Measurement of diffusion in the presence of shear flow

We demonstrate here a method whereby molecular diffusion coefficients may be measured in the presence of the deformational flow field of a rheo-NMR cell. The method, which uses a repetitive CPMG train of rf pulses interspersed with magnetic field gradient pulses, allows the anisotropic diffusion spectrum to be directly probed. We focus on the cylindrical Couette cell, for which the radial, tangential, and axial directions correspond to the hydrodynamic velocity gradient, velocity, and vorticity directions. While ideal Couette flow does not perturb the vorticity direction, it does perturb diffusion measurements for the velocity gradient direction, and to a lesser extent, the velocity direction. We show that with closely spaced gradient pulses operating in a flow-compensating mode, there exists a diffusion limit below which one cannot measure, that scales as T2γ˙4, where γ˙ is the shear rate and T the gradient pulse repetition period. For a typical rheo-NMR cell, and for the more challenging velocity gradient direction, diffusion rates above 10−12 m2 s−1 can be accurately measured (to 1% error) at shear rates up to 3 s−1. We demonstrate the use of the method in measuring the diffusion spectrum of a lyotropic lamellar phase under shear.