Experimental study of fluid transport in capillary systems

Acta Astronautica Vol. 13, No. 2, pp. 87-93, 1986

0094-5765/86 $3.00+ .00 © 1986 PergamonPress Ltd.

Printed in Great Britain.

Academy Transactions Note EXPERIMENTAL STUDY OF FLUID TRANSPORT IN CAPILLARY SYSTEMSt P. J. SELL a n d E. MAISCH

Fraunhofer-Institut ffir Grenzfl~ichen-und Bioverfahrenstechnik, Stuttgart, ER.G. and J. SIEKMANN

Universit~it-GH-Essen,Postfach 103764, 4300 Essen 1, F.R.G. (Endorsed by V. V. Gooosov:~ and L. G.

NAPOLITANO§;received 29

February 1984)

wetting kinetics of model tubes of different geometries has been studied experimentally under microgravity conditions by means of sounding rocket experiments. The experimental arrangement is discussed in some detail. Meniscus configurations in tubes of different shape and the liquid rise are determined from photographic pictures. Together with observed flow patterns valuable information concerning the hydrodynamic deformation of phase interfaces is obtained.

Abstract--The

1. INTRODUCTION In a previous paper[l], the motion of a fluid in simple capillary systems (model tubes of different geometry) has been dealt with experimentally (earth-based laboratory and sounding rocket experiments) and theoretically. Moreover, a brief description of the experimental arrangement was given. A comparison of test data with numerical calculations showed excellent agreement. It is the purpose of the present note to describe the experimental set-up in some detail and to supplement the results reported in [1]. In particular, interface shapes (menisci) and the capillary rise of liquids in tubes of different geometry are investigated.

2. EXPERIMENTAL SET-UP

In order to perform within the scope of the TEXUS* programme space-born wetting kinetics experiments by means of a ballistic rocket, the development of a programmed experimental set-up proved to be necessary. On a parabolic flight path the sounding rocket "Skylark" reaches an altitude of 256 km and offers for experimentation a residual gravitational acceleration of less than 10 -4 g for a period of approximately 360 sec, where g is the terrestrial value of the acceleration of free fall. During this time interval the experiments run off autonomously. A complete module of the wetting kinetics experiment, assembled ready for flight, is shown in Fig. 1. Equipment and test devices, combined in a block circuit, are displayed in Fig. 2. Objective of the experiments

is the investigation of the liquid rise in model tubes of different geometries and, in particular, the study of the dynamics of interfaces (menisci). In the course of the preparation of the experiments, it turned out that the exact positioning of the liquid in the reservoir, together with the condition of forming a plane meniscus, was a major problem. To solve this problem, special attention was given to the design of the lower part of the experiment (test) chamber shown in Fig. 3. Wetting aids (textile fabric) and wetting closures (teflon layer, contact angle of i05 degrees) are suitable to position the test liquid (desalinated water, p = 998,23 kgm 3 (20°C), tr = 71,8 mN/m) in the reservoir in such a way that a plane surface was formed. The free liquid surface in the reservoir has virtually no effect on the menisci in the test tubes. After attaining the coasting phase, where a state of microgravity prevails, a slide at the intake is opened and a precalculated quantity of liquid is pushed slowly by a piston into the reservoir. This test liquid spreads along the wetting aids, ascends in the rising aids, forms a free surface and, having reached the standpipes, rises in the latter. At the beginning of the wetting kinetics experiments proper, the~liquid is at the upper ends of the stand pipes. The penetration into the test tubes is recorded by a camera located behind the pane of glass. Results of preliminary experiments concerning the rise of liquids in test tubes under simulated weightlessness[ 1] were utilized to set the test parameters, e.g. length and speed of the film, illumination, etc. Components of the experiment chamber are demonstrated in Fig. 4.

3. PREPARATION AND CONTROL OF EXPERIMENTS

tDedicated to Prof. Dr.phil. LL.D.h.c. Henry G6rtler on the occasion of his seventy-fifth birthday. :~Academy Member (Section l). §Academy Member (Section 2). *Technologische Experimente unter Schwerelosigkeit. 87

To ensure good wetting conditions during the experiments, the test chamber was filled with humid air (relative humidity 70%-75%) prior to the launch of the sounding rocket. Thus a thin film of water was generated in the test tubes. In addition wetting tests were carried out before

P. J. SELL et al.

88

groundglo~l~

~

: ~one ofgloss i /etting closure wettingaid i

,illingpositionsensor

Fig. 3. Experiment chamber for wetting kinetics experiments under reduced gravity.

Fig. 1. Module (ready for flight) for the wetting kinetics experiment (TEXUS III B, launched April 30, 1981). The experiment chamber is in the background (left), in front of it the film camera, on the right from the camera are the pressure tank and the control device. the beginning of the experiment. In these tests liquid drops were spread on the outer wall of the test tubes by means of a hypodermic syringe. These wetting tests yielded static contact angles of less than 10 degrees on the tubes. Furthermore, during the experiment, the radiant heat of the lightning installation lead within the test chamber to temperatures of approximately 37°C. Owing to this rise in temperature, the relative humidity in the chamber dropped to roughly 30%, At the same time, the water film evaporated to some extent, however, it was always guaranteed that the tubes were covered at least by an adsorbed layer of water.

sink~

Since the process of filling the reservoir takes place outside the field of view of the camera, several filling position sensors were installed for controlling purposes. Among other things, the sensors should provide information concerning the liquid inflow into the reservoir. Figure 5 displays the response of the sensors during the filling process, which lasted about 100 sec. This follows from pressure measurements shown in Fig. 6. The volume of the reservoir is 0,167 - l0 -3 m 3, the area is 8,33 • 10 3 m 2. With these data we obtain a speed of rise amounting to (0,167 - 10 -3 m3)/(8,33 • l0 -2 m 2 ' l02 s) = 0,20 • l0 -3 m/s. After having reached the support of the stand pipes, the speed increases to 0,26 • l0 3 m/s. In Fig. 5 the calculated rise of the liquid-level was drawn as a solid line. The response of the sensors has been marked by dots. The deviations from the calculated curve, as registered by the sensors, are due to the liquidfilled textile fabric (wetting aids) and the arrangement of the rising aids. They are about 10 mm high and have an outer diameter of approximately 7 ram. During preliminary tests it was observed that external menisci were

test cobin

lift

Fig. 2. Block diagram for the TEXUS IIIB wetting kinetics experiment.

Fluid transport in cap!Uary systems

89

test tubes. The temperature distributions, measured at these two places, are graphed in Fig. 7. During the experiments one notices a continuous rise of the temperature from 27°C to 33°C within the liquid. Inside the chamber the course of the temperature showed the same behaviour as in the liquid until the illumination was switched on. Because of the lamps the interior was heated up to 37°C prior to the start of the experiment. Due to the inflow of cooler fluid into the tubes, the temperature dropped about 2°C-35°C at this measuring point.

4. DISCUSSION OF EXPERIMENTAL RESULTS

4.1 General observations In addition to information read by the sensors, a 16 mm color film was available for interpretation. The essential phases of the experiment were recorded by cinephotography. The critical state, namely the inflow of the liquid into the test tubes, was registered with a camera speed of 200 frames per second. Photographic pictures were of such a quality that particles suspended in the liquid and profiles of menisci could be recognized even at the highest camera speed. Only the border zones of the pictures were out of focus. Figures 8 and 9 exhibit photo assemblies of motion pictures of the liquid rise in a conical and a sinusoidal tube, respectively. Shapes of menisci (assemblies of film cuttings) in (a) cylindrical, (b) conical and (c, d, e) sinusoidal test tubes are displayed in Fig. 10. As mentioned elsewhere[l], liquid columns in a low gravitational environment rise more slowly than under terrestrial conditions (simulation experiments). Another important conclusion, drawn from photographic interpretation, is the fact that at the visible parts of the test tubes semispherical menisci have not been observed. This points out a fundamental difference between spaceborn experiments and earth-based simulation tests in the laboratory, where exact hemispherical menisci do occur. On account of the varying interface shapes, driving forces are smaller than those arising in case of a hemispherical meniscus. Figure 11 shows the liquid rise as a function of time for the five test tubes under consideration. For further details, reference is made to [2].

Fig. 4. Experiment chamber (disassembled). formed on the rising aids.Thus a plane rise of the free surface up to this level was not possible. In virtue of this volume displacement, the response of the sensors 1-4 was delayed. Disregarding a slight asymmetry, as concluded from the missing indication of sensor 6, the filling of the reservoir proceeded as anticipated. The standpipes, dipped into the free surface, ensured that at the beginning of the wetting kinetics experiment the liquid actually happened to be at the upper end of these pipes. In order to control the temperature during the experiment, a temperature sensor was mounted within the liquid outside the test chamber, and another sensor within the chamber between the illuminated backwall and the

water inlet

h[mmL! =5

10c0tion of filling position senso-s

10 =4

Ill 2 3

200

2~0

36o" t [s] I

start

filling process

end

Fig. 5. Rise (h) of test liquid vs time (t) in the reservoir under reduced gravity. Comparison between the theoretically and the experimentally determined rise (filling position sensors).

P. J. SELL e t

90

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100

150

200

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40o t [ s ]

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(a)

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so

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Fig. 6. (a) Pressure distribution in the reservoir. (b) Pressure distribution in the experiment chamber.

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Fig. 7. Temperature distribution within the experiment chamber and the test liquid during the wetting kinetics experiment under reduced gravity.

Fluid transport in capillary systems I hlmm

Fig. 8. Photo assembly of motion pictures (conical tube b, h = liquid height, t = time).

91

Fig. 9. Photo assembly of motion pictures (sinusoidal tube e, h = liquid height, t = time).

I J

At : 0,2s~ ] " " ~

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tube (a)

(c)

(e)

(d)

(b)

Fig. 10. Menisci during liquid rise in test tubes of different geometry.

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Fig. 11. Rise h(t) of menisci ... in five different test tubes (measures in mm).

t [s]

P. J. SELLet al.

92

4.2 Flow near an advancing meniscus Since the advancing liquid cannot penetrate the interface, the axial laminar flow in the tube must turn around radially outwards before reaching the meniscus. This can be demonstrated by following the analysis of Karnis and Mason[3]. We consider the axisymmetric flow of an incompressible viscous fluid in a tube of radius R. At the center of the air-liquid meniscus (see Fig. 12), we attach the origin of cylindrical polar coordinate system (z, r). For the sake of simplicity, the interface is assumed to be flat. Far behind the meniscus, the velocity profile u*(cx) is parabolic u*(cx) = 2fi(1 - a2),

(1)

where a = r/R, and fi is the average liquid velocity given by

'rrR'- '

(2)

!? being the volumetric flow rate through the tube. Now the meniscus advances in the positive z-direction with velocity ft. To render the flow stationary, we let the tube move with a velocity - f t . This gives a velocity distribution relative to the meniscus u(a) = u*(a) - ~ = fi(l - 2a-').

Qaa,(ot) = fA, u(c0dA

x

+

r Or

(51

tO = o.

According to [3], an approximate analytic solution yields f, + : ~ cd(1 - c~2) • {1 - e x p ( - ~ - - ) } ,

(6)

where 13 = - z/R. It is readily seen that eqn (6) reduces to the stream function for parabolic flow for [32 --+ ~: f, = ~ a:(l - cd).

(4)

(7)

Equation (6) is exact for high 13 and allows the prediction that the streamlines turn backwards near the advancing meniscus. The streamline pattern 0 = constant behind the interface is given by

r = +-X/2 -2

- 2ot2)otdotd~b

= l)'od(l - a2),

r Or

(3)

Next we consider a long liquid cylinder of radius r. The base (BB') of the cylinder is at the meniscus and the top (AA') is far away from it. Then the flux Q through AA' is

= R2fo2~f~gt(1

while the flux through BB' is zero. Now the liquid cannot accumulate within the cylinder and thus flows radially outwards from its side. The flow relative to the meniscus slows down and there results a stagnation pressure acting on the meniscus. If the Reynolds number (Re = rid~v, with d as the tube diameter and v as the kinematic viscosity) is very small, the flow field behind the meniscus formed by an incompressible Newtonian fluid can be determined by solving the creeping-flow approximation to the NavierStokes equations with appropriate boundary conditions. With 0(r, z) as the Stokes stream function we obtain

1+ -

I

x 11 - e x p ( - ~ 2 2 ) ]

'

(8) } ' - ' 1 ''z

inertial

and illustrated in Fig. 13. Clearly, the streamlines exhibit a fountain-like shape, This has been confirmed also experimentally by flow visualization techniques employing suspended particles. At the tube wall a backflow of fluid relative to the advancing meniscus occurs. Further details are discussed in I1] and [2].

reference frame

5. CONCLUSIONS Wetting kinetics experiments within the TEXUS programme have shown that interfaces in model tubes of different geometry are not as stable as those observed moving reference frame meniscus

-u

Fig. 12. Liquid flow in a test tube (schematic), coordinate systems, notation.

Fig. 13. Streamline pattern near advancing meniscus.

93

Fluid transport in capillary systems under terrestrial conditions. Evaluation of motion pictures of the liquid rise in cylindrical and conical tubes exhibits strongly deformed menisci. Thus the capillary force, which acts as the driving force of the transport process, and hence the speed of rise of the advancing meniscus, are smaller as compared with results obtained from simulation experiments in an earthbound laboratory. Concerning experimental results with sinusoidally shaped tubes, it turns out that the deformations at the narrow passes are not as strong as in liquid-liquid systems. Flow visualization of the flow pattern near the interface by means of suspended particles reveals that the fluid moves towards the meniscus in a fountain-like manner. Thus a stagnation pressure arises at the interface.

Acknowledgement--The financial support of the project by the

Bundesministerium for Forschung und Technologie is gratefully acknowledged.

REFERENCES

1. E J. Sell, E. Maisch and J. Siekmann, Fluid transport in capillary systems under microgravity, Acta Astronautica 11, 577-583 (1984). 2. E. Maisch, Zweiphasenstrrmungen unter dem Einglu8 von Kapillarkr~iften (Untersuchungen an Modellsystemen unter verminderter Schwerkraft), Doktorarbeit Universit~it-GHEssen (1982). 3. A. Karnis and S. G. Mason, The flow of suspensions through tubes, VI. Meniscus effects, J. Colloid and Interface Sci. 23, 120-133 (1967).