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Development of a Flow Visualization Apparatus for Fluidin a Rotating Cylinder

Andrea P. Rubio1 and David L. MartinDepartment of Physics and Engineering, University of Central Oklahoma, Edmond, OK73034

This work is in two parts. In the first part we propose a flow visualization technique toobserve the flow behavior in a closed system. Experiments of this nature require theflow visualization material be added at the beginning of the experiment and remainstable with the flow during the course of the experiment. We also attempted to satisfythe condition of neutral buoyancy with our flow visualization media. The second partconstitutes the construction of a structure to rigidly support a platform and a drive mecha-nism to rotate a fluid confined to a right circular cylinder about a horizontal axis. ©2004Proceedings of the Oklahoma Academy of Science

We anticipated testing condition 4 fromthe list above by using the colored immis-cible droplet in a known flow situation, suchas the flow in a partially filled cylinder ro-tating abut a vertical axis of rotation, this isa well known flow situation. Aliphatic hy-drocarbons are reasonably immiscible.Gasoline and water mixed together is anexample; however, this fails in the neutrallybuoyant part of the criteria. Halogen con-taining hydrocarbons, such as carbon tetra-chloride, exceed the density of water, and ifone could prepare the appropriate mixtureof aliphatic hydrocarbon and halogen con-taining hydrocarbon one would have a neu-trally buoyant immiscible fluid. Thebrightly colored part of the liquid could beformed by adding some agent that wassoluble in the immiscible phase but notsoluble in the aqueous or bulk fluid.

In the following section we illustratesome of the flow visualization agents em-ployed along with experimental observa-tions of some visualization methods forstatic and rotating fluid situations.

Support Framework for Drive Drivelinesand Cell Assembly for Rotating Fluidabout a Horizontal Axis of Rotation

We were advised by Dr. Evan Lemleyin the Department of Physics and Engineer-ing at the University of Central Oklahoma

1Current address: Department of Aerospace Engineer-ing, University of Oklahoma, Norman, OK 73019

INTRODUCTION

Flow VisualizationThis study was designed to observe the be-havior of fluid confined to a rotating rightcircular cylinder in the instances of rotationabout a vertical axis and horizontal axes.Both situations require the flow visualiza-tion material be added once to a fixed vol-ume of fluid in the confining vessel.

We adopted a minimal number of con-ditions that we wished our flow visualiza-tion material to satisfy: (1) brightly coloredfor photographic, video, and visualizationpurposes, (2) immiscible in water (the bulkfluid) so it would not be absorbed, (3) neu-trally buoyant so it would not exhibit anybehavior influenced by density differencesbetween the flow visualization material andthe bulk fluid, and (4) emulate the behav-ior of a similar fluid element of the bulkfluid.

The first condition from the list aboveamounted to having a number of brightlycolored immiscible fluid droplets in water.G. I Taylor (1932) did work that dealt withthe stability and droplet size of oil dropletsin water subjected to a shear stress. Ourdroplet idea had theoretical credibility basedon his work.

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(personal communication, 2002) aboutstructures and trusses built to withstandlarge loads under a variety of conditions. Herecommended a truss structure fromHibbeler (1993), which we adopted as thebase unit of our structure. The details aregiven in the Materials and Methods.

MATERIALS AND METHODS

Flow VisualizationWe attempted flow visualization efforts withtraditional items, such as dyes and food col-oring. They have some inherent difficulties,including becoming diluted in the bulk fluidover time, which makes their integrity anissue. They are also more dense than water(Smits and Lim 2000) and must be dilutedto become neutrally buoyant. We illustratea couple of examples of our experiments inFigs. 1 and 2. The examples show qualita-tive features of the flow field apart from thedensity problem, but they are plagued bythe physical phenomena of diffusion andwere unsuitable for our purposes. Colorphotographs of the figures in this paper aregiven in a version of the paper posted on

the website www.physics.ucok.edu/~dmartin/ at the link Taylor Paper.

We resorted to our plan mentioned inthe introduction. We wanted a fluid thatwas immiscible in water, neutrally buoyant,and brightly colored. We consulted with Dr.D. M. Hellwege an organic chemist in theDepartment of Chemistry, University ofCentral Oklahoma, who suggested (per-sonal communication, 2003) a mixture ofpentane and methylene chloride with solidiodine as a coloring agent. He suggestedthis mixture because it was the least toxicmixture that would satisfy our problem.

We solved the neutral buoyancy prob-lem with Archimedes’s principle. The so-lution is V1/V2 = (1 – ρ2)/(ρ1 – 1), where V1

is the volume of the high density compo-nent, V2 is the volume of the low densitycomponent, ρ2 is the density of the low den-sity component, and ρ1 is the density of thehigh density component. The high densitycomponent used was methylene chloride,and the low density component was pen-tane. We have assumed an average densityof the mix of 1.00 g/cm3, and the total vol-ume of the mix was the sum of the originalvolumes. We obtained our stock methylene

Figure 2. Crystal Violet employed as a flowvisualization aid. Stain shows some de-parture from actual fluid motion

Figure 1. Green food coloring employed asa flow visualization aid. The food color-ing trace emulates the qualitative featuresof the fluid motion apart from the changeof elevation of the dye.

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chloride, pentane, and solid iodine from theDepartment of Chemistry at the Universityof Central Oklahoma. We employed bu-rettes to prepare our mixture to the appro-priate volume ratios. We then added solidiodine to the mixture until we decided wehad a bright enough red color suitable forvideo and photography. We added the im-miscible droplets in a number of ways, in-cluding the use of Pasteur’s pipettes, medi-cine droppers, and burettes both above andbelow the water level

Construction of the framework for thehorizontal rotation assemblyThe unit structure suggested by Dr. Lemleyfrom Hibbeler (1993) is shown in Fig. 3. Ourdesign required that we concatenate threeunit structures parallel to the rotational axisand one unit structure across the end per-pendicular to the axis of rotation. The sideand end views of our structure are shownin Fig. 4. We employed 5.08 x 5.08 x 0.64 cmL-shaped aluminum for construction of thebase and top of the structure as well as thevertical struts that connected the top and

bottom. The cross members that made upthe individual unit structures were made upof 5.08 x 0.32 cm flat aluminum. The topcross members that supported the motordrive lines and cell supports were 5.08 x 2.54x 0.32 cm channel aluminum. The top andbottom were assembled first and bolted to-gether. The individual flat cross memberswere assembled in place on the base struc-ture; holes were drilled and the flat alumi-

Figure 3. Single truss element for bearinglarge loads from Hibbeler (1993).

Figure 4. Long side of assembly with dimensions and angles to be employed as supportframework for drive motor and cylinder for rotation of partially filled cylinder about ahorizontal axis. Top parallel to the axis of rotation. Bottom figure is the end view.

FLOW VISUALIZATION APPARATUS

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num parts of the assembly were bolted inplace.

The cell was a blend of acrylic pipe andPlexiglas; this gave us the capability to con-struct a number of different sized contain-ers inexpensively compared to other clearmaterials such as glass. The cell was a modi-fication of a design we originally employedin some of our experiments with fluids ro-tating about a vertical axis of rotation. Ourinitial cell design was made from stockacrylic of 16.51 cm inner diameter and 0.64cm wall thickness. The cell was open endedand had a length of 17.78 cm. One of theends was centered and glued to a 30.48 x30.48 cm Plexiglas square that was 0.64 cmthick. The lid was a 3.81 cm ring cut fromthe stock acrylic pipe mentioned above thatwas split down its length and spread so thatthe acrylic pipe fit tightly inside. The splitring was centered in another 30.48 x 30.48cm square of Plexiglas and glued; the acrylicpipe could be removed after a certain curetime for the cement. Four aligned 0.64 cmholes were drilled in each Plexiglas square.A 16.51 cm inner diameter O-ring was in-serted into the lid and the container wasfilled to the desired fill volume and boltedtogether with 0.64 cm x 22.86 cm long car-riage bolts with felt washers on the cell sideand flat washers on the outside of the felt tocompress the felt for a tight fit. A proto-typeof our cell is shown in Fig. 5. Our leak test-ing consisted of bolting the assembly to-gether snugly and turning the entire assem-bly horizontal. The procedure was repeateduntil no leaks were observed.

Thoroddsen and Mahadevan (1997)cited a number of variables associated withthe coating flows for fluids confined to ahorizontally rotating right circular cylinder.One of these variables is the aspect ratio, A,which is descriptive of the cylinder geom-etry. A is given by A = L/R, where L is thelength of the cylinder and R is the cylinderradius. Our cell radius and aspect ratio were8.25 cm and 2.15, respectively. The cellThoroddsen and Mahadevan used most intheir work was R = 6.25 cm and A = 7.8.

Other cells Thoroddsen and Mahadevanworked with had the following radius andaspect ratios: R = 2.35 cm, A = 16.0, R = 3.8cm, A = 15.4, R = 7.1 cm, A = 8.2 and R = 14.6cm, A = 5.9, respectively. A comparisonshows that our cell radius is about half oftheir largest and slightly larger than the onethey used. The aspect ratios employed intheir work were considerably larger thanours.

RESULTS

Flow VisualizationWe prepared our mixtures with burettes.This gave us the capability to prepare ourmixtures to the nearest 0.01 ml. The iodinewas added and gave a reasonably bright redcolor. A photograph of our mixture sus-pended in water is shown in Fig. 6. We werecareful in preparing our mixtures and madeabout 100 ml so that adherence to the neu-tral buoyancy condition should be fairlyclose. Based on our tolerances, our preci-sion should be two parts volume in ten thou-sand.

We had a number of experimental diffi-culties. We encountered problems with thefluid adhering to the tip of the Pasteur pi-pette and the burette. We usually had toshake the droplet loose or deliver a largervolume and hope the volume of fluid wouldbreak up into usable droplet sizes, which itsometimes did. We tried adding droplets

Figure 5. Cell constructed of 16.5 cm I. D.acrylic pipe Plexiglas ends and O-rings forseals.

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above the level of the fluid; however, thesedroplets had a downward vertical compo-nent of velocity. Droplets introduced in thisfashion would head to the bottom of thevessel and would continuously reboundfrom the bottom to the top, changing com-position as this rebounding process contin-ued. The neutral buoyancy condition waslost quickly and our immiscible fluid wasrendered useless as a flow visualization aid.Usually at the end of a sequence of bouncesall of the immiscible fluid would settle onthe bottom of the vessel. Our usual vesselwas a glued acrylic and Plexiglas assembly.Our immiscible mixture of methylene chlo-ride-pentane-iodine had a disastrous effecton our vessel. The methylene chloride-io-dine-pentane mixture dissolved the bottomof the vessel and rendered it useless.

Construction of the Framework for theHorizontal Rotation AssemblyWe began construction of the assembly asindicated in Fig. 4. We started with the vari-ous types of structural aluminum describedin the Materials and Methods. The top wasidentical to the bottom and was bolted ontothe uprights. Fig. 7 shows the entire frame-work assembly completed. The motor, cellassembly, and drive lines have yet to bemounted on the framework. Johnson (1988)constructed an apparatus to effect the hori-zontal rotation of fluids. A device similarto his was used in the work of Thoroddsenand Mahadevan (1997). The finished ver-

sion of our framework for rotating a fluidabout a horizontal axis with drive lines,motor and cell assembly included is shownin Fig. 8. The system at this stage is still isin need of testing. The first spin with a par-tially filled cell was with pure water shownin Fig. 9. At this time we had difficulty de-termining the speed of rotation and can pro-vide only estimates. We were still address-ing the determination of rotation speed. Thecell shown in Fig. 9 was approximately 1/4full and rotating at an estimated speed of 3-5 rotations per second.

DISCUSSION

Flow VisualizationWe concede to having difficulty in control-ling droplet size, stability, and location in

Figure 6. Droplet suspension of immis-cible droplets in water Figure 7. Fully assembled framework for

rotating a partially filled right circular cyl-inder about a horizontal axis of rotation

Figure 8. Apparatus fully assembled withmotor, drive lines and cell. The apparatusis ready for testing.

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the vessel. A successful dispersion is shownin Fig. 6. One needs to be careful when put-ting organic mixes in polymer based vessels.Plexiglas-acrylic vessels have a great dealof appeal, such as the cost of materials andease of fabrication of a particular cell design.However, we were not able to control drop-let size or placement within the bulk fluid.The very act of attempted droplet placementintroduced a vertical velocity component tothe droplet so we had no control over posi-tion. Any contact of the mixture with thesurface of the vessel for any length of timewould completely render the vessel useless.We did the majority of our work with theimmiscible organic materials with glass ves-sels.

We believe the immiscible mixturedroplet idea has merit, but we encounteredsome problems. The experiment assumeda neutrally buoyant mixture had been pre-pared. A method should be developed todeliver an immiscible stationary droplet atany depth in the fluid. The immiscible fluidmix needs to be stable in the aqueous envi-ronment. Ours was stable for short dura-tions, but after time, the instabilities wouldcause our droplet to settle on the bottom ofthe vessel rendering the vessel useless.

We only had time to attempt one mix.Other mix possibilities should be attemptedand tested for reproducibility. Our approach

to the immiscible droplet problem wasbased on toxicity of the reagents used. Amore appropriate procedure would be toconduct the study based on the physicalproperties of the mix pair. One would hopeto keep this as simple as possible and useonly binary mixes. The problem has enoughvariables without introducing additionalones. We would recommend staying awayfrom anything as complex as a ternary mix.The immiscible droplet problem should bea study in design, physical properties, andchemical equilibrium. The most obviousvariables to be addressed would be interfa-cial surface tension, viscosity, and stabilityof the mix in the bulk fluid. The compo-nents of the mix should be more soluble inone another than in the bulk fluid, a ques-tion that still needs to be addressed.

ACKNOWLEDGMENTS

We thank the Joe Jackson College of Gradu-ate Studies and Research for funding thisproject. We also wish to thanks the Joe Jack-son College of Graduate Studies and Re-search for support as an UndergraduateResearch Assistant for the semesters of fall2002, spring 2003, and fall 2003 for AndreaRubio. D. L. M. thanks the Joe Jackson Col-lege of Graduate Studies and Research forrelease time support during the fall of 2002.

REFERENCES

Hibbeler RC. 1993. Statics and mechanics of materials.Englewood Cliffs (NJ) Prentice Hall. 210 p.

Johnson RE. 1988. Steady state coating flows inside arotating horizontal cylinder. J Fluid Mech 190:321-342.

Smits AJ, Lim TJ, editors, 2000. Flow visualization: tech-niques and examples. London: Imperial CollegePress: 396 p.

Taylor GI. 1932. The viscosity of a fluid containingsmall drops of another fluid. Proc Roy Soc A 138:41-48.

Thoroddsen ST, Mahadevan L. 1997. Experimentalstudy of coating flows in a partially filled horizon-tally rotating cylinder. Experiments in Fluids 23: 1-13.

Received: May 28, 2004; Accepted January 19, 2005

Figure 9. First spin of cylinder partiallyfilled with fluid. The cylinder was about1/4 full. The cell rotational speed wasabout 5 rotations per second.

A.P. RUBIO and D.L. MARTIN