Magnetohydrodynamic effects on a charged colloidal sphere with arbitrary double-layer thickness

2010 ◽  
Vol 133 (13) ◽  
pp. 134103 ◽  
Author(s):  
Tzu H. Hsieh ◽  
Huan J. Keh
Keyword(s):  
Layer Thickness ◽  
Double Layer ◽  
Colloidal Sphere ◽  
Double Layer Thickness

The primary electroviscous effect in a suspension of spheres with thin double layers

1983 ◽  
Vol 132 ◽  
pp. 337-347 ◽  
Author(s):  
E. J. Hinch ◽  
J. D. Sherwood
Keyword(s):  
Layer Thickness ◽  
Double Layer ◽  
High Surface ◽  
Particle Radius ◽  
Double Layers ◽  
Asymptotic Results ◽  
Electroviscous Effect ◽  
Surface Potentials ◽  
Double Layer Thickness

We study the primary electroviscous effect in a suspension of spheres when the double layer thickness κ−1 is small compared with the particle radius a. The case of a 1–1 symmetric electrolyte is examined using the methods of Dukhin & coworkers (1974), whilst the asymmetric electrolyte is studied along lines similar to those of O'Brien (1983). Sherwood's (1980) asymptotic results for high surface potentials and high Hartmann numbers are extended and complemented.

scholarly journals Insight into Debye Hückel length (κ−1): smart gravimetric and swelling techniques reveals discrepancy of diffuse double layer theory at high ionic concentrations

2021 ◽  
Author(s):  
Talal AL-Bazali
Keyword(s):  
Layer Thickness ◽  
Double Layer ◽  
Critical Concentration ◽  
Ionic Concentration ◽  
Diffuse Double Layer ◽  
Ionic Concentrations ◽  
Osmotic Water ◽  
Ionic Valence ◽  
High Concentrations ◽  
Double Layer Thickness

AbstractSmart gravimetric and swelling techniques were utilized in this work to examine the validity of the Debye Hückel length (κ−1) equation when shale interacts with highly concentrated salt solutions. The swelling and shrinkage behavior of two different shales, when exposed to monovalent and divalent ionic solutions (NaCl, KCl and CaCl2) at concentrations ranging from 2 to 22%w/w was observed and measured. Shale swelling and shrinkage results show that Debye Hückel length (κ−1) equation seems to work adequately at low ionic concentrations where osmotic water flow out of shale plays a major role in decreasing the diffuse double layer thickness by withdrawing water out and thereby shrinking κ−1. At high ionic concentration levels, the flow of associated water into the diffuse double layer negates the withdrawal of osmotic water out of the diffuse double layer which could maintain κ−1 or possibly increase it. Data on measured ionic uptake into shale suggests that excessive ionic diffusion into shale, especially at high concentrations, leads to higher electrical repulsion between alike ions in the diffuse layer which could lead to the expansion of the diffuse double layer thickness. Furthermore, swelling and shrinkage data analysis for shale suggests the existence of a ‘critical concentration’ below which the Debye Hückel length equation works. Above the critical concentration, the validity of the Debye Hückel length equation might be in question. The critical concentration is different for all ions and depends on ionic valence, hydrated ion diameter, and clay type.

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