Fluid Flow and Solute Transport though a Fracture Intersecting a Canister - Analytical Solutions for the Parallel Plate Model

2003 ◽  
Vol 807 ◽  
Author(s):  
L. Liu ◽  
I. Neretnieks
Keyword(s):  
Fluid Flow ◽  
Solute Transport ◽  
Flow Rate ◽  
Analytical Solutions ◽  
Parallel Plate ◽  
Spent Nuclear Fuel ◽  
Volumetric Flow Rate ◽  
Single Fracture ◽  
Plate Model ◽  
Specific Scenario

ABSTRACTIn this paper, we are concerned with a specific scenario where a large fracture intersects, at its center, a canister that contains spent nuclear fuel. Assuming that a nuclide is free to release from the canister into groundwater flowing through the fracture, a detailed formulation of the volumetric flow rate and the equivalent flow rate are made for the parallel plate model. The formulas proposed have been validated by numerical examinations; they are not only simple in forms but also universal in applications where the flow may be taken normal, inclined or parallel to the axis of the canister. Of great importance, they provide a convenient way to predict the average properties of fluid flow and solute transport through a single fracture with spatially variable apertures.

scholarly journals Analytical Solution for Heat Transfer in Electroosmotic Flow of a Carreau Fluid in a Wavy Microchannel

2019 ◽  
Vol 9 (20) ◽  
pp. 4359 ◽  
Author(s):  
Saima Noreen ◽  
Sadia Waheed ◽  
Abid Hussanan ◽  
Dianchen Lu
Keyword(s):  
Fluid Flow ◽  
Flow Pattern ◽  
Flow Rate ◽  
Electroosmotic Flow ◽  
Linear Problem ◽  
Perturbation Technique ◽  
Volumetric Flow Rate ◽  
Carreau Fluid ◽  
Long Wavelength ◽  
Wide Range

This article explores the heat and transport characteristics of electroosmotic flow augmented with peristaltic transport of incompressible Carreau fluid in a wavy microchannel. In order to determine the energy distribution, viscous dissipation is reckoned. Debye Hückel linearization and long wavelength assumptions are adopted. Resulting non-linear problem is analytically solved to examine the distribution and variation in velocity, temperature and volumetric flow rate within the Carreau fluid flow pattern through perturbation technique. This model is also suitable for a wide range of biological microfluidic applications and variation in velocity, temperature and volumetric flow rate within the Carreau fluid flow pattern.

Feasible Analytical Solutions for Electrostatic Parallel-Plate Actuator or Sensor

2004 ◽  
Vol 10 (3) ◽  
pp. 359-369 ◽  
Author(s):  
R. Y. Vinokur
Keyword(s):  
Quality Factor ◽  
Analytical Solutions ◽  
Parallel Plate ◽  
Nanoelectromechanical Systems ◽  
Capacitive Sensors ◽  
Plate Model ◽  
Sensors And Actuators ◽  
Analytical Results ◽  
Factor Effect ◽  
Close Form

This paper presents several analytical solutions for the conventional electrostatic parallel-plate model and explains the effect of the quality factor decrease with the voltage applied. Such a model is of importance in the development of electrostatic (capacitive) sensors and actuators including acoustical transducers and loudspeakers, and micro/nanoelectromechanical systems (MEMS/NEMS). It serves to reveal and interpret the basic phenomena (in particular, the “pull-in” instability and “negative spring” effect) but there is still some room for new effects and analytical results, although the model is nonlinear and provides rather computational than comprehensible close-form relationships as “negative quality factor effect” described in this paper. The new results obtained can be supportive to analyze, test, and design electrostatic sensors and actuators.

scholarly journals Shear-Thinning Fluid Flow in Variable-Aperture Channels

Proceedings ◽  
2019 ◽  
Vol 48 (1) ◽  
pp. 28
Author(s):  
Alessandro Lenci ◽  
Vittorio Di Federico
Keyword(s):  
Fluid Flow ◽  
Pressure Gradient ◽  
Flow Rate ◽  
Geometric Model ◽  
Shear Thinning ◽  
Single Fracture ◽  
Fracture Aperture ◽  
Nonlinear Phenomenon ◽  
Hydraulic Aperture ◽  
Fluid Rheology

Non-Newtonian fluid flow in a single fracture is a 3D nonlinear phenomenon that is often averaged across the fracture aperture and described as 2D. To capture key interactions between fluid rheology and spatial heterogeneity, we adopted a simplified geometric model to describe aperture variability, consisting of adjacent one-dimensional channels with constant aperture, each drawn from assigned aperture distribution. The flow rate was then derived under the lubrication approximation for the two limiting cases of an external pressure gradient that was parallel/perpendicular to the channels; these two arrangements provided an upper/lower bound to fracture conductance. Fluid rheology was described via the Prandtl–Eyring shear-thinning model. Novel closed-form results for flow rate and hydraulic aperture were derived and are discussed; different combinations of parameters describing the fluid rheology and variability of the aperture field were considered. In general, flow rate depends, in a nonlinear fashion, on the dimensionless pressure gradient and distribution parameters.

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