Viscosity, liquid flow, and energy conservation in continuum mechanics

Viscosity describes how easily a liquid can flow under an applied stress. Dimensionally, it is the product of an elastic modulus and a timescale. The significance of these quantities in determining the viscosity of a liquid can be seen after considering a simple model for liquid flow, in which the flow results from the instantaneous storage of elastic energy and its subsequent dissipation. The modulus then corresponds to the short-time elastic modulus and the timescale is that associated with particle rearrangements. Interestingly, applying conservation of energy, as introduced in continuum mechanics, naturally provides the basis for this way to think about liquid flow. Additionally, the result naturally connects to viscoelastic behavior, emphasizing its applicability to liquids in general, and opening up interesting possibilities to expand the contents often taught in continuum mechanics courses.