What is Oldroyd b fluid?
The Oldroyd-B fluid is a special non-Newtonian fluids and its transport behavior cannot be properly described by the typical relation between shear rate and shear stress in a simple shear flow. For this reason many models of constitutive equations have been proposed for these fluids [1], [2], [3].
What is Giesekus fluid?
Giesekus, “A simple constitutive equation for polymer fluids based on the concept of deformation dependent tensorial mobility,” J. Non-Newtonian Fluid Mech. Non-Newtonian Fluid Mech.
What is Rate type fluids?
Rate type constitutive theories are developed for describing the response of inhomogeneous fluids whose material properties can depend upon the shear rate and the mean normal stress, within a general thermodynamic setting.
How is Weissenberg number calculated?
The Weissenberg number W e = λ 1 U / L is since the characteristic length and the characteristic velocity speed are both equal to 1 for this problem.
How is Deborah number calculated?
It is defined as the ratio of viscous forces to elastic forces of a material which is equal to the relaxation time times the shear or strain rate: Wi = λdγ / dt or Wi = λ·dε / dt. The Weissenberg number can be used to describe the flow of a material with a constant stretch history like simple shear.
What is shear rate in fluids?
Shear rate is the rate at which a fluid is sheared or “worked” during flow. In more technical terms, it is the rate at which fluid layers or laminae move past each other. Shear rate is determined by both the geometry and speed of the flow.
What is Rod climbing?
The rod climbing effect, also known as Weissenberg effect, occurs in non-Newtonian fluids due to imbalance in normal stresses which pull the liquid inwards and make it climb.
What is Pseudoplastic fluid?
In contrast to a Bingham fluid, a pseudoplastic fluid is a fluid that increases viscosity as force is applied. A typical example is a suspension of cornstarch in water with a concentration of one to one. This cornstarch behaves like water when no force is applied; however, it is solidified as force is applied.
What does a high Deborah number mean?
At higher Deborah numbers, the material behavior enters the non-Newtonian regime, increasingly dominated by elasticity and demonstrating solidlike behavior. For example, for a Hookean elastic solid, the relaxation time tc will be infinite and it will vanish for a Newtonian viscous fluid.
Is blood Newtonian fluid?
Because of that, blood behaves as a non-Newtonian fluid. As such, the viscosity of blood varies with shear rate. Blood becomes less viscous at high shear rates like those experienced with increased flow such as during exercise or in peak-systole. Therefore, blood is a shear-thinning fluid.
How is viscosity calculated?
There are several formulas and equations to calculate viscosity, the most common of which is Viscosity = (2 x (ball density – liquid density) x g x a^2) ÷ (9 x v), where g = acceleration due to gravity = 9.8 m/s^2, a = radius of ball bearing, and v = velocity of ball bearing through liquid.
How does the Weissenberg effect work?
The Weissenberg effect is a phenomenon that occurs when a spinning rod is inserted into a solution of elastic liquid. Instead of being thrown outward, the solution is drawn towards the rod and rises up around it. This is a direct consequence of the normal stress that acts like a hoop stress around the rod.