The motion of two spheres falling along their line of centres in a Boger fluid

In this experimental investigation the motion of two identical spheres, both accelerating from rest at the same time along the centre line of a cylindrical tube filled with a Boger fluid, is determined as a function of time. It is shown that if two spheres are far apart, the wake of the lower sphere...

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Bibliographic Details
Published in:	Journal of non-Newtonian fluid mechanics Vol. 79; no. 2; pp. 191 - 212
Main Authors:	Bot, E.T.G, Hulsen, M.A, van den Brule, B.H.A.A
Format:	Journal Article
Language:	English
Published:	Amsterdam Elsevier B.V 01-11-1998 Elsevier
Subjects:	Boger fluid Cross-disciplinary physics: materials science; rheology Drag force Exact sciences and technology Fluid dynamics Fundamental areas of phenomenology (including applications) Non-newtonian fluid flows Physics Rheological measurements Rheology Stable separation distance Techniques and apparatus Two-sphere interactions Stable separation distance Drag force Two-sphere interactions Boger fluid Viscoelastic fluid Falling sphere viscosimeter Relative motion Drag Particle interactions Terminal velocity Instrumentation Spherical particle Experimental study Rheological properties
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Summary:	In this experimental investigation the motion of two identical spheres, both accelerating from rest at the same time along the centre line of a cylindrical tube filled with a Boger fluid, is determined as a function of time. It is shown that if two spheres are far apart, the wake of the lower sphere induces a higher velocity for the upper sphere. For not too large distances between the spheres, however, it is found that the velocity of the lower sphere increases considerably for decreasing distance between the spheres. The result of these two effects is that the spheres attract for large distances but separate for small distances. This behaviour eventually results in a stable distance which is found to be independent of the initial distance. This stable distance increases when the Deborah number increases, whereas the presence of the cylindrical tube wall reduces the stable distance. The observed interactions between the spheres are in sharp contrast to the results of Riddle et al. [J. Non-Newtonian Fluid Mech. 2 (1977) 23–35], who found a critical value for the initial distance in several shear-thinning fluids.
ISSN:	0377-0257 1873-2631
DOI:	10.1016/S0377-0257(98)00106-2