Fluid Viscosity and Shear Flow

Viscosity Basics

• In gases and liquids, molecules move freely and collide which results in exchange of momentum
• Shear stresses in real fluids occur due to colliding particles exchanging momentum; this is called viscosity
• Viscosity is a fluid's property describing resistance to shear deformation
• Viscosity can be thought of as a measure of a fluid's fluidity

Ideal vs. Real Flow

• Viscosity influences the velocity profile of a real fluid flowing between two solid boundaries
• At boundaries, the fluid velocity becomes zero, adhering to the walls which is known as the no-slip condition

Sheared Flow

• Laminar flow occurs when fluid flows in parallel layers
• Viscosity dominates in laminar flow
• Adjacent fluid particles travel different distances over time in sheared flow
• Shear stress, denoted by τ, exists between fluid layers

Coefficient of Viscosity

• In laminar flow of Newtonian fluids, shear stress is proportional to the velocity gradient (dv/dy)
• The constant of proportionality (µ) is known as absolute viscosity or dynamic viscosity
• The formula for this is: τ = µ(dv/dy)
• μ is measured in units of Pa s, kg/(m s), or Ns/m²

Kinematic Viscosity

• The coefficient of kinematic viscosity (ν) is also frequently used
• The formula is: ν = µ/ρ, where ρ is fluid density
• Kinematic viscosity (ν) is measured in units of m²/s

Calculating the Coefficient of Viscosity

• The bottom plate is held stationary while the top plate moves at a constant velocity due to a force (F)
• The fluid between the plates undergoes shearing, creating a velocity gradient
• Shear stress is defined as τ = F/A, where A is the area of the top plate in contact with the fluid

Viscosity Types

• The gradient of the curve gives the coefficient of viscosity
• Dilatant (shear thickening) fluids increase in viscosity with the rate of shear strain
• Pseudoplastic (shear thinning) fluids decrease in viscosity with the rate of shear strain

Flow Regimes: Laminar and Turbulent Flow

• Viscosity allows for two distinct flow regimes: laminar and turbulent
• Laminar flow occurs when fluid path lines are smooth and regular
• Turbulent flow occurs when fluid motion is irregular
• Turbulent flow is disorganized, chaotic, unsteady, and three-dimensional