Epstein s equation

The first theory of the thermal force acting on a particle which took thermal creep into account was developed by Epstein (1929), using the slip formula proposed by Maxwell (1880). Epstein s equation was of the form... 

Example 11.3 Using Epstein s equation, calculate the thermal force on a 1-p.m-diameter glycerol particle in air at standard pressure and temperature when it is placed in a temperature gradient of 1000°C/cm. 

Brock (1962a) extended and improved Epstein s equation by taking into account convective flow near the particle and by using more com-... 

Using Brock s equation, determine the thermophoretic force on a 1-p.m-diameter glycerol particle. For this calculation use C = 1.147, C, = 2.20, and Cm = 1.146. How does this estimate of thermal force compare with the estimate made by using Epstein s equation (Eq. 11.11) ... 

The correction on the tortuosity term in Kozeny-Carman equation was initiated by Foscolo et al. (89) however, they repeated the error of Kozeny s work, which was pointed out later by Epstein (65). The tortuosity model of Foscolo et al. (89) was not in agreement with experiments, although the same line of investigation was continued by Puncochar and Drahos (66). 

In practical work a great deal of trouble is avoided by making the measurements at equal intervals x1 - 0, x2 — xlf..., xn-xn v R. Wegscheider (Zeit. phys. Chem., 41, 52, 1902) employed Simpson s rule for integrating the velocity equations for the speed of hydrolysis of sulphonic esters and G. Bredig and F. Epstein (Zeit. anorg. Chem., 42, 341, 1904) in their study of the velocity of adiabatic reactions. 

Equation (11) is expected to apply even for H < (Grbravcic et al., 1976) and for annulus Reynolds number one or two orders of magnitude larger than the upper limit of Darcy s law (Epstein et al., 1978). 

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