Blood Flow As A Casson Fluid Essay
1 THE PROBELM
This problem was chosen from Problems for Biomedical Fluid Mechanics and Transport Phenomena section 8, because of my interest in biomedical engineering. How the body works on the most fundamental chemical and physical levels is something that has always fascinated me. This problem, and others in the section on blood flow, offered me a chance to delve deeper into how the body works as well as transport phenomena.
The problem gave us a solved velocity distribution for flow of a Casson fluid in a very narrow blood vessel. The blood in this case is treated as a two phase fluid where the phases are governed by a constitutive equation relating shear stress, viscosity, and shear rate. This equation would be replaced by Newton’s law of Viscosity if the fluid was Newtonian, but since it is not, a separate specific equation (or model) is needed to define the velocity and flow rate of blood in this vessel. The relations shown above (taken from the same chapter as the problem) are used to describe the fluid when the shear stress is above or below a certain yield stress. Normally, only solids and other pseudoplastics have a yield stress which, when met, will cause the object to have fluid-like motion. This only applies to blood because of the nature of the particles floating in plasma. These particles will deform and align themselves with the direction of flow when faced with a stress. Because of this property, an increase in shear stress…