Tubular membranes of silicone rubber can be used for bubble less aeration of water. A cross section

Question:

Tubular membranes of silicone rubber can be used for €œbubble less€ aeration of water. A cross section of the tube is shown in the figure (right-hand column). Pure oxygen (O2) gas is pressurized to 2.0 atm inside a section of silicone rubber tubing of inner diameter 12.7 mm and wall thickness 3.2 mm. The tubing is immersed in a large volume of an aqueous solution. Silicone rubber is permeable to oxygen (O2) gas, but is also hydrophobic so that water does not seep through the rubber. The O2gas €œdissolves€ into the silicone rubber with a concentration C (mole A/m3silicone rubber) diffuses through the wall of the tubing, and then re-dissolves into the water of concentration CAˆž, which is maintained at a concentration of 0.005 mol/m3.  

a. Develop an equation, in final integrated form, to predict the O2 flux across the tube wall from r = R1 to r = Ro, using C'A to describe the concentration of O2 dissolved in the tube wall material itself. State all assumptions. You may neglect convective mass-transfer resistances associated with the liquid boundary layer surrounding the tube. 

b. At the conditions given above, determine the flux of oxygen to the water (r = Ro) if the well-mixed aqueous phase maintains the dissolved O2 concentration at 0.005 mole O2/m3

Potentially useful data: The solubility of dissolved O2 in the silicone polymer is defined by a linear relationship pA = C'A/S, where PA is the partial pressure of O2 gas (atm), S is the solubility constant of O2 dissolved in the silicone polymer (S = 3.15 × 10-3 mmole O2/cm3 · atm at 25°C), and C'A is the concentration of O2 dissolved in the silicone rubber (mmol O2/cm3). The solubility of O2 gas in silicone rubber in contact with 2.0 atm O2 gas at 25°C is C'A* = 6.30 mole O2/m3 of silicone rubber. The Henry€™s law constant (H) of 0, in water is 078 atm · m3 water/gmole at 25°C. Silicone tube cross section r = R, r = R. %3D 100% O2 gas Liquid water 0.005 mole O,/m³ 2.0 atm 12.7 mm 3.2-mm wall

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For  book-img-for-question

Fundamentals Of Momentum Heat And Mass Transfer

ISBN: 9781118947463

6th Edition

Authors: James Welty, Gregory L. Rorrer, David G. Foster

Question Posted: