Falling sphere

Falling ball viscometers are based on Stokes law, which relates the viscosity of a Newtonian fluid to the velocity of the falling sphere. If a sphere is allowed to fall freely through a fluid, it accelerates until the viscous force is exactly the same as the gravitational force. The Stokes equation relating viscosity to the fall of a soHd body through a Hquid may be written as equation 34, where ris the radius of the sphere and d are the density of the sphere and the hquid, respectively g is the gravitational force and p is the velocity of the sphere. 

Sutterby, J. L. Trans. Soc. Rheol. 17 (1973) 559. Falling sphere viscometry. I. Wall and inertial corrections to Stokes law in long tubes. 

Capillary pipette Falling sphere Parallel plate Falling coaxial cylinder Stress relaxation Rotating cylinder Tensile creep... 

For falling sphere viscometry, it is most convenient to define a viscosity ratio based on constant particle dimensions and terminal velocity (S7) ... 

Sutterby (S7) gave a useful tabulation of the viseosity ratio, defined in Eq. (9-8), for relatively low Re and a. These values, intended primarily to correct for departures from Stokes law in falling sphere viscometry, are shown in Fig. 9.6. Reynolds number is defined using the measured Uj and defined in Eq. (9-9). The curve for a = 0 accounts for departures from the creeping flow approximations in an unbounded fluid, and the relative displacement of the other curves indicates the wall effect. 

The number of moles of the solid chemical in the sphere is N = (4/3)ttPpslm, and this is diminished by the mass transfer from the falling sphere into the stagnant fluid. At the surface of the sphere the concentration of the solute is 5, the saturation solubility, and far from the sphere it is zero. Thus,... 

Cupprammonium Solution. This solvent for NC used in determination of its viscosity by the falling sphere method, contains 30 2 g of pure Cu, 165 2g of NH40H (26 to 25%... 

The falling sphere instrument is representative of this class of viscometer and is employed with higher viscosity liquids. A stainless steel ball is allowed to sink through a column of the liquid under test, and the time taken to fall from one designated level to another at its terminal falling velocity is recorded. In order that the terminal... 

Ladenburg s. Correction for Falling Spheres—When a sphere falls in a cylinder whose dimensions are of the same order of magnitude as the sphere, Stokes equation must be modified to take account of the wall and bottom effects. This is necessary since the displacement action of the sphere interferes with its motion. Ladenburg (1907) supplied the necessary corrections. For the wall-effect, Ladenburg gave the correction as... 

Empirical relationships of similar form for mass transfer in packed beds, to falling spheres, to flat plates, and other relevant geometries are given in several excellent text books [48-51]. 

Old observations on spheres falling through liquids are collected by Muncke.12 The falling sphere method seems to have been first used for viscous liquids (tar, glycerol) by Schottner, ho used 2-4 cm. diam. spheres in a vessel of 20 cm. diam. With. 13 cm. diam. tubes the rate of fall was slower. The values of 97 were larger than those found by Poiseuille s method. 

A ball-and-bucket type of viscometer in which the ball is fixed and the bucket falls was used by Beal and Docksey.i A falling sphere viscometer for opaque liquids was described by McDowell and Walker, Michell s viscometer ... 

Onsager and Fuoss viscosity equation, 125 order in liquids, 1 oriented molecules, 152, 155 0rsted s piezometer, 58 orthobaric density, 48, 327 Oseen correction for falling sphere equation, 87... 

Stormer viscometers, concentric cylinder viscometers, rotating spindles, falling spheres, etc. Because these viscometers expend part of their energy in accelerating the particles, this produces change in their orientation, and because voidage in the bed is affected by the immersed objects, the data on apparent viscosity of fluidized beds have to be carefully examined. 

We had to choose one of the earliest and least precise of the numerous methods for viscosity measurements that have been developed over the years, because the falling-sphere method was the only one that could be adapted to low-temperature measurements. The determination of viscosity was made by measuring the resistance to motion of a falling sphere in the fluid. Since the viscosities measured in our experiments on aqueous-organic mixtures at cryogenic tern-... 

---