Viscosity

From Chemepedia
Figure 1. Viscosities

Viscosity () is the property of a fluid that resists movement between adjacent layers in the fluid. Viscosity can be thought of as a fluids resistance to an applied force [1]. Viscosity is similar to shear forces in solids. For example, in figure 1 the blue fluid has a lower viscosity than the orange fluid. It can be said that the orange fluid has a greater resistance to forces applied to it.

Figure 2. Laminar shear

If you have two infinite in dimension parallel plates as in Figure 2 and the top plate is moving at a constant velocity while the bottom plate is stationary, the velocity of the fluid touching the top plate is the same as the upper plates velocity. However the velocity of the fluid layer directly under it is slightly slower. This pattern of decreasing velocity happens as you go down in the y direction. The fluid layer that is touching the bottom stationary plate has a velocity equal to 0. This force that is responsible for the change in velocity of the fluid is viscous drag. Newton's Law of Viscosity for a laminar flow is,


            (1)

where:

  • is the force applied to the top plate
  • is the area of each plate
  • is the proportionality constant, viscosity of the fluid
  • is the velocity in the z direction
  • is the distance in the y direction

In equation (1), as approaches 0, in other words if the velocity does not change linearly with respect to y, then:

            (2)

In equation (2), which is applicable for SI units, is the shear stress or force per unit area () and is in units of N/m2. If we wish to get the equation applicable for English units:

            (3)

Where lbm*ft/lbf*s2.

In equation (3) the gravitational conversion factor () must be added in. Here is in units of lbf/ft2. The units of viscosity () in the cgs system are g/cm*s, also known as poise.

Useful Conversions When Working With Viscosity

cp poise g/cm*s

Pa*s N*s/m2 kg/m*s cp lbm/ft*s

References

  1. Geankoplis, Christie John. Transport Processes and Separation Process Principles. Pearson Education Inc, 2015. ISBN 0-13-101367-X. Book.