Academia.eduAcademia.edu

Figure 1 – uploaded by Ganesan Subramanian

See full PDFdownloadDownload figure
Fig. 1 Schematic representation of carrier-mediated transport (facil- itated diffusion) through a liquid membrane where D; and c; denote the diffusion coefficient and concentration of species j (j = S, L and LS), respectively; cr is the total carrier concentration; cs(0) is the interfacial concentration of solute; and dis the membrane thickness. Here, we can assume that Ds = Dr, = Drs = D. We have chosen that cs(0) = cr =a. Equations 2-4 are transformed to a dimensionless state by introducing the following parameters:

Figure 1 Schematic representation of carrier-mediated transport (facil- itated diffusion) through a liquid membrane where D; and c; denote the diffusion coefficient and concentration of species j (j = S, L and LS), respectively; cr is the total carrier concentration; cs(0) is the interfacial concentration of solute; and dis the membrane thickness. Here, we can assume that Ds = Dr, = Drs = D. We have chosen that cs(0) = cr =a. Equations 2-4 are transformed to a dimensionless state by introducing the following parameters:

Related Figures (6)

Fig. 2 Dimensionless concentration profiles C; plotted from Eqs. 13-15 for all values of dimensionless parameter N when M = 0.1. Solid lines represent the analytical solution obtained in this work; dotted lines represent the numerical solution
Fig. 2 Dimensionless concentration profiles C; plotted from Eqs. 13-15 for all values of dimensionless parameter N when M = 0.1. Solid lines represent the analytical solution obtained in this work; dotted lines represent the numerical solution
Fig. 3 Dimensionless concentration profiles C; plotted from Eqs. 13-15 for all values of dimensionless parameter N when M = 1. Solid lines represent the analytical solution obtained in this work; dotted lines represent the numerical solution
Fig. 3 Dimensionless concentration profiles C; plotted from Eqs. 13-15 for all values of dimensionless parameter N when M = 1. Solid lines represent the analytical solution obtained in this work; dotted lines represent the numerical solution
Fig. 5 A plot of dimensionless concentration profiles C; through a membrane. Curves are plotted using Eqs. 13-15. Solid lines represent the analytical solution presented in this work; dotted lines represent the numerical solution Fig. 4 Dimensionless concentration profiles C; plotted from Eqs. 13-15 for all values of dimensionless parameter N when M = 5. Solid lines represent the analytical solution obtained in this work; dotted lines represent the numerical solution
Fig. 5 A plot of dimensionless concentration profiles C; through a membrane. Curves are plotted using Eqs. 13-15. Solid lines represent the analytical solution presented in this work; dotted lines represent the numerical solution Fig. 4 Dimensionless concentration profiles C; plotted from Eqs. 13-15 for all values of dimensionless parameter N when M = 5. Solid lines represent the analytical solution obtained in this work; dotted lines represent the numerical solution
Figures 2, 3, and 4 represent a series of dimensionless concentration species for various values of the dimen- sionless parameters N and M. From these figures, the concentration species of Cj and C7, reach the maximum value | at X = 0 and the minimum value 0 at X = 1. The concentration C7; reaches the maximum value | at X = 1 and the minimum value 0 at X = 0. Moreover, all con- centration species are linear when N = 0.1. It is evident that the dimensionless concentration Cj slowly increases when JN increases. Furthermore, we noticed that there is a simultaneous increase in the values of concentration C7 as N increases and a simultaneous decrease in the values of concentration C7, as N decreases. In addition, our analyt- ical results were compared with the simulation results. The dimensionless concentration species C; is shown in Fig. 5 for M = 0.05 and N = 50. From this figure, it is evident that the concentration Cj increases initially, attains its maximum value at X=0O.1 and then decreases. We
Figures 2, 3, and 4 represent a series of dimensionless concentration species for various values of the dimen- sionless parameters N and M. From these figures, the concentration species of Cj and C7, reach the maximum value | at X = 0 and the minimum value 0 at X = 1. The concentration C7; reaches the maximum value | at X = 1 and the minimum value 0 at X = 0. Moreover, all con- centration species are linear when N = 0.1. It is evident that the dimensionless concentration Cj slowly increases when JN increases. Furthermore, we noticed that there is a simultaneous increase in the values of concentration C7 as N increases and a simultaneous decrease in the values of concentration C7, as N decreases. In addition, our analyt- ical results were compared with the simulation results. The dimensionless concentration species C; is shown in Fig. 5 for M = 0.05 and N = 50. From this figure, it is evident that the concentration Cj increases initially, attains its maximum value at X=0O.1 and then decreases. We
Adding Eqs. 34 and 37, we get Eq. 13 in the text. Similarly, we can get Eqs. 14 and 15.
Adding Eqs. 34 and 37, we get Eq. 13 in the text. Similarly, we can get Eqs. 14 and 15.
580 California St., Suite 400
San Francisco, CA, 94104
© 2025 Academia. All rights reserved