Rod Climbing of 0.5 wt% MW 4×106 and MW 8×106 PEO solutions laden with 2.0 wt% 10-20nm silica nanoparticles

Daniel D. Joseph
University of Minnesota, August 2005

It is well known that polymeric liquids will climb a rotating rod, whereas Newtonian fluids will not climb. The climb is associated with nonlinear effects, normal stresses, which cannot occur in Newtonian fluids in which the stress is determined by the instantaneous values of the velocity gradient. A perturbation theory for rod climbing was derived by Joseph and Fosdick 1973 and tested in experiments by Joseph, Beavers and Fosdick 1973 and Beavers and Joseph. They showed that the small climb at low angular velocities is proportional to  where  and  are the coefficients of the first and second normal stress differences, respectively. For our qualitative study here we are interested in large climbs outside the domain of validity of perturbation theory which are shown in the photographs just below. These photographs of 0.5 wt% PEO solutions with nanoparticles can be compared with photographs of the climb in the same solution without particles. In fact, without particles there is no measurable climb to show at any angular velocity. This goes to show that that the addition of the silica particles is roughly like a gigantic increase in the molecular weight of the polymer in which enormous climbs with a somewhat different shape configuration than those shown below can be observed; for example, see Fig.1.3 in Tanner 1985 or Fig. 2.3-1 in Bird, et al 1987.

(i) Apparatus

The rod is fixed vertically by the rotor of a Dynapath CNC Mill which can provide a range of 0.04-65 rev/s for the rotating speed. A video system, including a CCD camera and a signal processing setup, is connected with the CNC Mill. The container for liquid is located on the steel table and below the rotor. Both the rotation and the location of rod can be exactly controlled by a feed-back control system.

(ii) Properties of the liquids used in the experiments



Surface Tension




0.5 wt% 4M/2%



0.5 wt% 8M/2%



Table 1. Liquid properties

(iii) Photographs of rod climbing

(a) W = 0.000 rev/s                                        (b) W = 0.072 rev/s

(c) W = 0.265 rev/s                                        (d) W = 0.417 rev/s

(e) W = 0.833 rev/s                                        (f) W = 1.667 rev/s

(g) W = 5.000 rev/s                                        (h) W = 8.333 rev/s

Fig. II.1. Sequence of photos with different rotating speeds in rod climbing experiment for 0.5 wt% 4M/2% solution.


(a) W = 0.000 rev/s                                        (b) W = 0.052 rev/s

(c) W = 0.093 rev/s                                        (d) W = 0.121 rev/s

(e) W = 0.154 rev/s                                        (f) W = 0.273 rev/s

(g) W = 0.840 rev/s                                        (h) W = 1.388 rev/s

Fig. II.2. Sequence of photos with different rotating speeds in rod climbing experiment for 0.5 wt% 8M/2% solution.

Last Modified: Thursday, 11-Aug-2005 13:30:18 CDT
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