The interpretation of electrokinetic potentials and the inaccuracy of the DLVO theory for anatase sols

Webb, Joseph T.; Bhatnagar, Praneet; Williams, Dale G.

doi:10.1016/0021-9797(74)90379-8

Cited by 18 publications

(8 citation statements)

References 27 publications

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“…where 0 and 4~ are spherical polar coordinates with gravity acting in the 0 = 7r direction, A(R, )`), B(R, )`), and G(R, )`) the hydrodynamic correction functions (10), and t the time. By integrating [24], the limiting trajectory for particle capture can be located and used to compute the capture efficiency (10). This limiting trajectory corresponds to those trajectories furthest from the reference sphere which still lead to particle capture and are charac-terized by the upstream coordinates R = oo and 0 = 01ira.…”

Section: Gravity-enhanced Flocculation Experimentsmentioning

confidence: 99%

“…electrophoretically determined ~" potential is commonly used as the characteristic potential in the calculation of the electrostatic repulsive force, although the relationship between the ~" potential and the surface potential remains unclear (24). Brownian tlocculation experiments with monodisperse systems have verified several of the qualitative features of the DLVO theory (25)(26)(27), and have yielded estimates of both the Hamaker constant (18,28,29) and an effective surface potential (25,27).…”

Section: Introductionmentioning

confidence: 99%

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Prediction and measurement of initial flocculation rates in quiescent media

Melik

Fogler

1985

Journal of Colloid and Interface Science

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Initial flocculation rate experiments were carried out with a dilute suspension of bidisperse polystyrene spheres (0.166 and 0.255 gm in radius) under normal gravity conditions and, using a centrifuge, under conditions of an enhanced gravitational flow field. These experiments were designed to study the effect of differential creaming between small and large particles on the flocculation process and also to ascertain some of the fimitations associated with the DLVO theory of electrostatic stabilization. A turbidity technique which accounts for the simultaneous effects of flocculation and creaming was developed to determine the initial flocculation rate. By comparing theoretically predicted rates with experimentally observed ones for each monodisperse system under normal gravity, the Hamaker constant was determined to be A = 2.87 + 0.36 × 10-14 erg for a retarded attractive potential, and the surface potential was found to be ~0 =-12.7 + 0.5 mV. The corresponding ~" potentials ranged from-19 to-32 inV. However, the predicted stability factors for the bidisperse system were over 6 orders of magnitude greater than the measured values when the ~" potentials were substituted for #0 in the chosen electrostatic repulsion model, whereas, correct stability predictions were made with the characteristic potential of-12.7 mV. Under conditions of an enhanced gravitational flow field, the bidisperse flocculation rate increased with increasing gravitational force; in accordance with our previous theoretical predictions. For the larger gravitational forces studied, there appears to be a high degree of coupling between Brownian motion and gravitational forces.

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Section: Gravity-enhanced Flocculation Experimentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Prediction and measurement of initial flocculation rates in quiescent media

Melik

Fogler

1985

Journal of Colloid and Interface Science

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“…For the case of water, however, the most ubiquitous and important polar liquid, measurement of its viscosity in the presence of a strong, uniform field presents a strong challenge (as discussed later in this section), and to our knowledge no such direct measurements have been reported. Over the past six decades, therefore, the magnitude of the viscoelectric effect in water has been only indirectly estimated by extrapolation from its values for organic liquids ( 8 ), from estimates of its effect on electrokinetic phenomena ( 11 , 14 – 19 ), or by other approaches ( 7 , 12 , 20 , 21 ). These estimated values, as expressed in the viscoelectric coefficient f , vary over more than three orders of magnitude, ranging from f ∼10 −17 –2.5 × 10 −14 (V/m) 2 ( SI Appendix , Section 7 ).…”

mentioning

confidence: 99%

“…For completeness, we note that results contradictory to the viscoelectric model have also been reported ( 22 ) (i.e., suggesting a decreased water viscosity in an electric field). The reasons for the large span of these estimated f values were attributed to various factors such as solid/liquid coupling, varying ionic sizes, and varying water permittivity ( 12 , 19 ); however, while these factors may play some role, there is no evidence that they could lead to such large discrepancies.…”

mentioning

confidence: 99%

“…In all cases, viscosity changes were assumed to occur only in the nonuniform, rapidly decaying electrostatic potential near charged surfaces immersed in water. Changes in electrophoretic mobility, electro-osmosis, or hydrodynamic dissipation or water mobility between similarly charged solid surfaces were then attributed to some mean viscosity increase in these thin surface-adjacent layers ( 7 , 11 , 12 , 14 – 21 ). In practice, however, the effect on these electrokinetic phenomena of viscosity or water mobility changes in the thin layers where such nonuniform, rapidly decaying fields are present is not easy to quantify reliably, especially in the presence of salt ions ( 12 ).…”

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confidence: 99%

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Direct measurement of the viscoelectric effect in water

Jin

Hwang

Chai

et al. 2021

Proc. Natl. Acad. Sci. U.S.A.

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The viscoelectric effect concerns the increase in viscosity of a polar liquid in an electric field due to its interaction with the dipolar molecules and was first determined for polar organic liquids more than 80 y ago. For the case of water, however, the most common polar liquid, direct measurement of the viscoelectric effect is challenging and has not to date been carried out, despite its importance in a wide range of electrokinetic and flow effects. In consequence, estimates of its magnitude for water vary by more than three orders of magnitude. Here, we measure the viscoelectric effect in water directly using a surface force balance by measuring the dynamic approach of two molecularly smooth surfaces with a controlled, uniform electric field between them across highly purified water. As the water is squeezed out of the gap between the approaching surfaces, viscous damping dominates the approach dynamics; this is modulated by the viscoelectric effect under the uniform transverse electric field across the water, enabling its magnitude to be directly determined as a function of the field. We measured a value for this magnitude, which differs by one and by two orders of magnitude, respectively, from its highest and lowest previously estimated values.

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Analytical solutions for viscoelectric effects in electrokinetic nanochannels

Ma,

Ramachandran,

Santiago

2024

Electrophoresis

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Understanding electrokinetic transport in nanochannels and nanopores is essential for emerging biological and electrochemical applications. The viscoelectric effect is an important mechanism implicated in the increase of local viscosity due to the polarization of a solvent under a strong electric field. However, most analyses of the viscoelectric effect have been limited to numerical analyses. In this work, we present a set of analytical solutions applicable to the physical description of viscoelectric effects in nanochannel electrokinetic systems. To achieve such closed‐form solutions, we employ the Debye–Hückel approximation of small diffuse charge layer potentials compared to the thermal potential. We analyze critical parameters, including electroosmotic flow profiles, electroosmotic mobility, flow rate, and channel conductance. We compare and benchmark our analytical solutions with published predictions from numerical models. Importantly, we leverage these analytical solutions to identify essential thermophysical and nondimensional parameters that govern the behavior of these systems. We identify scaling parameters and relations among surface charge density, ionic strength, and nanochannel height.

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The interpretation of electrokinetic potentials and the inaccuracy of the DLVO theory for anatase sols

Cited by 18 publications

References 27 publications

Prediction and measurement of initial flocculation rates in quiescent media

Prediction and measurement of initial flocculation rates in quiescent media

Direct measurement of the viscoelectric effect in water

Analytical solutions for viscoelectric effects in electrokinetic nanochannels

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