What Is a Fluid? — Question 9

Question 9

Volume resistance does not classify a fluid

Three samples undergo gentle compression and sustained small shear tests. The idealized observations are summarized below. Sample P is nearly incompressible and reaches a fixed shear deformation. Q is nearly incompressible and continues shearing. R compresses appreciably and continues shearing. The fluid samples are known to be ordinary single-phase liquid or gas under the test conditions.

1. Identify the solid-like sample and assign liquid-like or gas-like behavior to the other two. Which observation separates the solid from the fluids?

2. Assess the claims: “Any material that resists volume change is a solid and “A fluid cannot be in mechanical equilibrium because it offers no resistance.

Question 9 - Solution

Volume resistance does not classify a fluid

(a) Derivation and calculation

Under maintained shear,$$\dot\gamma_P\to0,\qquad Q,R:\ \text{continued deformation}.$$$$\boxed{P:\ \text{solid-like}},\quad\boxed{Q:\ \text{liquid-like}},\quad\boxed{R:\ \text{gas-like}}.$$Small volume change distinguishes Q from R under the stated ordinary-phase assumptions, but does not distinguish P from Q.

(b) Result and interpretation

Compression and shear are separate responses:$$\left|\frac{\Delta V}{V}\right|\ll1\ \not\Rightarrow\ \dot\gamma\to0.$$$$\sum\mathbf F=0,\quad F_t=0,\quad F_n\ne0$$$$\text{are compatible with a fluid at rest}.$$A liquid can strongly resist volume change while lacking persistent static shear resistance.

Physical check

No pressure-versus-volume constitutive law is inferred from these qualitative observations.