THE JouRNAL oF HISTOCHEMISTRY AND CYTOCHEMISTRY
`Copyright© 1977 by The Histochemical Society, Inc.
`
`Vol. 25, No.7, pp. 774-780, 1977
`Printed in U.S.A.
`
`UNIFORM LATERAL ORIENTATION, CAUSED BY FLOW FORCES, OF FLAT
`PARTICLES IN FLOW-THROUGH SYSTEMS
`
`V. KACHEL, E. KORDWIG AND E. GLOSSNER
`Max-Planck-Institut fur Biochemie, Abteilung fur experimentelle Medizin, D8033 Martinsried,
`West Germany
`
`Received for publication January 25, 1977
`
`Recently, it was shown that the lateral orientation of sperm cells disturbs the deoxyribonu(cid:173)
`cleic acid distribution measured by fluorescence in a laterally laser-illuminated flow system.
`The present results show how flat particles may be influenced to assume a uniform lateral
`orientation. This was achieved by choosing the geometrical dimensions of the hydrodynamic
`focusing flow path. High speed photographs of fixed chicken erythrocytes oriented in experi(cid:173)
`mental chambers are presented.
`
`The optical flow-through instruments com(cid:173)
`monly used illuminate cells radially with a
`laser beam. Gledhill et al. (1) have shown that
`the deoxyribonucleic acid distribution curves of
`different sperm cell types consist of a peak with
`an extension to higher fluorescence values,
`when measurements with the fluorescence ex(cid:173)
`cited by a radially incident laser beam are per(cid:173)
`formed. Based on a number of observations,
`they conclude that the shape of the distribution
`curves is disturbed, probably due to the fact
`that the flat sperm cells are oriented in a ran(cid:173)
`dom way in the optical sensing zone of the flow
`system. Sperm cells did show deoxyribonucleic
`acid distribution curves without extension to
`the right (8) when measured in our axially
`illuminating "Fluvo-Metricell" (5) instrument.
`If, however, radial laser illumination is used,
`disturbances in the orientation are best avoided
`by orienting all cells uniformly. In the follow(cid:173)
`ing, we describe a simple method to uniformly
`orient flat cells by flow forces.
`
`transaxial direction is determined by constrict(cid:173)
`ing forces. In the following the constricting
`forces will be treated as two equal but counter(cid:173)
`acting forces, fh and fv. The quantity of these
`two concentrating forces depends on the degree
`of constriction of the flow path in the horizontal
`or the vertical direction, respectively. We de(cid:173)
`fine the degree of constriction by the ratios A/a
`and B/b, of the horizontal or vertical dimension
`of the flow path at the particle inlets (the outlet
`of the particle injection tube) A and B to the
`respective horizontal or vertical dimension at
`the end of the constricting paths a and b. In the
`following, we discuss the movement of particles
`along the line of symmetry of revolution (flow
`axis). If the symmetry of revolution does not
`exist, we consider those particles that move
`along the intersection line of the vertical and
`horizontal planes of symmetry leading through
`the flow path. Thus, the particles can be consid(cid:173)
`ered as moving along a straight line through
`the flow system, and additional side forces that
`may act outside the planes of symmetry can be
`neglected. Three different types of flow paths
`which influence the moving particles will be
`discussed.
`
`REGULAR OCCURRENCES IN A LAMINAR
`HYDRODYNAMIC FOCUSING FLOW PATH
`In a focusing flow system, the fluid flow is
`determined by the pressure change in the flow
`FLOW CONSTRICTION NOT AFFECTING THE
`from wider cross-sections of the flow path to
`LATERAL ORIENTATION
`that in its smaller cross-sections (Fig. 1). Be(cid:173)
`cause the walls of the constricting flow path,
`Figure 2 shows cross-sections of flow paths,
`whereby A/a = B/b, i.e., the cross-sections
`e.g., the walls of a tapered tube, exert concen(cid:173)
`trating and accelerating forces on the fluid, it
`along the flow path, are transformed according
`to the law of similarity. If we neglect the fric(cid:173)
`needs higher velocities (the principle of mass
`tion of the tube walls (potential flow), every
`conservation) to pass through smaller cross(cid:173)
`partial area of the cross-section A x B may be
`sections. The accelerating forces are exerting
`their effect in the axial direction, whereas the
`fitted into the reduced but similar cross-section
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`
`

`

`LATERAL CELL ORIENTATION BY FLOW FORCES
`
`775
`
`a x b. The dimensions of the cross-sections in
`flow will be smaller, but the shape itself will
`stay similar; i.e., a partial square field F some(cid:173)
`where in the cross-section A x B appears in the
`cross-section a x b also as a square field F', but
`reduced by the factor a/ A or b/B (both are equal
`in this case; see Fig. 2, right panel). Similar
`reduction of the laminar flow areas implies that
`no preferential side force is affecting the flow or
`the particles moving in the flow. These parti(cid:173)
`cles enter the flow in a random orientation. The
`constricting or focusing forces try to compress
`them laterally and orient them with their long-
`
`est extension in the main flow direction as pre(cid:173)
`viously described in ( 7). However, the a priori
`lateral orientation remains unchanged.
`
`FLOW CONSTRICTION CAUSING VERTICAL
`ORIENTATION
`Let us assume a change in the geometrical
`dimensions of the constricting flow path, so
`that similarity no longer exists between the
`cross-sections A x B and a x b (Fig. 3A). A/a >
`Bib implies fh > f,.. A small square field in the
`flow cross-section A x B no longer appears as a
`reduced square field in the cross-section a x b.
`
`A
`
`flow
`
`direction
`
`FIG. 1. Dimensions and forces exerted in an usual focusing flow path with symmetry of revolution. fh,
`constricting flow forces that have a horizontal effect; fv. flow forces acting vertically. A, horizontal
`dimension of the flow path at the particle inlet; a, horizontal dimension of the orifice or nozzle; B, vertical
`dimension of the flow path at the particle inlet; b, vertical dimension of the orifice or nozzle.
`
`FIG. 2. Examples of the cross-sections of the flow path, if the condition A/a= B/b is fulfilled. By the law
`of similarity no preferential side forces influence the flow and the particles in flow. Every area in the cross(cid:173)
`section A x B of the flow, e.g., the square field F, is found as a equally shaped field in the cross-section ax b,
`but scaled down (square field F'). For explanation of lettering see Figure 1.
`
`1-----------
`
`

`

`776
`
`KACHEL, KORDWIG AND GLOSSNER
`
`b
`
`FIG. 3. A, cross-sections of a flow path where A/a > B/b. For lettering see Figure 1. The dissimilar
`transformation of the cross-sections causes preferential horizontal side forces which generate additional up
`and down flow components. These components are responsible for the vertical orientation of flat cells. B,
`detailed conditions of the flow around a particle. The main flow direction is normal to the plane of the paper.
`The decreased vertical force fv enables a superpositioned flow in an up and down direction at both sides of the
`vertical plane of symmetry. These flow components are indicated by the thin arrows. The torque M produced
`by them rotates flat cells to the stable vertical orientation.
`
`by the flow to the upper and lower areas of the
`constricted cross-section a x b. This additional
`up and down flow, caused by the increased
`horizontal constriction of the flow path, orients
`flat cells in a vertical position (Fig. 3B). Cells
`that initially were in a horizontal orientation
`are now in an unstable position. Small distor(cid:173)
`tions initiate the change of the orientation from
`the unstable horizontal to the stable vertical
`position. In this stable position the horizontal
`forces fh are normal to the flat sides of the
`particles.
`
`FLOW FORCES CAUSING HORIZONTAL ORIENTA(cid:173)
`TION
`
`If the dimensions of the flow constriction are
`chosen such that A/a < B/b, then fh < fv. Under
`these conditions the increased vertical flow
`compression causes horizontal orientation of
`flat particles. The mechanism is the same as
`that described above.(Fig. 4).
`
`A
`FIG. 4. Cross-sections of a flow path where A/a<
`B/b. The conditions are inverted compared to those
`described in Figure 3. Flat cells are horizontally
`oriented.
`
`It is transformed to a rectangular field with its
`longer extent in the vertical direction. The flow
`itself no longer follows the law of similarity. By
`reasons of mass conservation an additional
`transformation of the laminar flow takes place.
`One part of the fluid at the right and left sides
`of the cross-section A x B has to be transported
`
`DEMONSTRATION OF THE ORIENTATION EFFECT
`
`Figure 5 shows schematic diagrams and Fig(cid:173)
`ure 6 shows authentic photographs of the two
`plexiglass chambers that we constructed to
`demonstrate the uniform orientation of flat par(cid:173)
`ticles. Both chambers were mounted on a Zeiss
`
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`

`LATERAL CELL ORIENTATION BY FLOW FORCES
`
`777
`
`Universal microscope. To photograph the mov(cid:173)
`ing cells, a short time illuminating device was
`used, as previously described (2, 3). The parti(cid:173)
`cle flow was controlled by the regulating device
`of our Metricell instrument (4). Because fixed
`chicken erythrocytes are flat, we used them as
`test particles. Figure 7 depicts these cells sus(cid:173)
`pended in distilled water while passing through
`the orifices of both chambers. The sheath fluid
`also consisted of distilled water. The applied
`suction was about 0.2 atmosphere. Because the
`cover slip of the chambers interferes with the
`horizontal planes of symmetry, the straight
`particle path at the intersection line between
`both symmetry planes could not be used in this
`experiment. Therefore, the particles moved in
`the vertical planes of the symmetry and
`slightly below its horizontal planes of symme-
`
`try. As the results indicate, this fact does not
`influence the orientation effect strongly.
`
`DISCUSSION
`Cells that are horizontally oriented do show
`an increased horizontal spread. This clearly is
`explained by the decrease of the hydrodynamic
`focusing in the horizontal direction in that case.
`To obtain a reasonable spread into the direction
`that focuses, to a lesser degree, the outlet width
`of the particle tube, leading into this direction
`should be as small as possible. Another possi(cid:173)
`bility to induce a reasonable cell spread could
`be a second focusing stage without lateral ori(cid:173)
`entation. Some of the horizontally oriented
`cells are in their longer extension not oriented
`along the flow axis. The small angle of 12° in
`the horizontal constriction and rough walls
`
`Chamber for vertical
`
`orientation:
`
`top view
`
`Side V18W
`(section through centre)
`
`a
`
`U coverglass
`~~1IOn
`
`A:6mm
`a =1101-m
`B =2mm
`b=250~o~m
`A/a= 55
`Bib= 8
`
`if _rJ
`
`/
`
`.
`
`ilium.
`
`Chamber
`
`for horizontal orientation
`
`top view
`
`side view
`(section through centre)
`
`b
`
`A=1mm
`a :150~o~m
`B=2mm
`b = 75~o~m
`AA:I= 6
`Bib= 27
`
`FIG. 5. Schematic diagrams of the two plexiglass chambers used to demonstrate the lateral orientation of
`flat cells.
`
`

`

`FIG. 6. Photographs of the flow paths of both experimental chambers. A, vertically orienting chamber; B,
`horizontally orienting chamber. 1, sheath fluid inlet; 2, particle tube; 3, orifice; 4, suck connection.
`
`778
`
`

`

`LATERAL CELL ORIENTATION BY FLOW FORCES
`
`779
`
`FIG. 7. Photographs of fixed chicken erythrocytes passing through the orifices of both chambers. The
`cells are suspended in distilled water. Suction 0.2 atmosphere. Flow speed about 3 m/sec. A, vertically
`oriented cells; B, horizontally oriented cells.
`
`may produce a velocity gradient in the horizon(cid:173)
`tal direction that initiates particle rotation
`around the vertical axis (6). A rough estimation
`taken from our first series of photographs indi(cid:173)
`cates that more than 90% of ali ceiJs are uni(cid:173)
`formly oriented in the lateral direction. Some
`ceiis are not yet oriented. The reason for that
`may be that it requires some time for ceiJs to
`assume the desired uniform orientation, partic(cid:173)
`ularly if ceiJs have first been in the unstable
`inverted orientation. One would think it possi(cid:173)
`ble for ceiJs to reach 100% uniform orientation.
`This could be achieved by optimizing the orient(cid:173)
`ing flow path and the flow conditions and/or by
`use of cascading orientation stages.
`An orientation device of the described type
`could easily be incorporated into every existing
`focusing flow system. The focusing flow path,
`which in most cases consists of a conical tube
`with symmetry of revolution, would have to be
`replaced by a flow path whereby unilateral con(cid:173)
`striction would be preferred. The most simple
`flow path exhibiting an increased unilateral
`constriction consists of a tube with an elliptical
`cross-section, also ending in an eiJiptical outlet.
`
`The long axis of this eiJiptical outlet would
`have to be located at right angles to the long
`axis in the cross-section of the constricting el(cid:173)
`liptical tube.
`
`LITERATURE CITED
`
`1. Gledhill BL, Lake S, Steinmetz LL, Gray JW,
`Crawford JR, Dean PN, Van Dilla MA: Flow
`microfluorometric analysis of sperm DNA con(cid:173)
`tent: effect of cell shape on the fluorescence dis(cid:173)
`tribution. J Cell Physiol 87:367, 1976
`2. Kachel V: Methoden zur Analyse und Korrektur
`apparativ bedingter Messfehler beim elektron(cid:173)
`ischen Verfahren zur Teilchengriissenbestim(cid:173)
`mung nach Coulter. Thesis, Technische Univer(cid:173)
`sitiit Berlin, D82, 1972
`3. Kachel V: Methodik und Ergebnisse optischer
`Formfaktoruntersuchungen bei der Zellvolu(cid:173)
`menmessung nach Coulter. Microsc Acta 75:419,
`1974
`4. Kachel V: Basic principles of electrical sizing of
`cells and particles and their realization in the
`new instrument "Metricell." J Histochem Cyto(cid:173)
`chem 24:211, 1976
`5. Kachel V, Glossner E, Kordwig E, Ruhenstroth(cid:173)
`Bauer G: Fluvo-Metricell, a combined cell vol(cid:173)
`ume and cell fluorescence analyzer. J Histo(cid:173)
`chem Cytochem 25:804, 1977
`
`

`

`780
`
`KACHEL, KORDWIG AND GLOSSNER
`
`6. Kachel V, Menke E: Hydromechanic flow prop(cid:173)
`erties of flow-through systems, Flow Cytometry
`and Sorting. Edited by M Melamed, P Mulla(cid:173)
`ney, M Mendelsohn. J Wiley, New York, in
`press
`7. Kachel V, Metzger H, Ruhenstroth-Bauer G:
`Der Einfluss der Partikeldurchtrittsbahn auf
`
`die Volumenverteilungskurven nach dem Coul(cid:173)
`ter-Verfahren. Z Ges Exp Med 153:331, 1970
`8. Van Dilla MA, Gledhill BL, LakeS, Dean PN,
`Gray JW, Kachel V, Barlogie B. GOhde W:
`Measurement of Mammalian Sperm Deoxyribo(cid:173)
`nucleic Acid by Flow Cytometry. Problems and
`Approaches. J Histochem Cytochem 25:763, 1977
`
`