scholarly journals Mathematical Model for Estimating Parameters of Swelling Drug Delivery Devices in a Two-Phase Release

Polymers ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2921
Author(s):  
Amanina Setapa ◽  
Naveed Ahmad ◽  
Shalela Mohd Mahali ◽  
Mohd Cairul Iqbal Mohd Amin
Keyword(s):  
Mathematical Model ◽  
Drug Delivery ◽  
Diffusion Coefficient ◽  
Drug Release ◽  
Effective Diffusion Coefficient ◽  
Moving Boundary ◽  
Effective Diffusion ◽  
Moving Boundary Problem ◽  
Two Phase ◽  
Drug Delivery Devices

Various swelling drug delivery devices are promising materials for control drug delivery because of their ability to swell and release entrapped therapeutics, in response to physiological stimuli. Previously, many mathematical models have been developed to predict the mechanism of drug release from a swelling device. However, some of these models do not consider the changes in diffusion behaviour as the device swells. Therefore, we used a two-phase approach to simplify the mathematical model considering the effect of swelling on the diffusion coefficient. We began by defining a moving boundary problem to consider the swelling process. Landau transformation was used for mitigating the moving boundary problem. The transformed problem was analytically solved using the separation of variables method. Further, the analytical solution was extended to include the drug release in two phases where each phase has distinct diffusion coefficient and continuity condition was applied. The newly developed model was validated by the experimental data of bacterial cellulose hydrogels using the LSQCURVEFIT function in MATLAB. The numerical test showed that the new model exhibited notable improvement in curve fitting, and it was observed that the initial effective diffusion coefficient of the swelling device was lower than the later effective diffusion coefficient.

scholarly journals NUMERICAL INVESTIGATION OF THE RELEASE OF DRUG FROM A DRUG-DELIVERY DEVICE

2012 ◽  
Vol 09 ◽  
pp. 119-126
Author(s):  
M. GARSHASBI ◽  
H. KAMAL GHARIBI
Keyword(s):  
Drug Delivery ◽  
Moving Boundary ◽  
Numerical Solutions ◽  
The Body ◽  
Moving Boundary Problem ◽  
Delivery Device ◽  
Drug Delivery Device ◽  
Finite Differences Method ◽  
Dominant Process ◽  
Drug Delivery Devices

In this study a mathematical model for the release of drug from porous, nonswelling transdermal drug-delivery devices to a perfect sink is considered. The drug is postulated to diffuse in both the solvent-filled pores and the body of the polymer. The limit in which the dissolution of drug is the dominant process is considered and a moving boundary problem governing drug release is derived. This model is solved numerically under some spacial conditions. Furthermore, another limit case in which the dissolution process is not so rapid is investigated and analytical and numerical solutions based on Fourier series solution and finite differences method are derived. Finally, the numerical and analytical solutions are compared to show the ability of the proposed numerical procedures.

Diffusion of Heavy Oil in SiO2 Model Catalyst and FCC Catalyst

2012 ◽  
Vol 550-553 ◽  
pp. 158-163 ◽  
Author(s):  
Zi Yuan Liu ◽  
Sheng Li Chen ◽  
Peng Dong ◽  
Xiu Jun Ge
Keyword(s):  
Diffusion Coefficient ◽  
Pore Size ◽  
Effective Diffusion Coefficient ◽  
Pore Diameter ◽  
Effective Diffusion ◽  
Model Catalyst ◽  
Average Pore ◽  
Diffusion Factor ◽  
Fcc Catalyst ◽  
Fcc Catalysts

Through the measured effective diffusion coefficients of Dagang vacuum residue supercritical fluid extraction and fractionation (SFEF) fractions in FCC catalysts and SiO2model catalysts, the relation between pore size of catalyst and effective diffusion coefficient was researched and the restricted diffusion factor was calculated. The restricted diffusion factor in FCC catalysts is less than 1 and it is 1~2 times larger in catalyst with polystyrene (PS) template than in conventional FCC catalyst without template, indicating that the diffusion of SFEF fractions in the two FCC catalysts is restricted by the pore. When the average molecular diameter is less than 1.8 nm, the diffusion of SFEF fractions in SiO2model catalyst which average pore diameter larger than 5.6 nm is unrestricted. The diffusion is restricted in the catalyst pores of less than 8 nm for SFEF fractions which diameter more than 1.8 nm. The tortuosity factor of SiO2model catalyst is obtained to be 2.87, within the range of empirical value. The effective diffusion coefficient of the SFEF fractions in SiO2model catalyst is two orders of magnitude larger than that in FCC catalyst with the same average pore diameter. This indicate that besides the ratio of molecular diameter to the pore diameter λ, the effective diffusion coefficient is also closely related to the pore structure of catalyst. Because SiO2model catalyst has uniform pore size, the diffusion coefficient can be precisely correlated with pore size of catalyst, so it is a good model material for catalyst internal diffusion investigation.

Diffusion of Zinc in Two-Phase Mg-Al Alloy

2007 ◽  
Vol 263 ◽  
pp. 189-194
Author(s):  
Ivo Stloukal ◽  
Jiří Čermák
Keyword(s):  
Diffusion Coefficient ◽  
Diffusion Coefficients ◽  
Effective Diffusion ◽  
Residual Activity ◽  
Diffusion Path ◽  
Al Alloy ◽  
Serial Sectioning ◽  
Two Phase ◽  
Interphase Boundaries ◽  
The Mean

Coefficient of 65Zn heterodiffusion in Mg17Al12 intermetallic and in eutectic alloy Mg - 33.4 wt. % Al was measured in the temperature region 598 – 698 K using serial sectioning and residual activity methods. Diffusion coefficient of 65Zn in the intermetallic can be written as DI = 1.7 × 10-2 m2 s-1 exp (-155.0 kJ mol-1 / RT). At temperatures T ≥ 648 K, where the mean diffusion path was greater than the mean interlamellar distance in the eutectic, the effective diffusion coefficient Def = 2.7 × 10-2 m2 s-1 exp (-155.1 kJ mol-1 / RT) was evaluated. At two lower temperatures, the diffusion coefficients 65Zn in interphase boundaries were estimated: Db (623 K) = 1.6 × 10-12 m2 s-1 and Db (598 K) = 4.4 × 10-13 m2 s-1.

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