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a : :' Scaling and Acceptable Acceleration Level Throughout this report, the quantitative discussion of the ef- fect of gravity on the phenomena involved has been in terms of a steady value of the acceleration imposed on the system. This is In part because any such estimates appropriately begin with a discussion of the effect of a steady m~crogravity background. But it is also due to the fact that our current detailed understanding of the scaling laws and dynamic response pertains primarily, but not exclusively, to the case of a constant, spatially homogeneous acceleration. The task group recognizes, however, that the micro- gravity environment is characterized by both a steady background and transient excursions in both the magnitude and orientation of the acceleration vector, and that these excursions are not neces- sariTy small and are potentially rich in spectral content. A concern that must be addressed when discussing the po- tential of microgravity research is that of acceleration levels that are necessary or desirable to meet a given scientific objective. Al- though much attention has been given to this question, there is no single numerical value that pertains to the wide spectrum of microgravity experiments. Indeed, the task group suggests that even within the context of a single experiment, there again is no single value of a minimum acceptable acceleration level. Such a value always represents a trade-off between various competing 86

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87 parameters that conspire with gravity to affect the phenomena under study. There will be inevitable constraints In our ability to vary these competing parameters at will. This point of view can be illustrated by amplifying some of the scaling arguments given previously. Consider, for example, particulate systems ~ which fluid ve- locities or velocity gradients are generated by the action of buoy- ancy, as ire the gravity settling of clouds of combustible particles, suspensions, and colloidal dispersions. The unportance of such fluid motion is measured by the magnitude of the dimensionless Grashof number, Or = ~ppl3/p~2 Thus, for sedimentation to be negligible, we must have Gr << I. In this sunple example we see that lowering 9 from its normal value 90 has the identical dynamical effect as lowering the density mismatch, up between the phases, reducing the characteristic length scale, i, or raising the fluid kinematic viscosity, L,. Arriving at acceptable acceleration levels, then, represents a compromise between the desired spatial extent of an experiment (which may in turn be set by the spatial resolution of instrumentation), the degree to which the chemical system of interest may be made isopycnic, and the ability to alter fluid properties. For example, if the spatial extent ~ to be 3 cm, working with a fluid of the viscosity of water, lo-2 cm2/s, and nearly neutrally buoyant systems, Ap/p 10-2, we have 9 << IJ/13~p/p) ~ 10~3cm2/~~ 10-690 Increases In length scale or density mismatch can be compensated for by either decreases in the gravitational level or increases in fluid viscosity, or both. Such scaling arguments can and must be made in each case where a microgravity experiment is contemplated. Futhermore, they are seldom as sunple as the preceding example and often in- volve subtleties. Consider as a second example the growth of aggress gates. The geometrical properties of such aggregates may exhibit a fractal scaling behavior between a lower and upper length scale, and it is reasonable to require data over at least three decades of scale in order to make quantitative measurements of the frac- tal dimension. Consider an aggregate composed of particles of

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88 size 10 ~m, and assume a tower cutoff of the length scale of 10 particle diameters. (Such estanates of the lower cutoff may be oh tained from computer simulation, for example.) Then aggregates of macroscopic dimension 1~ (lOpm)(lOJ(103) ~ 105,um~ lOcm might be required for accurate determination of fractal dimen- sion. Requiring the sedanentation velocity to be small wiD lead to scaling arguments very similar to those given above. However, another consideration, namely the structure integrity of the ag- gregate, must be taken into account. Sedimentation, however slow, will exert a hydrodynamic force on the particles, which, for a loose flee, will scale in the following way: F~ a,uV where a is a typical particle size, ~ is the fluid viscosity, and V is the sedimentation velocity. Furthermore, V ~ (^p/p~gl2/p so that Fin supple Knowledge of the strength of the attractive force holding the ag- gregate together may be used with the above estunates to set acceptable gravitational levels in order that the aggregate not be torn apart by the hydrodynamic forces. Again it should be empha- sized that such acceptable gravitational levels are for a particular system, and may be altered by altering some other property of the system. Acceptable leveb of Jitter" or transients in m~crogravity may also be arrived at by use of scaling arguments. However, in order to do so we require information on the dynamical response, and in particular on the resonant frequencies of the system un- der consideration. This information ~ often lacking, and must be determined through ground-based dynamic testing, theoretical calculations, or both. In summary, the task group finds that, without considering unusual ~naterial properties or unreasonable tolerance on density

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89 matches, levels of 10~6 to 1~6 g would allow experiments of reason- able scale to be relatively free of buoyancy-driven flows. However, the task group emphasizes that each experiment implies a sepa- rate set of requirements, and that many of them may well involve gravitational levels of substantially lower magnitude.