Engineering & Science
Reddy-Doraiswamy Liquid Diffusivity Correlation (Two-Regime V_B / V_A)
Estimate liquid molecular diffusivity D_AB = K * SQRT(M_B) * T / (μ_B * (V_A * V_B)^(1/3)) (× 10^-5 cm^2/s) with automatic K = 0.010 vs. 0.0085 volume-ratio switching!
Eliminating Wilke-Chang’s guessed association factor φ via two-regime V_B / V_A switching!
K. A. Reddy and L. K. Doraiswamy (Industrial & Engineering Chemistry Fundamentals, 1967) replaced Wilke-Chang’s subjective association parameter φ across 96 binary liquid systems by introducing symmetric cube-root molar volume (V_A * V_B)^(1/3) and switching the proportionality constant automatically at solvent-to-solute molar-volume ratio V_B / V_A = 1.5: K = 10 × 10^-8 (0.010 in units of 10^-5 cm^2/s) when V_B / V_A <= 1.5, and K = 8.5 × 10^-8 (0.0085) when V_B / V_A > 1.5!
Check ethanol/organic solute (V_A = 74.0 cm^3/mol) in water (M_B = 18.02 g/mol, V_B = 18.7 cm^3/mol, μ_B = 0.89 cP at 298.15 K): V_B / V_A = 0.2527 <= 1.5 selects K = 0.010 and predicts D_AB = 1.276 × 10^-5 cm^2/s; conversely, dissolved water (V_A = 18.7) in benzene (M_B = 78.11, V_B = 96.0, μ_B = 0.60 cP) triggers V_B / V_A = 5.1337 > 1.5 (K = 0.0085) -> D_AB = 3.072 × 10^-5 cm^2/s!
| Solute–Solvent Pair (298.15 K) | Volume Ratio V_B / V_A | Selected Constant K | Reddy-Doraiswamy D_AB (× 10^-5 cm²/s) |
|---|---|---|---|
| Organic Solute (VA=74.0) in Water (VB=18.7) | 0.2527 (<= 1.5) | 0.0100 | 1.276 × 10^-5 cm²/s |
| Water (VA=18.7) in Benzene (VB=96.0) | 5.1337 (> 1.5) | 0.0085 | 3.072 × 10^-5 cm²/s |
| Invalid T <= 0, μ_B <= 0, or V <= 0 | Undefined | Error Guard | "Invalid Diffusivity Inputs" |
Reddy-Doraiswamy Liquid Diffusivity D_AB (× 10^-5 cm²/s)
Automatically switches between K = 0.010 (V_B / V_A <= 1.5) and K = 0.0085 (V_B / V_A > 1.5) across temperature B2 (K), solvent viscosity B3 (cP), solvent molar mass B4 (g/mol), solute molar volume B5 (cm^3/mol), and solvent molar volume B6 (cm^3/mol).
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0, B5 <= 0, B6 <= 0), "Invalid Diffusivity Inputs", ROUND(IF(B6 / B5 <= 1.5, 0.01, 0.0085) * SQRT(B4) * B2 / (B3 * ((B5 * B6) ^ (1 / 3))), 3))Solvent-to-Solute Molar Volume Ratio V_B / V_A
Evaluates B6 / B5 to audit which Reddy-Doraiswamy regime (<= 1.5 vs. > 1.5) governs transport.
=IF(OR(B5 <= 0, B6 <= 0), "Invalid Diffusivity Inputs", ROUND(B6 / B5, 4))Try the example
Use the original values or change them to test your understanding.