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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
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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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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.
Representative terms from entire chapter:
acceptable acceleration
