Single-shot velocity mapping by rewinding of velocity encoding with Echo-Planar Imaging.

The ability of single-shot NMR imaging methods to follow the time evolution of a velocity distribution within an object is strongly limited by the phase errors accumulated as velocity maps are acquired. In the particular case of Carr-Purcell based sequences combined with Echo Planar Imaging acquisition, phase accumulates through subsequent images, hampering the possibility to acquire several velocity maps, which would be useful to determine transient behavior. In this work, we propose the use of a rewinding velocity encoding module applied after the acquisition of each image during the CPMG echo train. In this way, the first velocity module imparts a velocity dependent phase prior to the image acquisition and the second pair cancels this phase out before the next refocusing radiofrequency pulse is applied. The performance and limits of this method are studied by acquiring 100 images of a co-rotating Couette cell over a period of 1.6 s as a function of the rotation speed. The method is applied to determine the kinematic viscosity of a water/alcohol mixture, which is a relevant topic in many physical, chemical and biological processes.

Flow force and torque on submerged bodies in lattice-Boltzmann methods via momentum exchange.

We review the momentum exchange method to compute the flow force and torque on a submerged body in lattice-Boltzmann methods by presenting an alternative derivation. Our derivation does not depend on a particular implementation of the boundary conditions at the body surface, and it relies on general principles. After the introduction of the momentum exchange method in lattice-Boltzmann methods, some formulations were introduced to compute the fluid force on static and moving bodies. These formulations were introduced in a rather intuitive, ad hoc way. In our derivation, we recover the proposals most frequently used, in some cases with minor corrections, gaining some insight into the two most used formulations. At the end, we present some numerical tests to compare different approaches on a well-known benchmark test that support the correctness of the formulas derived.