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For example, a system of fixed composition is stable to thermal fluctuations when (∂ u ̂ / ∂T ) v ̂ ≡ c ̂ v > 0 and to pressure fluctuations when (∂ v ̂ / ∂p ) T < 0. These expressions involve only equilibrium properties. Comparable inequalities also exist governing stability to compositional fluctuations occurring in binary mixtures at constant pressure and temperature. These involve only derivatives of the respective species chemical potentials with respect to composition, again all equilibrium properties
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For example, a system of fixed composition is stable to thermal fluctuations when (∂ u ̂ / ∂T ) v ̂ ≡ c ̂ v > 0 and to pressure fluctuations when (∂ v ̂ / ∂p ) T < 0. These expressions involve only equilibrium properties. Comparable inequalities also exist governing stability to compositional fluctuations occurring in binary mixtures at constant pressure and temperature. These involve only derivatives of the respective species chemical potentials with respect to composition, again all equilibrium properties.
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Actually, any independent trio of thermodynamic variables will do, e.g., the set of variables (T, p, ψ ̂ ) in place of (T, p, l), or, as in Section 4, the set (s ̂, v ̂, ψ ̂ ). The choice is strictly a matter of convenience
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Actually, any independent trio of thermodynamic variables will do, e.g., the set of variables (T, p, ψ ̂ ) in place of (T, p, l), or, as in Section 4, the set (s ̂, v ̂, ψ ̂ ). The choice is strictly a matter of convenience.
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Rather, the failure of conventional hydrodynamics to confirm Onsager reciprocity could, for example, be attributed to the inapplicability of any one of the constitutive relations (4.2) or, even if all correct, the possible inconsistency of the assumption of identical diffusivities appearing therein
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Rather, the failure of conventional hydrodynamics to confirm Onsager reciprocity could, for example, be attributed to the inapplicability of any one of the constitutive relations (4.2) or, even if all correct, the possible inconsistency of the assumption of identical diffusivities appearing therein.
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2 appearing therein should be suppressed
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In fact, as noted by Rosner [23] for mixtures of chemically similar gases possessing comparable molecular weights, all three diffusivities (D, υ, α) are invariably of the same order of magnitude, such that the dimensionless Schmidt and Lewis numbers, Sc = υ/D and Le = D/α, both possess values near unity
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In fact, as noted by Rosner [23] for mixtures of chemically similar gases possessing comparable molecular weights, all three diffusivities (D, υ, α) are invariably of the same order of magnitude, such that the dimensionless Schmidt and Lewis numbers, Sc = υ/D and Le = D/α, both possess values near unity.
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