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Your startup company is proposing a design of an artificial liver that can remove a specific toxin,c, from patients by passing their blood through the lumen of a hollow fiber tube at an average laminar velocity of vo. The tube has a length 10ẞr cm and has a reactive surface material at r = R that consumes the toxin via a first-order reaction kinetics. 2.1. (10%) Starting with the conservation of mass, develop a dimensionless closed-form mathematical model that will allow you to estimate the rate of removal of the toxin based on the device parameters. 2.2. (90%) Using your model, do a case study assuming k₁ = 1.125 × 10¯s−1 and Deff 1 x 10-6 -6 cm² S ' = and a partition coefficient for c of = 0.2, provide an effective design with numerical values that optimizes the rate of removal of c while the flow remains in the laminar regime. Assume the boundary conditions in the radial direction are r = = 0, = = 0, r = R,-Deff = kƒ (Co - c) where kƒ is an appropriate mass dc dr transfer coefficient. dc dx\r=R

Your startup company is proposing a design of an artificial liver that can remove a specific toxin,c, from patients by passing their blood through the lumen of a hollow fiber tube at an average laminar velocity of vo. The tube has a length 10ẞr cm and has a reactive surface material at r = R that consumes the toxin via a first-order reaction kinetics. 2.1. (10%) Starting with the conservation of mass, develop a dimensionless closed-form mathematical model that will allow you to estimate the rate of removal of the toxin based on the device parameters. 2.2. (90%) Using your model, do a case study assuming k₁ = 1.125 × 10¯s−1 and Deff 1 x 10-6 -6 cm² S ' = and a partition coefficient for c of = 0.2, provide an effective design with numerical values that optimizes the rate of removal of c while the flow remains in the laminar regime. Assume the boundary conditions in the radial direction are r = = 0, = = 0, r = R,-Deff = kƒ (Co - c) where kƒ is an appropriate mass dc dr transfer coefficient. dc dx\r=R

Human Anatomy & Physiology (11th Edition)
Human Anatomy & Physiology (11th Edition)
11th Edition
ISBN:9780134580999
Author:Elaine N. Marieb, Katja N. Hoehn
Publisher:Elaine N. Marieb, Katja N. Hoehn
Chapter1: The Human Body: An Orientation
Section: Chapter Questions
Problem 1RQ: The correct sequence of levels forming the structural hierarchy is A. (a) organ, organ system,...
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Your startup company is proposing a design of an artificial liver that can remove a specific toxin,c, from patients by passing their blood through the lumen of a hollow fiber tube at an average laminar velocity of vo. The tube has a length 10ẞr cm and has a reactive surface material at r = R that consumes the toxin via a first-order reaction kinetics. 2.1. (10%) Starting with the conservation of mass, develop a dimensionless closed-form mathematical model that will allow you to estimate the rate of removal of the toxin based on the device parameters. 2.2. (90%) Using your model, do a case study assuming k₁ = 1.125 × 10¯s-1 and Deff: 1 × 10-6 cm² S ' = and a partition coefficient for c of = 0.2, provide an effective design with numerical values that optimizes the rate of removal of c while the flow remains in the laminar regime. Assume the boundary conditions in the radial direction are r = 0, ac = dc dr dc = 0, r = R, -Deff ax | | _ = kƒ(Co - c) where kƒ is an appropriate mass transfer coefficient. dx r=R
Transcribed Image Text:Your startup company is proposing a design of an artificial liver that can remove a specific toxin,c, from patients by passing their blood through the lumen of a hollow fiber tube at an average laminar velocity of vo. The tube has a length 10ẞr cm and has a reactive surface material at r = R that consumes the toxin via a first-order reaction kinetics. 2.1. (10%) Starting with the conservation of mass, develop a dimensionless closed-form mathematical model that will allow you to estimate the rate of removal of the toxin based on the device parameters. 2.2. (90%) Using your model, do a case study assuming k₁ = 1.125 × 10¯s-1 and Deff: 1 × 10-6 cm² S ' = and a partition coefficient for c of = 0.2, provide an effective design with numerical values that optimizes the rate of removal of c while the flow remains in the laminar regime. Assume the boundary conditions in the radial direction are r = 0, ac = dc dr dc = 0, r = R, -Deff ax | | _ = kƒ(Co - c) where kƒ is an appropriate mass transfer coefficient. dx r=R
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