In continuous flow electrophoresis the axial flow structure changes from a fully developed rectilinear form to one characterized by meandering as power levels are increased. The origin of this meandering is postulated to lie in a hydrodynamic instability driven by axial (and possibly lateral) temperature gradients. Experiments done at MSFC show agreement with the theory

Rhodes, P. H.

Saville, D. A.

Snyder, R. S.

English

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V 1582' 3207
FLOW AND THERMAL EFFECTS IN CONTINUOUS FLOW ELECTROPHOKESIS
D. A. Saville
Princeton University
Princeton, N.J. 08544
P. H. Rhodes & R. S. Snyder
George C. Marshall Space Flight Center
Marshall Space Flight Center, Alabama
ABSTRACT
In continuous flow electrophoresis the axial flow structure
changes from a fully developed rectilinear form to one characterized
by meandering as power levels are increased. The origin of this
meandering is postulated to lie in a hydrodynamic instability driven
by axial (and possibly lateral) temperature gradients. Experiments
done at MSFC show a noteworthy agreement with the theory.
136
https://ntrs.nasa.gov/search.jsp?R=19820024195 2020-03-21T06:21:37+00:00Z
FLOW AND THERMAL EFFECTS IN CONTINUOUS FLOW ELECTROPHORESIS
D. A. Saville
Department of Chemical Engineering
Princeton University
Princeton, New Jersey 08544
P. H. Rhodes and R. S. Snyder
George C. Marshall Space Flight Center
Marshall Space Flight Center, Alabama
INTRODUCTION
In one application of continuous flow electrophoresis the objec-
tive is the f^iMjtiona^ Lon of biological cell populations rather than
separation. The problems encountered with cells arise from the fact
that the mobility differences are very small and so large electric
fields are required. In the chamber a buffer fluid is inserted at the
top and the sample (which consists of a suspension of the biological
cells in the buffer solution) enters just below the buffer inlet. As
fluid moves through the chamber in a more or less laminar flow an elec-
tric field is applied across the flow. The purpose of the electric
field is to move the particles laterally at a rate proportional to
their mobility. Then, at the bottom of the chamber, a set of collec-
tion tubes picks up the various fractions. This technique has been
highly developed for many purposes but relatively unsuccessful for the
fractionation of cell populations.
137
BUFFER FLOW
SAMPLE INLET-
! X*
ORIGINAL PAGE IS
OF POOR QUALITY
\ ,
E^LECTRODE
SIDE WALL
• FRONT COOLING SURFACE
Figure 1. Chamber Schematic
In the conventional device, one has the familiar parabolic velocity
profile along with a similar temperature profile because of the applied
electric field and the associated Joule heating. To restrict the
temperature rise the thickness of the chamber is kept small with cooling
on the front and rear faces. Difficulties arise from a
phenomenon known as electro-osmosis. In the chamber cross-section the
applied electric field acts on the diffuse charge along the front and rear
surface to induce flow. Since the chamber is closed by electrode membranes
at either end, there is a return flow down the center of the chamber. This
flow deforms the sample cross^ section and stretches it out into a crescent
shape. The longer the sample stays in the device, the higher the electric
field, and the larger the sample diameter compared to the chamber thickness,
the more electro-osmosis works to thwart matters. Thus, when the fractions
are collected at the bottom of the chamber, the fractionation is poorer than
it might have been. To overcome this the chamber can be made thicker to
decrease the electro-osmotic shear across the sample cross-section. This
works up to a point but produces some severe scale-up problems.
138
Changing from the narrow gap device (^ 1.5 mm) to a wider one (^5 mm)
increases the temperature rise by an order of magnitude. Thus a small
increase of 2-3°C in the narrow gap device is raised to a value that
is almost unsatisfactory from the standpoint of biological viability.
More importantly, since the Grashof number is changed by the fifth
power of the thickness ratio because of the Joule heating, buoyancy
effects become very important. This changes the structure of the flow
dramatically and makes it possible for the flow to be hydrodynamically
unstable. Experiments show that as the power is increased, the sample
stream begins to twist and meander. Eventually the performance is
completely unsatisfactory for any sort of fractionation process.
HYDRODYNAMIC INSTABILITY
The instability seems to depend upon the orientation of the chamber
and at one point it was argued as to whether this is a really an in-
stability or related to some other phenomena associated with the hydro-
dynamics or characteristics of the chamber. A first order stability
analysis was carried out wherein there is an CLXAtlt temperature gradient
[1]. Such gradients could arise from uneven heating or cooling or from
entrance effects. It turns out, according to the analysis, that fluids
confined laterally but un-confined above and below are very sensitive
to hydrodynamic instabilities. Whereas the critical Rayleigh number
for fluids confined between two horizontal plates is 1700, the critical
Rayleigh number is 6 if the plates are vertical and the walls isothermal.
If the walls are perfectly insulated, which means that any disturbance
is reflected back into the chamber, the critical Rayleigh number becomes
inversely proportionalto the aspect ratio. For the chambers under study
_2
this ratio is 10 and so the critical Rayleigh number is much smaller.
Thus the temperature gradient required to produce the instability is
only a fraction of a degree per centimeter.
139
ORIGINAL PAGE
BLACK AND WHITE PHOTOGRAPH
Ut ttHSItMCMT sir UP
1 «-FfIR««RVOIS
' H.OWCHAMKR
i «AC« Lian
4 SVHIHGIPUMT
s (UTALOOCC* (TNCMUTOD VOLT/UK I
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t.EHCTH 77 o
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 : W 1
FIGURE 2. Experimental Apparatus
Experiments have been done at MSFC with the device shown schemati-
cally in Fig. 2. The dimensions of the chamber are 5 cm wide, 0.5 cm
thick and 30 cm long. Neutrally buoyant colored particles are introduced
through multiple ports at the top of the chamber and heating is produced
by an alternating field which eliminates electro-osmosis. The flow is
photographed and movable thermistors used to measure the temperature
gradients in the fluid so as to determine whether the flow disturbances
conform to the hydrodynamic Instability suggested by the theory. The
results of some of these experiments are in Figs. 3-6. The zero-power
case shows rectilinear flow with no disturbances. Measuring temperature
at all of the indicated positions gives the local Rayleigh number. As
a power is applied/ Fig. 4, one sees meandering of the sample streams.
The buffer fluid is heated and cooled unevenly as it proceeds into the
chamber and the buoyancy instability causes the redistribution shown.
Temperature gradients measured internally turned out to be very close to
the values predicted by the theory. Taking the velocity profile pre-
dicted by stability theory and superimposing this
140
FIGURE 3. Flow at Zero Power Input
FIGURE 4. -Flow at Power Input of 6.82 V,
141
- 10
;£ WHITE prfGTOQRAHH
u1 A III sin ~f coi gy
H 2
... b cm
H S 10
?<l ,i> cm
A l«l ARBITRARY AMPLITUDE
i Y - O
FIGURE 5. Superposition of antisymmetrical flow disturbance on
the base flow.
FIGURE 6. Flow at power input of 7.52 W.
142
OF POOR QUALITY
on the steady rectilinear flow produces the profile shown in Fig. 5 which
displays a structure similar to that shown in the previous photograph.
If the power is turned up to an even higher level, to produce a temperature
rise of 2-3 °C between the center of the chamber and the wall, patterns
shown in Fig. 6 are obtained showing the further development of the flow.
We now believe the cause of the meandering phenomenon is a hydrodynamic
instability arising from axial temperature gradients that are present
because of uneven heating and cooling of one sort or another. Presumably
these gradients could be suppressed if the cooling jackets were 'designed
carefully. On the other hand, a microgravity environment reduces the effect
of buoyancy and also circumvents the problem.
I GRAVITY
Figure 7. Axial Velocity Field at High Power Levels
143
—2d
U(y)
MAW FUOW
Figure 8. Axial Velocity Profile in Cross-section
Even if the heating problem is overcome the power increased without
instability, the buoyancy forces still work against one. Figure 7 shows
the velocity field in a cross-section of the chamber at power levels
necessary to produce fractionation. Here there is so much Joule heating
in the center that the buoyancy forces are large enough to cause a redistribu-
tion with downflow along the cold membranes on either side and upflow in
the center. For a chamber of finite dimension, this means there is a re-
circulation. Figure 8 shows the same .downflow configuration from the side
showing clearly the large trapped eddy. Here any sample would move in and
around this trapped eddy giving unsatisfactory results for any separation.
In a micro-gravity environment, this recirculation would be absent.
We how understand enough about these instabilities to design an
experiment to operate at low power levels in 1-g and at higher power in a
micro-gravity environment which would enable us to verify the theory and the
scaling laws.
144



Flow and thermal effects in continuous flow electrophoresis

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