Critical angular speed

For the set size of corpuscles, it is defined critical angular speed of... 

Problem 6-5. Honey on a Spoon . You must have observed that when you dip a spoon into honey (or other viscous fluid) withdraw it and hold the spoon horizontal, you can keep the honey from draining by rotating the spoon. If you rotate the spoon too slowly the honey will drain, but above a critical rotation speed the honey will not drain from the spoon. (Try this with water and it will not work ) We want to analyze this problem and see if we can t predict the critical speed of rotation required to keep the honey on the spoon. The honey forms a thin layer of thickness h(0) around the spoon. The spoon is modeled as a cylinder of radius R and rotates about its axis at angular velocity 2 so that the speed of the surface of the cylinder is U = HR. The force of gravity acts downward and tries to pull the fluid off the cylinder. 

Flack and co-workers developed a complex model that included the effects of evaporation on the rheological properties of the viscous fluid. Their work established the idea that only fluid viscosity, angular speed, and evaporative effects are important in determining the final film thickness. Dispense volume, dispense rate, and other factors seem not to be particularly critical in determining the final film thickness as long as the wafer is spun for a sufficiently long time. Yet, in spite of evaporative effects, the final thickness /if of the fluid can be fairly well predicted with an inverse power law relationship [Eq. (11.13)], where C is a constant depending on the viscosity and contains the effects of viscous forces. 

It can be seen from Fig. 20 that Mq 10 5 M0 yr 1 for the considered 60 M0 sequences. It should be stressed that, although the model is simplified and the analysis only qualitative, the derived mass loss rate at the H-limit is expected to be even quantitatively correct, since it is established by the rate of angular momentum loss which is associated with the mass loss. Once the critical rotational velocity is reached, the angular momentum loss rate is set by the expansion time scale of the star (i.e. its speed in the HR diagram) but does not depend on the value of the critical velocity. 

The assumption on which the above calculation is based, namely, equal angular velocity of the grinding media and the mill shell, is not fulfilled under actual operating conditions. Only at rotational speeds substantially higher than the theoretical critical speed will the grinding media remain in contact with the lining all round the circumference. 

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