wilke_1950#

C. R. Wilke, “A Viscosity Equation for Gas Mixtures”, J. Chem. Phys. 18, 517 (1950)

Source record · Catalogue · Review register

Source kind: theory

Recorded technique: Theory: a kinetic-theory approximation for the viscosity of a gas mixture from the pure components’ viscosities and molecular weights alone. Sutherland’s form as written by Buddenberg and Wilke (Eqs. 1-3), with the binary diffusion coefficient eliminated through the self-diffusion coefficients (Eqs. 4-9), for binary mixtures (Eqs. 10-11, ideal gas) and any number of components (Eqs. 12-14); compared with measured viscosities of binary and multicomponent mixtures at atmospheric pressure (Tables I-III, Fig. 1).

Materials in structured entries: None recorded.

Dataset quantities: None recorded.

Contents: 0 datasets; 0 formulas.

Curation notes#

Identity VALIDATED_WITH_WARNINGS by the library. The library pdf’s first page is the publisher’s cover; journal pages 517-519 are pdf pages 2-4. Single author (University of California, Berkeley).

THE RULE (p. 519, Eqs. 13-14, checked against the page image at 600 dpi): mu_m = sum_i mu_i / [1 + (1/x_i) sum_{j != i} x_j phi_ij], with phi_ij = [1 + (mu_i/mu_j)^(1/2) (M_j/M_i)^(1/4)]^2 / {(4/sqrt 2) [1 + (M_i/M_j)]^(1/2)}. mu_i are the pure components’ viscosities at the mixture’s temperature and pressure (Nomenclature, p. 519). Written with phi_ii = 1 (which Eq. 14 gives), this is mu_m = sum_i x_i mu_i / sum_j x_j phi_ij, the form of OEP 1 (its section 4.3), and (4/sqrt 2) [1 + M_i/M_j]^(1/2) = [8 (1 + M_i/M_j)]^(1/2). The binary form, Eq. (11) (p. 518), is the same rule for two components; Eq. (10), with the densities rho_1, rho_2, precedes the ideal-gas reduction. The paper states the equation ‘contains no empirical numerical constants, the constant 4/sqrt 2 coming from the kinetic theory’ (p. 518).

Extraction error in the library’s text: Eq. (14) and Eqs. (10)-(11) are rendered with (M_j/M_i)^(1/2) where the page prints the exponent 1/4. The image is authoritative; Table I’s phi values confirm 1/4 (below).

REPRODUCED (Table I, p. 518, phi_12 and phi_21 of 17 pairs at atmospheric pressure): Eq. (14) with the printed viscosities and modern molar masses gives He-A (20 C) 2.4192 and 0.2716 against the printed 2.417 and 0.2716; He-A (200 C) 2.3176 and 0.2788 (2.318, 0.2789); Ne-A (200 C) 1.6057 and 0.6166 (1.606, 0.6166); Ne-He (200 C) 0.4863 and 1.5523 (0.4862, 1.552); H2-A 1.8684 and 0.2383 (1.870, 0.2384); N2-CO2 1.3676 and 0.7277 (1.368, 0.7281); Ne-N2 1.6113 and 0.6550 (1.612, 0.6552); H2-N2 1.9103 and 0.2750 (1.905, 0.2750): within 0.3 %. One inconsistency: N2-O2 (27 C) prints phi_21 = 1.014, while its own phi_12 = 0.994 and the identity phi_21 = phi_12 (mu_2/mu_1) (M_1/M_2) give 1.005 (Eq. 14 gives 0.9938 and 1.0048); a slip in the table, not in the formula. Nothing is transcribed.

ACCURACY STATED: for the binary data of Fig. 1 (He-A, N2-O2, H2-A, C2H6-C3H8, H2-CCl2F2, C3H8-H2) the average deviation, excluding terminal points, is 0.97 %, and 0.49 % without hydrogen-argon, the least satisfactory (p. 518); for the thirteen multicomponent mixtures of Tables II and III, 1.9 % (p. 519). The mixture viscosities compared are Trautz and coworkers’ (1929-1931), Buddenberg’s (1948) and Herning and Zipperer’s (1936), cited in the table notes.

Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.

Datasets#

No datasets are recorded.

Formulas#

No formulas are recorded.

Corrections#

No dataset errata are recorded in this source record.

Formula corrections, where recorded, appear with their formulas above. Curation notes may also discuss corrections or unresolved interpretation. Consult the review register for the checks and decisions.