Application of temporal moments to interpret solute transport with time-dependent dispersion

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


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