Glossary: Cells Under Flow

Shear stress is an example of tangential stress. It acts parallel to a given surface and arises from a force applied parallel to the material surface (shear force). Shear stress (τ) is defined as force per unit area (τ = F/A, where τ = the shear stress, F = the force applied, and A = the cross-sectional area of the material surface).

Shear stress in fluids: In contrast to solids, fluids (liquids and gases) cannot resist deformation. Fluids flow continuously under applied shear force. The shear stress is primarily caused by the internal friction between adjacent layers of fluid in motion (viscosity). For fluids, shear stress τ is determined as a function of the shear rate.

Wall shear stress is the shear force exerted by the fluid in motion to the solid wall of a channel or tube (and vice versa). For example, in blood vessels and flow channels, shear stress acts on the endothelial cells lining the respective walls. This force is sensed by the cells and influences their behavior, morphology, and physiology.

Shear rate is defined as the change in velocity, at which one fluid moves over an adjacent layer. The shear rate is determined by both the vessel geometry and the flow speed, measured in reciprocal seconds (s-1).

Viscosity is the property of a fluid to resist flow that is caused by molecular friction. For example, water flows out of a bottle faster and more easily than honey does. Honey is more viscous than water because it has a higher resistance to flow. The absolute or dynamic viscosity is a measure of how a fluid resists the deformation of shear stress due to its intermolecular friction. It is given by the ratio of shear stress and shear rate. In Newtonian fluids, the viscosity is independent from the flow rate.

The Reynolds number (Re) describes whether a fluid flow is laminar or turbulent. The Reynolds number is given by the ratio of inertial forces to friction forces in in a fluid. This value is dimensionless. Laminar flow occurs at low Reynolds numbers whereas turbulent flow occurs at high Reynolds numbers. The critical Reynolds number, which indicates laminar flow in pipes and biological vessels, is Re=2000. A Reynolds number of above approximately Re 4000 is most likely to represent a turbulent flow.

Please read the section “The Different Types of Flow” for a description of unidirectional, pulsatile, and oscillatory laminar flow, as well as turbulent flow.