Bulk stresses due to deformation of the electrical double layer around a charged sphere

1978 ◽  
Vol 85 (4) ◽  
pp. 673-683 ◽  
Author(s):  
William B. Russel

A charged particle suspended in an electrolyte solution attracts ions of opposite charge and repels those of like charge. The surface charge and the resulting distributed charge in the fluid comprise an electrical double layer. When a shear flow deforms the diffuse part of the double layer from equilibrium, stresses are generated which make the effective viscosity of the suspension greater than it would be if there were no charges present. In this paper these stresses are calculated for a dilute dispersion of spheres which have small surface charges and which are surrounded by thin double layers. The viscosity is predicted to be Newtonian in extensional flow but shear-thinning with non-zero normal-stress differences in shear flow. For more complex flows a constitutive equation couples the bulk stress directly to the micro-structural deformation responsible for non-Newtonian effects.

Micromachines ◽  
2019 ◽  
Vol 10 (2) ◽  
pp. 100 ◽  
Author(s):  
Pablo García-Sánchez ◽  
Jose Flores-Mena ◽  
Antonio Ramos

We study theoretically the dielectrophoresis and electrorotation of a semiconducting microsphere immersed in an aqueous electrolyte. To this end, the particle polarizability is calculated from first principles for arbitrary thickness of the Debye layers in liquid and semiconductor. We show that the polarizability dispersion arises from the combination of two relaxation interfacial phenomena: charging of the electrical double layer and the Maxwell–Wagner relaxation. We also calculate the particle polarizability in the limit of thin electrical double layers, which greatly simplifies the analytical calculations. Finally, we show the model predictions for two relevant materials (ZnO and doped silicon) and discuss the limits of validity of the thin double layer approximation.


1949 ◽  
Vol 27b (7) ◽  
pp. 682-687
Author(s):  
A. J. Dekker

The mechanism suggested by Gurney for the formation of a double layer at the interface of a metal and a solution containing its ions is applied to a diffuse double layer. The diffuse part of the double layer is treated in a way that differs from Stern's method, leading to a more convenient formula for the potential ψδ of the diffuse part. Numerical values and a comparison with Stern's results are given.


1923 ◽  
Vol 5 (4) ◽  
pp. 479-504 ◽  
Author(s):  
Jacques Loeb

1. It is shown that the concentrations of different salts required to precipitate suspensions of gelatin-coated collodion particles in water are practically identical with the concentrations of the same salts required for the "salting out" of gelatin from aqueous solutions. Neither effect shows any relation to the electrical double layers surrounding the particles. 2. It is shown that at the isoelectric point of gelatin, suspensions of gelatin-coated collodion particles are not stable and it had been shown previously that gelatin is least soluble at the isoelectric point. The addition of salt increases both the solubility of gelatin in water as well as the stability of suspensions of gelatin-coated collodion particles in water, and both effects increase with the valency of one of the ions of the salt. 3. This latter effect is not due to any charges conferred on the gelatin particles by the salts, since the cataphoretic experiments show that salts like NaCl, Na2SO4, or CaCl2, which at the isoelectric point of gelatin increase the solubility of gelatin as well as the stability of suspensions of gelatin-coated collodion particles, leave the particles practically uncharged in the concentrations in which the salts are efficient. 4. It follows from all these facts that the stability of suspensions of gelatin-coated particles in water depends on the solubility of gelatin in water; e.g., on the chemical affinity of certain groups of the gelatin molecule for water. 5. Though crystalline egg albumin is highly soluble in water, the stability of collodion particles coated with crystalline egg albumin does not depend upon the affinity of the albumin molecule for water, but depends practically alone on the electrical double layer surrounding each particle. As soon as the P.D. of this double layer falls below 13 millivolts, the suspension is no longer stable. 6. The critical potential for the stability of suspensions of collodion particles coated with genuine egg albumin is the same as that for particles of boiled (denatured) white of egg. Since through the process of heating, egg albumin loses its solubility in water, it is inferred that egg albumin undergoes the same change when it forms a film around a solid particle like collodion. 7. The influence of electrolytes on the stability of suspensions of collodion particles coated with casein or edestin was similar to that of collodion particles coated with egg albumin. The experiments are, however, complicated by the fact that near the isoelectric point CaCl2 and even NaCl cause a suspension again at concentrations of about M/2 or 1 M, while still higher concentrations may cause a precipitation again. These latter effects have no connection with double layers, but belong probably in the category of solubility phenomena. 8. These experiments permit us to define more definitely the conditions for a general protective action of colloids. Protective colloids must be capable of forming a durable film on the surface of the suspended particles and the molecules constituting the film must have a higher attraction for the molecules of the solvent than for each other; in other words, they must possess true solubility. Only in this case can they prevent the precipitating action of low concentrations of electrolytes on particles which are kept in suspension solely by the high potentials of an electrical double layer. Thus gelatin films, in which the attraction of the molecules for water is preserved, have a general protective action, while crystalline egg albumin, casein, and edestin, which seem to lose their attraction for water when forming a film, have a protective action only under limited conditions stated in the paper.


ACS Nano ◽  
2021 ◽  
Author(s):  
Hyunho Kim ◽  
Mohamad I. Nugraha ◽  
Xinwei Guan ◽  
Zhenwei Wang ◽  
Mrinal K. Hota ◽  
...  

TAPPI Journal ◽  
2019 ◽  
Vol 18 (2) ◽  
pp. 93-99
Author(s):  
SEYYED MOHAMMAD HASHEMI NAJAFI ◽  
DOUGLAS BOUSFIELD, ◽  
MEHDI TAJVIDI

Cracking at the fold of publication and packaging paper grades is a serious problem that can lead to rejection of product. Recent work has revealed some basic mechanisms and the influence of various parameters on the extent of crack area, but no studies are reported using coating layers with known mechanical properties, especially for double-coated systems. In this study, coating layers with different and known mechanical properties were used to characterize crack formation during folding. The coating formulations were applied on two different basis weight papers, and the coated papers were folded. The binder systems in these formulations were different combinations of a styrene-butadiene latex and mixtures of latex and starch for two different pigment volume concentrations (PVC). Both types of papers were coated with single and double layers. The folded area was scanned with a high-resolution scanner while the samples were kept at their folded angle. The scanned images were analyzed within a constant area. The crack areas were reported for different types of papers, binder system and PVC values. As PVC, starch content, and paper basis weight increased, the crack area increased. Double layer coated papers with high PVC and high starch content at the top layer had more cracks in comparison with a single layer coated paper, but when the PVC of the top layer was low, cracking area decreased. No measurable cracking was observed when the top layer was formulated with a 100% latex layer.


2019 ◽  
Author(s):  
Divya Bohra ◽  
Jehanzeb Chaudhry ◽  
Thomas Burdyny ◽  
Evgeny Pidko ◽  
wilson smith

<p>The environment of a CO<sub>2</sub> electroreduction (CO<sub>2</sub>ER) catalyst is intimately coupled with the surface reaction energetics and is therefore a critical aspect of the overall system performance. The immediate reaction environment of the electrocatalyst constitutes the electrical double layer (EDL) which extends a few nanometers into the electrolyte and screens the surface charge density. In this study, we resolve the species concentrations and potential profiles in the EDL of a CO<sub>2</sub>ER system by self-consistently solving the migration, diffusion and reaction phenomena using the generalized modified Poisson-Nernst-Planck (GMPNP) equations which include the effect of volume exclusion due to the solvated size of solution species. We demonstrate that the concentration of solvated cations builds at the outer Helmholtz plane (OHP) with increasing applied potential until the steric limit is reached. The formation of the EDL is expected to have important consequences for the transport of the CO<sub>2</sub> molecule to the catalyst surface. The electric field in the EDL diminishes the pH in the first 5 nm from the OHP, with an accumulation of protons and a concomitant depletion of hydroxide ions. This is a considerable departure from the results obtained using reaction-diffusion models where migration is ignored. Finally, we use the GMPNP model to compare the nature of the EDL for different alkali metal cations to show the effect of solvated size and polarization of water on the resultant electric field. Our results establish the significance of the EDL and electrostatic forces in defining the local reaction environment of CO<sub>2</sub> electrocatalysts.</p>


Membranes ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 129
Author(s):  
Guilherme Volpe Bossa ◽  
Sylvio May

Poisson–Boltzmann theory provides an established framework to calculate properties and free energies of an electric double layer, especially for simple geometries and interfaces that carry continuous charge densities. At sufficiently small length scales, however, the discreteness of the surface charges cannot be neglected. We consider a planar dielectric interface that separates a salt-containing aqueous phase from a medium of low dielectric constant and carries discrete surface charges of fixed density. Within the linear Debye-Hückel limit of Poisson–Boltzmann theory, we calculate the surface potential inside a Wigner–Seitz cell that is produced by all surface charges outside the cell using a Fourier-Bessel series and a Hankel transformation. From the surface potential, we obtain the Debye-Hückel free energy of the electric double layer, which we compare with the corresponding expression in the continuum limit. Differences arise for sufficiently small charge densities, where we show that the dominating interaction is dipolar, arising from the dipoles formed by the surface charges and associated counterions. This interaction propagates through the medium of a low dielectric constant and alters the continuum power of two dependence of the free energy on the surface charge density to a power of 2.5 law.


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