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Dino Bousso (1933-1971)
● TITLE: The viscosity of air at high rates of shear
● AUTHOR: Bousso, D.
● SOURCE: M.Sc. thesis, Technion, Haifa, Israel (1960).
● LANGUAGE: Hebrew.
● SUPERVISOR: B. Popper (1927-2012)
● ADVISOR: M. Reiner (1886-1976)
The purpose of this investigation is to determine experimentally whether there is any dependence of the viscosity of air or rates of shear of the order of 107[1/sec]. The velocity gradients encountered in conventional gas viscometers being of a much lower order of magnitude, an instrument capable of meeting these demands was constructed.

The instrument utilizes Reiner's air bearing effect to maintain a very narrow gap between a flat rotating disk and platen of plans surface. When the gap is large, air is drawn out centrifugally from between the platens with a corresponding reduction of pressure tending to bring the platens together. However, when the gap reaches the order of a few microns, the air is no longer pumped out and a state of equilibrium is attained. If the gap is further reduced by applying an external load, pressure is built up until a new equilibrium position is reached.

In the instrument developed, a viscous moment is produced by two rotors consisting of plane disks of diameter 60 mm rotating on either side of a suspended cylindrical plate, the stator. This moment is measured by suitable means.

The rotors are mounted on collinear shafts. One shaft runs in a spherical roller bearings and is fixed axially. This permits it to adjust itself axially to external loads applied by means of a spring of weights using a lever system. The axis of rotation is horizontal. The air gap is varied by means of the axial load applied.

The rotors are mounted on spherical seats and have a moment of inertia about a perpendicular axis. When rotated they tend to align themselves dynamically with the axis of the major moment of inertia lying along the axis of rotation. This arrangement allows a greater degree of parallelism between rotor and stator than rotors mounted rigidly onto shafts would have permitted. In measuring the viscosity the size of the gap varied between 1 to 3 microns. Its value is calculated from the capacitance of the system of rotors and stator. The speed of rotation of the rotors is measured by means of discharge tube stroboscopes. The moment is measured directly in gram-millimeters. The viscosity is determined with an accuracy of 2% from the formula
ηa = K (M / nC)
where ηa is the apparent value of viscosity kg-sec/mm2.
M - the viscous moment in kg mm.
n - the speed of rotation in revolutions per minute
C - the capacitance in m μ F
K - a constant = 1.875 X 10-7.

Experimental results show a dependence of viscosity on the size of the gap; the viscosity apparently decreasing with the gap. The values measured are lover than those taken from tables. This decrease is due to slip of the gas molecules adjacent to the walls. This lowers the velocity gradient in the gas resulting in a smaller viscous moment.

The true value of the viscosity can be obtained by multiplying its apparent value by a correction factor calculated on the basis of the kinetic of gases,
η = ηa (1+ 2 ς / δ)
η - is the true value of viscosity
ς - a correction for slip of the order of the mean path (μ)
δ - the air gap (μ).

The value of ς, calculated from Maxwell's derivation, for air at atmospheric pressure at 27oC is 0.071μ. Knudsen and Timiriazeff suggest 0.7 to 0.9 of the mean free path giving 0.07 to 0.09μ respectively. It appears that the best fit is obtained by using Maxwell's correction. After correction for slip no dependence of viscosity on the velocity gradient can be detected within the limits of experimental error.

In view of utilizing the Reiner effects for a self-lubricating air thrust bearing, two series of experiments were carried out to establish relationships between the axial load P, the speed of revolution n, and the air gap δ. In the first series the rotors and stator were symmetrically arranged. The range of loads was 40-420 grams.

In the second series the stator was radially displaced relative to the rotors. The gap was measured for various displacements. In this asymmetrical state the rotors are not parallel to the stator but form a wedge-shaped gap whose load carrying capacity is considerably greater than in the symmetrical state because of a hydrodynamic effect. It was found that at a given load and speed the gap increases with the radial displacement to a maximum value and then decreases. This is due to the reduction in bearing area offsetting the effect of increased wedge angle. The gap reaches a maximum value of approximately 2 times that in the symmetrical state. The range of loads was 40 to 820 g corresponding to mean pressures from 2 to 40 g/cm2.

In the range tested the ratio of load to viscous moment is low in comparison with conventional bearings. Another unfavorable is the extreme sensitivity of bearing to foreign particles ratio present in the air. However, the fact that the load capacity for the heavier loads varies inversely as approximately the fourth power of the gap is encouraging. Further investigation is required to establish the load capacity as a function of rotor diameter, and profile on view of increasing the load capacity for a given viscous moment.

● 10 references.


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