Thermophoresis of a Micro-Particle in Gaseous Media with Effect of Thermal Stress Slip

Effects of thermal stress slip on thermophoresis and photophoresis

“…Note that the second term in the parentheses of Eq. (7b) for the thermal stress was erroneously omitted in the analyses of Li et al (2010) and Soong et al( 2010a). Also, the effect of thermal stress slip disappears if the effect of frictional slip vanishes.…”

“…(4a). A set of kinetic-theory values for complete energy and momentum accommodations appear to be C s ¼1.17, C t ¼2.18, and C m ¼1.14 (Talbot et al, 1980), whereas the value of C h has been used to be 1 (Lockerby et al, 2004;Li et al, 2010;Soong et al, 2010a) or 3 (Bakanov, 2004). The case without consideration of the effect of thermal stress slip is denoted by C h ¼ 0.…”

“…However, in the slip-flow range (l/ao0.3), the analytical prediction with the effect of thermal stress slip (finite values of C h ) in general fits with these experimental data better than that without the effect (with C h ¼0) does. The corresponding thermophoretic force obtained by Li et al (2010) with C h ¼1 omitting the second term in the parentheses of Eq. (7b) for the thermal stress is much smaller than our result in Fig.…”

“…Recently, the effect of thermal stress slip at the gas-particle interface, resulting from the variation of the gas temperature in both tangential and normal directions demonstrated by Maxwell (1879), Sone (1972), Lockerby et al (2004), andBakanov (2004), on the thermophoresis and photophoresis of an aerosol sphere has been examined to some extent (Li et al, 2010;Soong et al, 2010a). It appeared that the thermophoretic and photophoretic forces acting on an aerosol sphere predicted from analyses including partial effect of thermal stress slip are in better agreement with the available experimental data compared with those obtained by Brock (1962) and Mackowski (1989).…”

Thermophoresis of a particle in a concentric cavity with thermal stress slip

“…As C h D (i.e., in absence of thermal stress slip), Equation (2) becomes the well-known formula obtained by Brock (1962) that cannot predict reversed thermophoresis. A set of kinetic-theory values of the jump/slip coefficients for complete energy and momentum accommodations of gas molecules with the hard-sphere pair potential appear to be C s D 1:17, C t D 2:18, and C m D 1:14 (Talbot et al 1980), and the value of C h has been taken to be 1 (Lockerby et al 2004;Li et al 2010) or 3 (Bakanov 2004). According to Equation (2), particles with small Knudsen number and large thermal conductivity (e.g., l 6 a D 0:01 and k p 6 k D 100) may undergo thermophoretic motion with velocities of 10-50 mm 6 s in a temperature gradient of 0.01 K 6 mm.…”