(567bv) On Sharma Number Effects in Design of Extracorporeal Artificial Lung

A de no vo dimensionless group called Sharma number is introduced. It gives the ratio of the bulk mass transfer rate and the relaxational transfer rate. Expression for Sharma number in terms of Maxwell number which is the ration of diffusion rate and relaxational rate and contact time is developed from the Dobbins modification of the Dankwert's surface renewal theory. Danckwert developed the the surface renewal theories for prediction of mass transfer coefficient. He derived the mass transfer coefficient for the general case where the eddies stay at the surface for varied lengths of time and Higbie's penetration theory is a particular case when the contact times of the eddies are a constant. Dobbins noted that whereas the film theory assumes the concentration profile has reached steady state in the time of mass transfer and the Hibbie and Dankwert's theories account for the transient nature of difusion during the eddy contact time, they use of semi-infinite boundary condition. A revisit of Dobbins set of boundary conditions to the governing equation in concentration accounting for the damped wave diffusion and relaxation effects resulted in the identification of a dimensionless group, de no vo. The use of Sharma number and Maxwell number can be used to predict Sherwood number in mass exchangers used in artificial lungs. Extracorporeal devices are made to work outside the human anatomy and are connected to the patient by an arteriovenous shunt. They can be used to remove undersired chemicals from the human anatomy or substitute for a damaged or failed organ.A hollow-fiber artificial lung can be used in extracorporeal circulation to remove carbon dioxide from blood and add oxygen to the blood was patented by Terumo Corp., Japan. This device claims to use less blood and has greater mass transfer efficiency of gas transport across the hollow-fiber surface. The mass exchanger consists of a hollow fiber bundle accomodated along the axial direction of the housing, blood inlet port, blood outlet port, gas venting port. The contact between the gas stream and blood stream can be in counter-current, co-current and cross-current modes of contact. The concentration of solute on the blood side and gas side and amount of oxygen bound to hemoglobin, interface concentrations of gas and blood are important parameters in the operation. The blood and gas side mass transfer coefficients are used and an overall mass transfer coefficient is calcualted. The log mean area of the membrane per unit length, permeability of the membrane and the Henry;s law costant are used. A similar set of equations are developed for Carbon Dioxide.