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0 200 mm/s

Figure 8. Phase-encoded velocity techniques yield two-dimensional velocity profiles of laminar flow in models of aseptic processing. Phase-encoded velocity images result from Fourier transformation of gradient-induced cyclic phase iterations whose frequency depends on velocity (Figure 2). This velocity profile illustrates laminar flow of water through a 15.3 mm pipe at an average velocity of 79 mm/s.

6.3. Aseptic Processing Applications

Use of velocity profiles provided by MRI could prevent either under- or overcooking of foods during aseptic processing. Aseptic processing requires the heating of food at a prescribed temperature, for time sufficient to sterilize it, as it moves through a pipe. Packaging and sealing while still hot protect the product from spoilage. Undercooking, leading to spoilage, and overcooking, resulting in loss of desired sensory attributes (taste, texture) present a problem addressable by MRI flow techniques. Obviously the solution involves ensuring that all of the food material remains in the heating pipe for a time sufficient to sterilize, but no longer, to preserve quality. Velocity profiles of the food material, whether obtained by velocity encoding or time-of-flight techniques, can reveal velocities at any position in the pipe (McCarthy, et al., 1992a), leading to accurate calculations of residence time.

6.4. Extrusion Applications

Residence time as well as shear rate govern product quality in food extrusion; consequently velocity profiles provided by MRI flow techniques could assist in the construction and adjustment of extruders. As in aseptic processing, residence time determines cooking time, and often some portions of a batch cook less than others. This condition results in undesired quality variations. As shear rate influences texture, the data supplied by velocity profiles allow adjustment in screw speed and design to optimise shear rate and therefore quality and reproducibility. Knowledge of shear rates and residence times could verify or modify existing mathematical models of extrusion (McCarthy, et al., 1992b). Both phase encoded velocity and time-of-flight experiments produce velocity profiles, but a TOF technique yielded the first published MR images of fluid motion in an extruder.

The TOF technique used by McCarthy, et al. (1992b) to observe fluid velocities in an extruder imposed a single dark band across the barrel diameter; subsequent distortion of the band revealed fluid displacement, permitting calculation of radial velocities and comparison to theory. A radiofrequency pulse in the presence of a gradient dephased the magnetization of a 2 mm plane of fluid perpendicular to the image slice; the resulting dark band (Figure 9) persisted, decaying slowly by Ti mechanisms. An adjustable interval between formation of the band and acquisition of the image provided time for the band to stretch in the direction of fluid movement. Acquisition of images at several intervals depicted evolution of velocity profiles, illustrating linear drag flow (die open) and the combination of drag and parabolic pressure flow (die closed, no net flow). Velocity calculations from the fluid displacements compared well to theoretical predictions based on an analysis by Harper (1981), and modified by the authors to reflect an aspect perpendicular to the screw axis:

Figure 9. Distortion of a dark band by the motion of the helical screw of an extruder illustrates fluid flow patterns. A radiofrequency pulse in the presence of a vertical gradient déphasés the magnetisation of a 2 mm thick band across the extruder, while the screw rotates counterclockwise at 10 rpm. Data acquisition occurs once per revolution, at exactly the same position. Adjusting the time between band formation and acquisition allows observation of flow pattern development from 4 ms until decay of the band by T1 relaxation. Opening the terminal die of the extruder allows outflow, and the flow pattern appears linear from the barrel wall (outer edge) to the screw surface (middle). This illustration of drag flow contrasts with the flow pattern observed with a closed die (no net outflow), in which drag flow balances pressure flow, a parabolic back pressure, to form a velocity maximum 1/3 of the radial distance from the screw to the barrel (right).

Figure 9. Distortion of a dark band by the motion of the helical screw of an extruder illustrates fluid flow patterns. A radiofrequency pulse in the presence of a vertical gradient déphasés the magnetisation of a 2 mm thick band across the extruder, while the screw rotates counterclockwise at 10 rpm. Data acquisition occurs once per revolution, at exactly the same position. Adjusting the time between band formation and acquisition allows observation of flow pattern development from 4 ms until decay of the band by T1 relaxation. Opening the terminal die of the extruder allows outflow, and the flow pattern appears linear from the barrel wall (outer edge) to the screw surface (middle). This illustration of drag flow contrasts with the flow pattern observed with a closed die (no net outflow), in which drag flow balances pressure flow, a parabolic back pressure, to form a velocity maximum 1/3 of the radial distance from the screw to the barrel (right).

In the case of an open die (no back pressure, drag flow), the equation simplifies to and in the case of a closed die (no net flow, both drag and pressure flow), the equation simplifies to

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