Rheo-NMR Fundamentals

Mechanical rheometry requires a measurement of both stress and strain (or strain rate) and is thus usually performed in a simple rotating geometry configuration. Typical examples are the cone-and-plate and cylindrical Couette devices [1,14]. In stress-controlled rheometric measurements one applies a known stress and measures the deformational response of the material. In strain-controlled rheometry one applies a deformation flow and measures the stress. Stress-controlled rheometry requires the use of specialized torque transducers in conjunction with low friction air-bearing drive in which the control of torque and the measurement of strain is integrated. By contrast, strain-controlled rheometry is generally performed with a motor drive to rotate one surface of the cell and a separate torque transducer to measure the resultant torque on the other surface. 

While it is possible to perform rheo-NMR in large scale MRI systems, the use of microscopic geometries with sub-millilitre volumes is highly desirable, especially where expensive speciality materials are to be examined. Such sample volumes 

We will now describe the basic hydrodynamic relationships applicable in the case of steady-state flow in which the Eulerian velocity field is time-independent and written as v(r). Here the rate of strain elements are given by [1] 

Simple shear (also known as planar Couette flow) is achieved when fluid is contained between two plane parallel plates in relative in-plane motion. If the velocity direction is taken to be x, one has x = y, all other xa 3 zero and 

The coordinates (x, y, z) define the (velocity, gradient, vorticity) axes, respectively. For non-Newtonian viscoelastic liquids, such flow results not only in shear stress, but in anisotropic normal stresses, describable by the first and second normal stress differences (oxx-Oyy) and (o - ozz). The shear-rate dependent viscosity and normal stress coefficients are then [1] 

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