scholarly journals Sedimentation Velocity and Potential in Concentrated Suspensions of Charged Spheres with Arbitrary Double-Layer Thickness

2000 ◽  
Vol 227 (2) ◽  
pp. 540-552 ◽  
Author(s):  
Huan J. Keh ◽  
Jau M. Ding
Keyword(s):  
Layer Thickness ◽  
Double Layer ◽  
Sedimentation Velocity ◽  
Concentrated Suspensions ◽  
Double Layer Thickness ◽  
Charged Spheres

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.

In situ investigation of the stress evolution during deposition of Ti/Al-multi layer films as a function of layer thickness and substrate temperature.

2002 ◽  
Vol 749 ◽  
Author(s):  
St. Lackner ◽  
R. Abermann
Keyword(s):  
Tensile Stress ◽  
Substrate Temperature ◽  
Layer Thickness ◽  
Double Layer ◽  
Multilayer Film ◽  
Multilayer Films ◽  
Double Layers ◽  
Al Alloy ◽  
Double Layer Thickness

ABSTRACTIn order to further investigate the origin of growth instabilities in aluminium rich Ti/Al-alloy films, formed by simultaneous deposition of the two alloy components, from separate evaporation sources, we have investigated the growth stress of multilayer-films under UHV-conditions, formed by a variable number of double layers of Ti and Al, by in situ internal stress measurements. The thickness of the respective Ti/Al-double layer was varied between 6.25 nm and 25 nm and the thickness of the respective titanium and aluminium layer was chosen to achieve an overall composition of Ti25Al75in a 150 nm thick film. The multilayer films were deposited on 10 nm thick alumina substrate films at substrate temperatures of 350°C and 450°C. Microstructure and phase formation was investigated by TEM/TED-experiments.In summary, these experiments show diffusion of aluminium (compressive stress) into the underlying film during deposition of the first monolayers and then formation (stress free or small tensile stress) of aluminium precipitates on the surface of the multilayer film during each aluminium deposition. During the subsequent titanium deposition the aluminium surface precipitates spread in a circular region under alloy formation (tensile stress) (see also accompanying paper). The respective stress contributions are strongly dependent on the double-layer thickness and substrate temperature. The increasing magnitude of the different stress contributions in the early growth stage are interpreted to indicate that the various processes are limited to specific surface regions, which get larger as the number of double-layers increases. The average film stress built up in the respective multilayer film by superposition of the stress contributions mentioned above, is also strongly dependent on double layer thickness and substrate temperature.

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