A hydrodynamic/Brownian motion model of thermal diffusion in liquids

Physica A: Statistical Mechanics and its Applications

Volumn 356, Issue 2-4, 2005, Pages 279-293

  Bielenberg, James R ^a   Brenner, Howard ^b  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

^b Massachusetts Institute of Technology   (United States)

Author keywords

Liquids; Ludwig Soret effect; Soret effect; Thermal diffusion

Indexed keywords

BOLTZMANN DISTRIBUTIONS; DIFFUSION SEPARATION; LUDWIG-SORET EFFECT; SORET EFFECT;

BROWNIAN MOVEMENT; DIFFUSION IN LIQUIDS; FLUID MECHANICS; HYDRODYNAMICS; MATHEMATICAL MODELS;

THERMAL DIFFUSION;

EID: 28844447779     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2005.03.033     Document Type: Article

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56. More quantitatively, the results predicted by Eq. (9) for gases appear to be off the mark by an order-of-magnitude as shown by the following calculations. In terms of the thermal diffusion factor, α T, BA = T S T, BA, we have from Eq. (8) together with the fact that β = 1 / T for ideal gases that α T, BA = α A / D BA ∞ ≡ (α A / D AA ) (D AA / D BA ∞ ), where D AA is the self-diffusivity of the lighter of the two gases. However, for species A, α A / D AA ≡ Sc / Pr, where Sc = υ / D and Pr = υ / α are the respective Schmidt and Prandtl numbers for the pure gas, with D ≡ D AB = D BA the binary diffusivity. Now, consider the case of a mixture of noble gases. For monatomic gases, one has to a high degree of approximation [14, p. 861] that Sc ≈ 3 4 and Pr ≈ 2 3, whence for the noble gases, α A / D AA ≈ 1.1. On the other hand, since B is the heavier of the two species, it will invariably be true that D AA / D BA ∞ ≫ 1, with the latter ratio growing larger the greater the disparity in molecular weights and sizes. Thus, Eq. (9) applied to gases would result in the inequality α T, BA ≫ 1.1. By way of comparison, for mixtures of helium (A) with the other noble gases (B), experimental values of the thermal diffusion factor α T, BA at room temperature and pressure are as follows [12, p. 129]: neon=0.37, argon=0.38, krypton=0.44, xenon=0.43 and radon=0.64. These data, together with elementary gas kinetic-theory estimates [14, p. 526] of the diffusivity ratio D AA / D BA ∞, confirm the inapplicability of the present theory to gases, with Eq. (9) predicting thermal diffusion factors which are too high by a factor of about 10
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63. Actually, no experiments were conducted below the 'Kraft point' of (approx.) 5 °C, the temperature at which the surfactant crystallizes from solution. As such, over the experimental temperature range upon which Eq. (13) is based, the solute always behaved thermophobically. As such, the expected change in the direction of the SDS movement at the temperature T * was never actually observed, but only implied by Eq. (13)
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