Sedimentation Velocity and Potential in a Suspension of Charge-Regulating Colloidal Spheres

Ding, Jau M.; Keh, Huan J.

doi:10.1006/jcis.2001.7892

Cited by 13 publications

(18 citation statements)

References 23 publications

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“…(16) into the governing Eqs. (4) and (10)-(12) and boundary conditions (6a), (7a), (14), and (15), and equating like powers ofσ andσ b on both sides of the respective equations, we can obtain a group of linear differential equations and boundary conditions for each set of the functions u ij , p ij , μ ij ± , and ψ ij with i and j equal to 0, 1, and 2. After solving these perturbation equations, the results for the r and θ components of u, δp (to the second ordersσ 2 ,σσ b , andσ 2 b ), δμ ± , and δψ (to the first ordersσ andσ b , which will be sufficient for the calculation of the sedimentation velocity to the ordersσ 2 ,σσ b , andσ 2 b ) can be written as…”

Section: B Perturbation Solutionmentioning

confidence: 99%

“…Although the particle-interaction and boundary effects on the sedimentation of uncharged particles were analyzed extensively in the past, [7][8][9][10][11] not many studies about these effects on the sedimentation of charged particles have been reported. The particle interactions in the sedimentation of suspensions of charged colloidal spheres were investigated theoretically through the use of a unit cell model [12][13][14][15][16] and experimentally using a nondestructive back-light scattering technique. 17 On the other hand, Pujar and Zydney 18 described a general procedure to evaluate the sedimentation velocity of a charged spherical particle passing the center of an uncharged spherical cavity using a perturbation expansion in the small particle surface potential and Peclet number.…”

Section: Introductionmentioning

confidence: 99%

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Sedimentation of a charged colloidal sphere in a charged cavity

Keh

Cheng

2011

The Journal of Chemical Physics

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An analytical study is presented for the quasisteady sedimentation of a charged spherical particle located at the center of a charged spherical cavity. The overlap of the electric double layers is allowed, and the polarization (relaxation) effect in the double layers is considered. The electrokinetic equations that govern the ionic concentration distributions, electric potential profile, and fluid flow field in the electrolyte solution are linearized assuming that the system is only slightly distorted from equilibrium. Using a perturbation method, these linearized equations are solved for a symmetric electrolyte with the surface charge densities of the particle and cavity as the small perturbation parameters. An analytical expression for the settling velocity of the charged sphere is obtained from a balance among the gravitational, electrostatic, and hydrodynamic forces acting on it. Our results indicate that the presence of the particle charge reduces the magnitude of the sedimentation velocity of the particle in an uncharged cavity and the presence of the fixed charge at the cavity surface increases the magnitude of the sedimentation velocity of an uncharged particle in a charged cavity. For the case of a charged sphere settling in a charged cavity with equivalent surface charge densities, the net effect of the fixed charges will increase the sedimentation velocity of the particle. For the case of a charged sphere settling in a charged cavity with their surface charge densities in opposite signs, the net effect of the fixed charges in general reduces/increases the sedimentation velocity of the particle if the surface charge density of the particle has a greater/smaller magnitude than that of the cavity. The effect of the surface charge at the cavity wall on the sedimentation of a colloidal particle is found to increase with a decrease in the particle-to-cavity size ratio and can be significant in appropriate situations.

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Section: B Perturbation Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Sedimentation of a charged colloidal sphere in a charged cavity

Keh

Cheng

2011

The Journal of Chemical Physics

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“…[16] is elaborated in the Appendix. Equation [17] implies that the unit cell as a whole is electrically neutral. Equation [18] is a Neumann-type condition (22), which implies that the particle is nonconductive, and its surface is impermeable to ions.…”

Section: Theorymentioning

confidence: 99%

Sedimentation of Concentrated Spherical Particles with a Charge-Regulated Surface

Lee

Tong

Chih

et al. 2002

Journal of Colloid and Interface Science

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“…In real situations of diffusiophoresis, concentrated suspensions of particles may be encountered, and the particle interaction effects are important. To alleviate the complexity of multiple particles, unit cell models are often used to evaluate the particle interaction effects on the mean sedimentation velocity [24][25][26][27][28][29], average electrophoretic mobility [30][31][32][33][34][35][36][37], and effective electric conductivity [34][35][36][37][38] in suspensions of spherical particles. An agreement between the experimental electrophoretic velocity in a suspension of porous aggregates and the relevant cell-model predictions in a broad range of κa was obtained [39].…”

Section: Introductionmentioning

confidence: 99%

Diffusiophoresis in Suspensions of Charged Soft Particles

Lin

Keh

2020

Colloids and Interfaces

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The diffusiophoresis in a suspension of charged soft particles in electrolyte solution is analyzed. Each soft particle is composed of a hard core of radius r0 and surface charge density σ and an adsorbed fluid-penetrable porous shell of thickness a−r0 and fixed charge density Q. The effect of particle interactions is considered by using a unit cell model. The ionic concentration, electric potential, and fluid velocity distributions in a unit cell are solved as power expansions in σ and Q, and an explicit formula for the diffusiophoretic velocity of the soft particle is derived from a balance between the hydrodynamic and electrostatic forces exerted on it. This formula is correct to the second orders of σ and Q and valid for arbitrary values of κa, λa, r0/a, and the particle volume fraction of the suspension, where κ is the Debye screening parameter and λ is the reciprocal of a length featuring the flow penetration into the porous shell. The effects of the physical characteristics and particle interactions on the diffusiophoresis (including electrophoresis and chemiphoresis) in a suspension of charged soft particles, which become those of hard particles and porous particles in the limits r0=a and r0=0, respectively, are significant and complicated.

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Sedimentation Velocity and Potential in a Suspension of Charge-Regulating Colloidal Spheres

Cited by 13 publications

References 23 publications

Sedimentation of a charged colloidal sphere in a charged cavity

Sedimentation of a charged colloidal sphere in a charged cavity

Sedimentation of Concentrated Spherical Particles with a Charge-Regulated Surface

Diffusiophoresis in Suspensions of Charged Soft Particles

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