particle. In the limiting cases of large and small values of r(0)/a, the analytical solution describing the diffusiophoretic mobility for a charged soft sphere reduces to that for a charged rigid sphere and for a charged porous sphere, respectively.

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“…Using the concept of hydrodynamic thickness of the polymer layer and a method of re ections together with the technique of matched asymptotic expansions, they determined the boundary e ects on the particle movement to O( 2 ) in increasing powers of up to O( 3 ), where is the ratio of the polymer-layer length scale to the particle radius and is the ratio of the particle radius to the distance between the particle center and the boundary. On the other hand, the quasisteady motion of a sphere coated with a thin polymer layer normal to an inÿnite plane, which can be either a solid wall or a free surface, has been investigated (Kuo and Keh, 1999). A combined analytical-numerical exact solution of the hydrodynamic e ect exerted by the plane on the moving particle accurate to O( 2 ) was also obtained using the method of matched asymptotic expansions and a boundary collocation technique.…”

Section: Introductionmentioning

confidence: 99%