Newton's law for flow of biological fluids?

Answer 1

What is Viscosity of the Fluid?Viscosity is very important property of the fluids. While considering the fluid for various applications it is crucial to consider the viscosity of the fluid. The fluid flows in the form of various layers as shown in figure below. The top layer of the fluid flows at higher speeds, while the layers below it move at slightly lesser speed. Thus the layers of the fluid offer resistance to the flow of the adjoining layers. This property of the fluid is called as the viscosity of the fluid.

Viscosity of the fluid is defined as the property of the fluid that tends to resist the movement of one layer of the fluid over adjacent layer of the fluid.

Derivation of Viscosity Formula from Newton's Law of ViscosityIn the figure shown above, let us consider two layers separated by small distance dy. Let us suppose that the velocity of the lower layer is u, so the velocity of the upper layer will be u+du, where du is the small incremental velocity. Now, the top layer tends to offer resistance to the flow of bottom layer and bottom layer offers resistance to the flow of top layer.

The resistance to the flow is offered in the form of shear stress. Thus the adjoining layers of the fluid cause shear stress on the adjoining layers. The shear stress among the various layers of the fluid depends on rate of change of the velocity of the fluid with respect to its distance 'y' from the lowest layer of the fluid. Shear stress is denoted by τ (tau). This is also called as Newton's law of viscosity. It states that shear stress between various layers of the fluid is directly proportional to rate of shear strain.

Shear stress τ (tau) is given by: (refer the fig I linked)

Here µ (mu) is called as the coefficient of dynamic viscosity or merely viscosity. The term du/dy is the rate of shear strain or rate of shear deformation or velocity gradient. Thus viscosity is also defined as the shear stress required to produce unit rate of shear strain.

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Answer 2

Newton's law of viscosity states that the rate of flow of a biological fluid (such as blood) is directly proportional to the applied shear stress and inversely proportional to the viscosity of the fluid. This relationship helps explain how biological fluids behave under different conditions, such as in blood vessels where the flow must overcome resistance from vessel walls.