Blood Flow as a Casson Fluid
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 …show more content…
The final part of the problem is where the actual modeling can come in. What happens when the core radius is set to zero? What happens when the core radius is set equal to the wall radius? What does that pesky K even mean!?
Well, the K value is just a coefficient or constant that helps differentiate the equations for blood from that of a Newtonian fluid. Without the K value, the equations that describe Casson fluids would no longer describe Casson fluids, but something else entirely. Because the K is really just a scalar on the viscosity of the fluid in question, as K increases the volumetric flow rate decreases. This is usually true for all fluids: as viscosity goes up, so flow rate goes down.
As the core radius goes to zero, all the Rc/R values in the final equation (above) go to zero. This makes the entire bracketed portion 1. Because of this, the fluid is no longer effected by the core not flowing and the velocity profile resembles that of a Newtonian fluid! The volumetric flow rate is no longer being decreased by the bracketed section and Q increases proportional to how close to zero Rc …show more content…
Being able to model the behavior of blood as it becomes more viscous or has increased forces on it (stresses or pressure) can help create preventative and reparative treatments for people and animals suffering from arterial or heart diseases. We can create materials and artificial arteries that mimic the physical properties of real arteries, helping to maintain healthy blood flow if a person needs repairs. We can estimate the side effects of certain treatments or different injuries to the cardiovascular system!
This work is one way that engineers can help save lives and increase the average lifespan of a person. Future work in this field would include studying how the porosity and constant branching effects the flow of blood through a network of arteries. Or how chemical imbalances (high blood suger, sodium, pH levels, etc) in the blood can affect how blood flows through the veins! Obviously many of the chemical aspects of blood would affect the physical properties of how it flows and interacts with other parts of the cardio
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 …show more content…
The final part of the problem is where the actual modeling can come in. What happens when the core radius is set to zero? What happens when the core radius is set equal to the wall radius? What does that pesky K even mean!?
Well, the K value is just a coefficient or constant that helps differentiate the equations for blood from that of a Newtonian fluid. Without the K value, the equations that describe Casson fluids would no longer describe Casson fluids, but something else entirely. Because the K is really just a scalar on the viscosity of the fluid in question, as K increases the volumetric flow rate decreases. This is usually true for all fluids: as viscosity goes up, so flow rate goes down.
As the core radius goes to zero, all the Rc/R values in the final equation (above) go to zero. This makes the entire bracketed portion 1. Because of this, the fluid is no longer effected by the core not flowing and the velocity profile resembles that of a Newtonian fluid! The volumetric flow rate is no longer being decreased by the bracketed section and Q increases proportional to how close to zero Rc …show more content…
Being able to model the behavior of blood as it becomes more viscous or has increased forces on it (stresses or pressure) can help create preventative and reparative treatments for people and animals suffering from arterial or heart diseases. We can create materials and artificial arteries that mimic the physical properties of real arteries, helping to maintain healthy blood flow if a person needs repairs. We can estimate the side effects of certain treatments or different injuries to the cardiovascular system!
This work is one way that engineers can help save lives and increase the average lifespan of a person. Future work in this field would include studying how the porosity and constant branching effects the flow of blood through a network of arteries. Or how chemical imbalances (high blood suger, sodium, pH levels, etc) in the blood can affect how blood flows through the veins! Obviously many of the chemical aspects of blood would affect the physical properties of how it flows and interacts with other parts of the cardio