New solutions for solute transport in a finite column with distance-dependent dispersivities and time-dependent solute sources

2013 ◽  
Vol 487 ◽  
pp. 87-97 ◽  
Author(s):  
Kehua You ◽  
Hongbin Zhan
1986 ◽  
Vol 250 (2) ◽  
pp. F246-F255
Author(s):  
J. C. Williams ◽  
D. W. Barfuss ◽  
J. A. Schafer

To examine the hypothesis that fluid absorption is driven by transepithelial osmotic differences, we measured such differences in proximal tubules perfused under oil and attempted to increase the rate of fluid absorption (Jv) and hence the absorbate-perfusate osmotic differences by lowering the osmolality of the perfusate. We were able to consistently increase Jv in this manner only in proximal straight tubules perfused with a simple perfusate that contained no bicarbonate or amino acids. With the simple perfusate, a small but significant increase in the absorbate-perfusate osmolality difference was seen with increased Jv, which is expected if the volume absorption is driven by a transepithelial osmotic difference. In addition, lowering the perfusate osmolality from 290 to 160 mosmol/kg H2O increased the rate of solute absorption from 79 +/- 7 to 91 +/- 8 posmol . min-1 . mm-1; this increase was partly accounted for by an increase in the rate of absorption of glucose from 6.6 +/- 0.9 to 9.5 +/- 1.1 pmol . min-1 . mm-1. In contrast, with the complete perfusate in proximal straight tubules there was little or no increment in Jv, no change in transepithelial osmolality differences, and a decrease in the rate of solute transport with hypoosmolality from 136 +/- 21 to 87 +/- 22 posmol . min-1 . mm-1. In proximal convoluted tubules, similar results were obtained, but a time-dependent decline of Jv complicated the interpretation of the results in the convoluted tubules. It is hypothesized that the observed changes in solute transport with hypotonic perfusate may be the result of changes in membrane permeability that are subsequent to cell swelling.


Author(s):  
Sergei Fomin ◽  
Vladimir Chugunov ◽  
Toshiyuki Hashida

Solute transport in a fractured porous confined aquifer is modelled by using an equation with a fractional-in-time derivative of order γ , which may vary from 0 to 1. Accounting for non-Fickian diffusion into the surrounding rock mass, which is modelled by a fractional spatial derivative of order α , leads to the introduction of an additional fractional-in-time derivative of order α /(1+ α ) in the equation for solute transport. Closed-form solutions for solute concentrations in the aquifer and surrounding rocks are obtained for an arbitrary time-dependent source of contamination located at the inlet of the aquifer. Based on these solutions, different regimes of contaminant transport in aquifers with various physical properties are modelled and analysed.


2007 ◽  
Vol 129 (9) ◽  
pp. 1157-1163
Author(s):  
Sergei Fomin ◽  
Vladimir Chugunov ◽  
Toshiyuki Hashida

Solute transport in the fractured porous confined aquifer is modeled by the advection-dispersion equation with fractional time derivative of order γ, which may vary from 0 to 1. Accounting for diffusion in the surrounding rock mass leads to the introduction of an additional fractional time derivative of order 1∕2 in the equation for solute transport. The closed-form solutions for concentrations in the aquifer and surrounding rocks are obtained for the arbitrary time-dependent source of contamination located in the inlet of the aquifer. Based on these solutions, different regimes of contamination of the aquifers with different physical properties are modeled and analyzed.


Soil Research ◽  
1981 ◽  
Vol 19 (3) ◽  
pp. 287 ◽  
Author(s):  
LAG Aylmore ◽  
V Murali

Comparisons have been made between experimental breakthrough curves for phosphate ions in soil columns and computer simulations of solute transport based on a number of different adsorption models. These include single component linear and non-linear, instantaneous and dynamic adsorption models; as well as the model incorporating a combination of instantaneous and time-dependent components suggested in Part I. While certain portions of the complete breakthrough curves for phosphate could be reasonably approximated using simple one-component models, these generally failed badly to describe the shape and position of the experimental data over the complete range of the breakthrough curve. This was even more evident when both adsorption and desorption phases were considered. On the other hand, the model described in Part I combining instantaneous linear and a simultaneous time-dependent (dynamic) Freundlich-type adsorption components provided a good simulation of the experimental data over the full range of the breakthrough curves for both adsorption and desorption phases. Of particular significance is the ability of the model to handle successive experimental breakthrough curves with different amounts of residual adsorption. A method for 'normalizing' the solute transport equations to facilitate computer simulations is presented.


Sadhana ◽  
2020 ◽  
Vol 45 (1) ◽  
Author(s):  
Abhay Guleria ◽  
Deepak Swami ◽  
Nitin Joshi ◽  
Abhimanyu Sharma

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