Summary
An experimental study of the behaviour of rigid and deformable particles suspended in pseudoplastic and elasticoviscous liquids undergoing slowCouette flow was undertaken. The velocity profiles deviated slightly from those obtained forNewtonian fluids, but the measured angular velocities of rigid spheres showed that the rotation of the field was equal to half the velocity gradient. While the measured angular velocities of rods and discs were in accord with theory applicable toNewtonian liquids, in both non-Newtonian media there was a steady drift in the orbit towards an asymptotic value corresponding to minimum energy dissipation in the flow. Furthermore, discs in elasticoviscous solutions of polyacrylamide at higher shear stresses aligned themselves in the direction of the flow and ceased to rotate.
Migration of rigid particles across the planes of shear in the annul us of theCouette was also observed. In pseudoplastic liquids, the migration was towards the region of higher shear, whereas the opposite was true in elasticoviscous liquids.
The deformation, orientation and burst of pseudoplastic drops inNewtonian liquids and that ofNewtonian drops in pseudoplastic fluids were similar to those previously in completelyNewtonian systems. With elasticoviscous drops, however, the deformation was smaller than given by theory.
As in elasticoviscous fluids, two-body collisions of rigid uniform spheres in the pseudoplastic liquids were unsymmetrical and irreversible, thus differing from collisions inNewtonian systems where complete reversibility is observed.
While some of the observed phenomena in elasticoviscous suspensions could be qualitatively interpreted, particle behaviour in the pseudoplastic liquids could not be explained in terms of the known rheological properties of the fluids.
Zusammenfassung
Es wurde experimentell das Verhalten von festen und deformierbaren Teilchen untersucht, die bei der Suspension in strukturviskosen und viskoelastischen Flüssigkeiten einer langsamenCouette-Strömung ausgesetzt sind. Die Geschwindigkeitsprofile zeigten gewisse Abweichungen von denenNewtonscher Flüssigkeiten, aber die gemessenen Winkelgeschwindigkeiten der festen Kügelchen ergaben, daß die Drehung des Feldes gleich dem halben Geschwindigkeitsgradienten war. Die gemessenen Winkelgeschwindigkeiten der Stäbchen und Scheiben stimmten mit der Theorie, die auf Newtonsche Flüssigkeiten zutrifft, überein. In beiden nicht-Newtonschen Flüssigkeiten verschob sich jedoch die Kreisbahn stetig zu einem asymptotischen Wert, der einem Minimum der Dissipationsenergie der Strömung entsprach. Scheibchen in viskoelastischen Lösungen von Polyacrylamid richteten sich bei höherer Scherspannung in Strömungsrichtung aus und zeigten keine Drehung mehr.
Es wurden auch Wanderungen von festen Teilchen über die Scherebene im Spalt derCouette-Anordnung beobachtet. In strukturviskosen Flüssigkeiten erfolgte die Wanderung in Richtung der höheren Scherung, während auf elastische Flüssigkeiten das Gegenteil zutraf.
Die Deformation, Orientierung und das Aufbrechen strukturviskoser Tröpfchen inNewtonschen Flüssigkeiten und das Verhalten von Newtonschen Tröpfchen in strukturviskosen Flüssigkeiten waren den früher in rein-Newtonschen Systemen beobachteten Phänomenen ähnlich. Die Deformation der viskoelastischen Tröpfchen war jedoch kleiner als die von der Theorie vorhergesagt worden war.
Zweikörper-Zusammenstöße zwischen festen gleichförmigen Kügelchen in strukturviskosen Flüssigkeiten waren unsymmetritch und irreversibel. Darin unterschieden sie sich von Zusammenstößen inNewtonschen Flüssigkeiten, in denen völlige Umkehrbarkeit beobachtet worden war.
Während einige der beobachteten Phänomene in viskoelastischen Suspensionen qualitativ gedeutet werden konnten, ließ sich das Teilchenverhalten in strukturviskosen Flüssigkeiten nicht anhand der bekannten Theologischen Eigenschaften der Flüssigkeiten erklären.
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Abbreviations
- a; a′ (ϕ 1):
-
semi axis of revolution of spheroids; projection of this axis on theX 2 X 3-plane at ϕ1
- A :
-
function ofr e defined by equation (20)
- b; b′ (ϕ 1):
-
radius of a rigid sphere, undeformed drop and semi axis of equatorial diameter of rigid cylinder; projection of this axis on theX 2 X 3-plane at ϕ1
- B :
-
minor axis of a deformed liquid drop
- C, C 0;C′ :
-
orbit constant, orbit constant att = 0; dynamic orbit constant
- D :
-
geometrical deformation of a fluid drop
- E; E B :
-
calculated deformation of a fluid drop; deformation at burst
- F :
-
total normal force measured in the rheogoniometer
- f(λ) :
-
(19λ + 16)/(16λ + 16)
- G, G(R); G B :
-
velocity gradient, atR in theCouette annulus; value ofG at burst
- G′ :
-
measured velocity gradient
- h :
-
height of liquid in theCouette apparatus
- K, n :
-
constants for power law fluid
- L :
-
major axis of a deformed drop
- p 23,p 33 —P 22 :
-
tangential shear stress; normal stress difference
- r p :
-
particle axis ratio = a/b
- r e :
-
equivalent ellipsoidal axis ratio
- r 23,¯r 23 :
-
projection and average projection of unit length of rod axis on theX 2 X 3-plane
- R; R I ,R II :
-
radial distance of the particle center from the axis of rotation inCouette flow; radius of inner and outer cylinder ofCouette apparatus
- R c :
-
radius of the cone of the rheogoniometer
- R 23 :
-
axis ratio of the ellipse, projection of particle rotational orbit in theX 2 X> 3-plane
- t :
-
time
- T :
-
period of rotation of particle
- U 3 :
-
fluid velocity alongX 3-axis
- X 1,X 2,X 3 :
-
Cartesian coordinate axes of the external flow field
- ΔX 2,ΔX 3 :
-
distances along theX 2 andX 3 axes of a sphere center from the mid-point of the collision doublet axis
- α :
-
rheological constant
- α 2 :
-
spheroid integral
- χ :
-
γ/Gb η 0
- λ :
-
viscosity ratio =η 1 /η 0
- η 1 /η 0 :
-
respective apparent viscosities of the suspending and suspended phases
- γ :
-
interfacial tension
- τ :
-
total torque applied on the liquid in aCouette apparatus
- θ 1,ϕ 1 :
-
spherical polar coordinates referred to the polar axisX 1 of the external flow field
- ϕ a ,ϕ r :
-
rectilinear angles of approach and recession of collision doublet of rigid spheres
- ϕ m :
-
ϕ 1-orientation of principal axis of deformed drop in shear flow
- ω 1 :
-
angular velocity of a spheroid
- Ω(R); Ω I ,Ω II :
-
angular velocity of the fluid atR; angular velocities of the inner and outer cylinders of theCouette apparatus
- Γ 1 :
-
hydrodynamic torque
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This work was supported by the Defence Research Board of Canada (DRB Grant 9530-47).
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Gauthier, F., Goldsmith, H.L. & Mason, S.G. Particle motions in non-Newtonian media. Rheol Acta 10, 344–364 (1971). https://doi.org/10.1007/BF01993709
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DOI: https://doi.org/10.1007/BF01993709