In addition to the quantitative specification above, it is useful to have a concept of the microstructure of a liquid, since that is the underlying physical basis for its rheological properties. A liquid with isotropic structure is one with perfectly random microstructure organization; in an anisotropic liquid the microstructure has a preferential directional orientation. The organization of the structural elements determines the way the liquid will flow, and microstructural organization is influenced by three distinct flow factors:

 Factor 1. A liquid at rest (no flow) is isotropic.

 Factor 2. Flowing liquid may become anisotropic.

 Factor 3. Flow induced anisotropy decays when flow is stopped.

Anisotropic particles (or macromolecules) in a liquid may collect together to form even larger anisotropic groups, but overall if their orientations are random, the liquid remains isotropic. Examples of anisotropic particles are bentonite plates, red blood cells, tobacco mosaic virus, biological macromolecules (hyaluronic acid, myosin, collagen, Xanthan gum, Dextran, etc.), and synthetic polymer chains.

FIGURE 1. Spherical sections of two types of suspended particles in a liquid. Both the rod type particles and the coiled particles are randomly oriented throughout the volume so that the suspensions are isotropic.

The shear forces due to flow cause an overall anisotropic reorganization of the microstructure of the liquid. The work done in producing the anisotropic global structure and accompanying flow is of two types: a recoverable energy associated with structure formation which is identified with the elasticity, and a lost energy dissipated in structural formation and sliding which is associated with the viscosity. Generally the anisotropy is increased with the rate of flow and accompanying increase of the shear forces.

Neither the development nor loss of anisotropy is instantaneous because some finite time is required for the microstructure to change. The relaxation time is a measure of the rate at which the global structure changes in response to the change in flow. Thus, with changing flow, the degree of anisotropy changes with the speed and time duration of the flow. When returning to the quiescent state (no flow), the liquid relaxes to the original global isotropic condition . The force of reorientation to the isotropic condition of rigid microstructural elements is due to Brownian motion, while shape recovery of flexible microstructural elements is aided by internal springs. The larger the local structures, the longer the relaxation time.

FIGURE 3. When the flow is suddenly stopped, the initial anisotropy begins decaying to the final isotropic limit. Correspondingly, the anisotropy will decrease in a manner determined by the type of suspended particles. Treating this decrease as an exponential function of time, an apparent relaxation time is defined as the time for the initial anisotropy to decrease by a factor of 1/e = 0.3678.

When a viscoelastic liquid is subjected to oscillatory flow, the anisotropic stress, strain, and shear rate induce global anisotropy by rearrangement of the microstructure of the liquid. The anisotropy will vary during the flow cycle in an amount determined by the size of the period of oscillation and the relaxation time.

With increasing amplitude of oscillatory flow, the anisotropic structure of the liquid is called on to store progressively increasing energy. But the ability of the flow-induced anisotropic microstructure to store energy is limited by its nature. As the shear strain exceeds unit value, the type of structure present undergoes a change which is identified by a maximum value of elastic stress (i.e. the maximum attainable energy stored per unit volume per unit strain). This is termed the "elastic yield stress".

While the microstructural relaxation time governs the structural response occurring on the time scale of the period of rapid changes in flow, some materials exhibit an additional change in microstructure that occurs over a much longer time scale, an effect called thixotropy.

FIGURE 4. The elastic yield stress is identified by a maximum in the elastic yield stress which occurs near a shear strain of 1. The maximum locates the elastic yield stress and the yield strain. Note that the stress is the energy per unit volume/unit strain, and the elastic yield stress is a maximum in the storage capacity of the elastic microstructure.

In oscillatory tests of thixotropic viscoelastic materials, changes in viscosity and elasticity appear over a period of time that is substantially longer than the period of oscillation. For example, when flow is suddenly initiated, the viscosity and elasticity change with time while the oscillatory flow is maintained constant. Similarly, suddenly reducing the flow yields viscoelasticity that changes with time following the reduction. In some liquids these thixotropic effects also are seen when the viscosity and elasticity are measured for stepwise increasing amplitudes, then followed by decreasing amplitudes. In this situation the viscoelasticity is constantly trying to "catch up" with the flow condition and consequently the viscoelasticity for increasing flows differs from that for decreasing flows.

Increasing flow usually degrades the microstructure while at the same time increasing anisotropy, but in some liquids flow can induce a microstructural enhancement, giving rise to dilatancy. This property is identified by an anomalous increase in the viscosity or elasticity above the decrease expected with increasing flow amplitude. This condition occurs when the microstructure changes into a form that has an enhanced capacity for storage of elastic energy.

FIGURE 5. A thixotropic liquid exhibits a time dependent response to change in shear rate. Two types of time dependent flows are a suddenly initiated constant shear rate (left figure) and an incremental increase and decrease of shear rate (right figure). In both cases, the viscosity and elasticity change slowly with time.

Dilatancy is observed in measurement of the shear rate dependence of the viscosity and elasticity while holding the frequency of oscillatory flow constant.

 Thank you for visiting our technical note page.
Contact us if you would like to discuss this or any other rheological topic.