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396 CHAPTEA 10 MASS TRANSFEA 10.4 Controlled DRUG Delivery BY DISSOLUTION OF PILL COATING 10.4.1 Concepts Demonstrated Unsteady-state dissolution of a solid into a liquid
396 CHAPTEA 10 MASS TRANSFEA 10.4 Controlled DRUG Delivery BY DISSOLUTION OF PILL COATING 10.4.1 Concepts Demonstrated Unsteady-state dissolution of a solid into a liquid with transport described by a mass transfer coefficient with subsequent reaction. 10.4.2 Numerical Methods Utilized Solution of simultaneous ordinary differential equations with known initial conditions that have conditional slterations during the numerical solution. 10.4.3 Problem Statement (Adapted from Fogler, 4 p. 600) The pill to deliver a particular drug has a solid spherical inner core of pure drug D and is surrounded by a spherical outer coating of A that makes the pill palatable and helps to control the drug release. The outer coating and the drug dissolve at different rates in the stomach due to their difference in solubilities. Let CAS= concentration of coating in the stomach in mgcm3,CDS= concentration of drug in the stomach in mg/cm3, and CDB= concentration of drug in the body in mg/kg. Three different pill formulations are available: Pill 1 - Diameter of A=5mm, Diameter of D=3mm Pill 2 - Diameter of A=4mm, Diameter of D=3mm Pill 3-Diameter of A=3.5mm, Diameter of D=3mm Additional Information and Data Amount of drug in inner core of each pill =20mg Density of inner and outer layers =1414.7mg/cm3 Solubility of outer pill layer at stomach conditions =SA=1.0mg/cm3 Solubility of inner drug core at stomach conditions =SD=0.4mg/cm3 Volume of fluid in stomach =V=1.2 liters Residence time in stomach ==V/v0=4 hours, where v0 is the volumetric flow rate Typical body weight W=75kg Sherwood number =NSh=kLDABDD=2 (see Problem 10.3 for details) Effective Diffusivities of A and D in stomach DA=DD=0.6cm2/min A person takes all three pills at the same time. Assume that the stomach is well mixed and that the pills remain in the stomach while they are dissolving. (a) Plot CAS and CDS as a function of time for up to 12 hours after the pills are taken. (b) If the drug is absorbed into the body (from solution in the stomach into the blood stream) by an effective mass transfer rate of 10CDS in mg/ min, plot CAS and CDS under these conditions. (c) If the body metabolizes the drug with an effective first-order reaction rate of 1.0CDB in mg/kgmin, plot CDB in the body under the conditions of (b). (d) Under the conditions of (c), what is the estimated time that CDB is greater than 2.0103mg/kg, which is the minimum effective concentration level for the drug? (e) Please suggest a more effective layering of the three pills with the drug placed only in the center to increase the time for the effective level concentration of 2.0108mg/kg under the same conditions
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