The Electrophoretic Mobility and Electric Conductivity of a Concentrated Suspension of Colloidal Spheres with Arbitrary Double-Layer Thickness

Ding, Jau M.; Keh, Huan J.

doi:10.1006/jcis.2000.7383

Cited by 63 publications

(128 citation statements)

References 27 publications

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“…29,60 Although some of these factors have been considered to develop different analytical expressions for the calculation of electrical conductivity of colloids in the past. [63][64][65] However, these expressions are formulated for concentrated suspension of spherical particles in electrolyte solution (i.e., suspensions containing ions other than counterions) and are not presented in a form that can be easily compared with experimental data such that the authors used simulated values to test their models.…”

Section: Ph and Electrical Prediction With Existing Modelsmentioning

confidence: 99%

Factors affecting the pH and electrical conductivity of MgO–ethylene glycol nanofluids

2015

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Abstract. The pH and electrical conductivity are important properties of nanofluids that have not been widely studied, especially with regard to temperature and ultrasonication energy. To study the factors that affect the pH and electrical conductivity of magnesium oxide-ethylene glycol (MgO-EG) nanofluid, the effects of temperature, volume fraction, particle size and ultrasonication energy were investigated. Two different sizes of MgO were dispersed in EG base fluid up to the volume fraction of 3%, and the pH and electrical conductivity were monitored between the temperatures of 20 and 70°C. Characterization by transmission electron microscopy and size analyses revealed the morphology and sizes of the nanoparticle samples. The pH values dropped consistently with the increase of temperature, while electrical conductivity value increased with the increase of temperature. The experimental result showed that the increase in the MgO volume fraction increased both the pH and electrical conductivity values of the MgO-EG nanofluid. There was no recognizable influence of ultrasonication energy density on the pH and electrical conductivity of the nanofluid; therefore, it was concluded that temperature, volume fraction and particle size are the predominant factors affecting both the pH and electrical conductivity of MgO-EG nanofluid within the present experimental conditions.

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Section: Ph and Electrical Prediction With Existing Modelsmentioning

confidence: 99%

Factors affecting the pH and electrical conductivity of MgO–ethylene glycol nanofluids

2015

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“…According to the Kuwabara cell model, the liquid velocity at the outer surface of the unit cell must satisfy 16 and which mean, respectively, that there is no normal perturbation velocity at the outer surface of the cell 11,31 different from that due to the particle electrophoretic velocity (recall that the coordinate system is taken to travel with the particle) and that the vorticity is equal to zero at the outer surface of the cell. For the electrical potential, we have at the particle surface where Ψ p (r) is the electrical potential inside the particle and rp its relative permittivity.…”

Section: Basic Equations and Boundary Conditionsmentioning

confidence: 99%

“…Alternatively, Ding and Keh 31 suggested a different condition on ionic perturbations (N-t condition): or in terms of the function Y(r): after using again eqs 18, 20, and 21.…”

Section: Or In Terms Of the Function Y(r)mentioning

confidence: 99%

Numerical and Analytical Studies of the Electrical Conductivity of a Concentrated Colloidal Suspension

et al. 2006

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In the past few years, different models and analytical approximations have been developed facing the problem of the electrical conductivity of a concentrated colloidal suspension, according to the cell-model concept. Most of them make use of the Kuwabara cell model to account for hydrodynamic particle-particle interactions, but they differ in the choice of electrostatic boundary conditions at the outer surface of the cell. Most analytical and numerical studies have been developed using two different sets of boundary conditions of the Neumann or Dirichlet type for the electrical potential, ionic concentrations or electrochemical potentials at that outer surface. In this contribution, we study and compare numerical conductivity predictions with results obtained using different analytical formulas valid for arbitrary zeta potentials and thin double layers for each of the two common sets of boundary conditions referred to above. The conductivity will be analyzed as a function of particle volume fraction, φ, zeta potential, , and electrokinetic radius, κa (κ -1 is the double layer thickness, and a is the radius of the particle). A comparison with some experimental conductivity results in the literature is also given. We demonstrate in this work that the two analytical conductivity formulas, which are mainly based on Neumann-and Dirichlet-type boundary conditions for the electrochemical potential, predict values of the conductivity very close to their corresponding numerical results for the same boundary conditions, whatever the suspension or solution parameters, under the assumption of thin double layers where these approximations are valid. Furthermore, both analytical conductivity equations fulfill the Maxwell limit for uncharged nonconductive spheres, which coincides with the limit κa f ∞. However, some experimental data will show that the Neumann, either numerical or analytical, approach is unable to make predictions in agreement with experiments, unlike the Dirichlet approach which correctly predicts the experimental conductivity results. In consequence, a deeper study has been performed with numerical and analytical predictions based on Dirichlettype boundary conditions.

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“…The second one appears in studies by Ding and Keh 41 and not explicitly but equivalently in works of Levine and Neale, 1-2 Kozak and Davis, [42][43] Ohshima, 4-6 Keh and Hsu, 44 etc.…”

Section: Introductionmentioning

confidence: 99%

“…29 (We will call it SZ model or bc1 boundary case or frame, indistinctly.) The bc2 case joins the electrical Levine-Neale boundary condition with a Neumann condition proposed by Ding and Keh 41 on the local perturbed counterion concentration at the outer surface of the cell. As mentioned, this condition was already implicit in preceding models by Levine and Neale 1 and Ohshima.…”

Section: Introductionmentioning

confidence: 99%

Cell Model of the Direct Current Electrokinetics in Salt-Free Concentrated Suspensions: The Role of Boundary Conditions

2006

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In this paper, a general electrokinetic theory for concentrated suspensions in salt-free media is derived. Our model predicts the electrical conductivity and the electrophoretic mobility of spherical particles in salt-free suspensions for arbitrary conditions regarding particle charge, volume fraction, counterion properties, and overlapping of double layers of adjacent particles. For brevity, hydrolysis effects and parasitic effects from dissolved carbon dioxide, which are present to some extent in more "realistic" salt-free suspensions, will not be addressed in this paper. These issues will be analyzed in a forthcoming extension. However, previous models are revised, and different sets of boundary conditions, frequently found in the literature, are extensively analyzed. Our results confirm the so-called counterion condensation effect and clearly display its influence on electrokinetic properties such as electrical conductivity and electrophoretic mobility for different theoretical conditions. We show that the electrophoretic mobility increases as particle charge increases for a given particle volume fraction until the charge region where counterion condensation takes place is attained, for the abovementioned sets of boundary conditions. However, it decreases as particle volume fraction increases for a given particle charge. Instead, the electrical conductivity always increases with either particle charge for fixed particle volume fraction or volume fraction for fixed particle charge, whatever the set of boundary conditions previously referred. In addition, the influence of the electric permittivity of the particles on their electrokinetic properties in salt-free media is examined for those frames of boundary conditions.

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The Electrophoretic Mobility and Electric Conductivity of a Concentrated Suspension of Colloidal Spheres with Arbitrary Double-Layer Thickness

Cited by 63 publications

References 27 publications

Factors affecting the pH and electrical conductivity of MgO–ethylene glycol nanofluids

Factors affecting the pH and electrical conductivity of MgO–ethylene glycol nanofluids

Numerical and Analytical Studies of the Electrical Conductivity of a Concentrated Colloidal Suspension

Cell Model of the Direct Current Electrokinetics in Salt-Free Concentrated Suspensions: The Role of Boundary Conditions

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