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As the operator applies downward pressure to the glass, some of the air escapes between the stenciled hexagons. However, some air is trapped once the paste is compressed such that the dots meet: If y …

If the latter (former) is relatively small, then the material resembles an ideal spring (damper), and the viscosity is negligible (predominant). … If you wish, you could call $\eta^{\prime\prime}$ the dynamic or effective viscosity, but that might invite confusion, as $\eta^\star$ is also sometimes called the dynamic viscosity. …

It's convenient when modeling viscosity to relate the shear stress $\tau$ to the rate of change $\frac{d\gamma}{dt}$ in a corner angle that was originally 90°, as this parameter is easily accessible in … experiments: $$\tau\sim\frac{d\gamma}{dt}=\dot\gamma;$$ $$\tau=\mu\dot\gamma.$$ We call the constant of proportionality the viscosity $\mu$. …

You've identified a failure mode (or edge case, or limitation) of applying certain lumped-component models: It's not generally meaningful to talk about their associated length. Relatedly, we never wor …

The idealized viscous liquid (represented by the lumped-component damper/dashpot in the Maxwell model) has infinite stiffness for instantaneous movements. You state this yourself in your constitutive …

The equation you give is derived under the following conditions (I quote from Bird et al.'s Transfer Phenomena): (a) The flow is laminar. (b) The density is constant ("incompressible flow"). (c) The f …

You've essentially discovered a failure mode (or edge case, or limitation) of applying certain lumped-component models: They're all assumed to have the same length, or alternatively, it's not meaningf …

Shear stress arises whenever we load a material in any way other than equitriaxial stress. (Equitrixial stress, also known as dilatational stress, corresponds to equal normal stresses in all three ort …

Its constitutive equation is $$\sigma(t)=\mu\dot\varepsilon(t),$$ where $\mu$ is the viscosity; note that we're now working with the time derivative of the strain. …

You could ask the same question about an object hung from a mechanical spring: If the forces at the final equilibrium position sum to zero, why isn’t the object still moving, or why did it ever decele …

The volumetric or dilatational stress can be defined as one-third the trace of the stress tensor. If a body is exposed to hydrostatic pressure $P$ alone, then the external forces act as normal to the …

An unbalanced shear load on an element causes both translation and rotation; by the parallel-axis theorem, the load can be replaced by a force acting on the center of the element plus a moment around …