Engineering & Science
Scheibel Liquid Diffusivity Correlation (Organic Solute–Solvent Molar Volume)
Estimate dilute organic liquid molecular diffusivity D_AB = 0.0082 * T * (1 + (3 * V_B / V_A)^(2/3)) / (μ_B * V_A^(1/3)) (× 10^-5 cm^2/s) without empirical association factors!
Correcting Stokes-Einstein breakdown when solvent molecules are comparable to or larger than the solute!
Classical Stokes-Einstein assumes a giant solute sphere moving through a continuum of tiny solvent molecules—failing badly in hydrocarbon and organic mixtures where solvent molar volume V_B rivals or exceeds solute molar volume V_A! Edward G. Scheibel (Industrial & Engineering Chemistry, 1954) modified Stokes-Einstein with a geometric packing term (1 + (3 * V_B / V_A)^(2/3)): D_AB = 8.2 × 10^-8 * T * (1 + (3 * V_B / V_A)^(2/3)) / (μ_B * V_A^(1/3)) cm^2/s (or 0.0082 * ... in units of 10^-5 cm^2/s)!
Evaluate toluene (V_A = 118.2 cm^3/mol) diffusing in n-hexane (V_B = 106.3 cm^3/mol, μ_B = 0.60 cP at 298.15 K): geometric packing factor 1 + (3 * 106.3 / 118.2)^(2/3) = 2.9380 yields D_AB = 2.439 × 10^-5 cm^2/s, rising to 3.777 × 10^-5 cm^2/s at 323.15 K (μ_B = 0.42 cP)!
| Organic Solvent Condition (VA = 118.2, VB = 106.3 cm³/mol) | Viscosity μB (cP) | Scheibel D_AB (× 10^-5 cm²/s) | Mass-Transfer Regime |
|---|---|---|---|
| 25 °C Extractor (298.15 K) | 0.60 cP | 2.439 × 10^-5 cm²/s | Ambient Liquid-Liquid Extraction |
| 50 °C Heated Column (323.15 K) | 0.42 cP | 3.777 × 10^-5 cm²/s | +54.9% Faster Pore Diffusion |
| Invalid T <= 0, μB <= 0, or V <= 0 | Undefined | "Invalid Scheibel Inputs" | Positivity Guard |
Scheibel Dilute Organic Liquid Diffusivity D_AB (× 10^-5 cm²/s)
Computes 0.0082 * T * (1 + (3 * V_B / V_A)^(2/3)) / (μ_B * V_A^(1/3)) across temperature B2 (K), solvent viscosity B3 (cP), solute boiling molar volume B4 (cm^3/mol), and solvent boiling molar volume B5 (cm^3/mol).
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0, B5 <= 0), "Invalid Scheibel Inputs", ROUND(0.0082 * B2 * (1 + ((3 * B5 / B4) ^ (2 / 3))) / (B3 * (B4 ^ (1 / 3))), 3))Scheibel Geometric Molar-Volume Packing Factor 1 + (3 V_B / V_A)^(2/3)
Isolates the dimensionless molecular-size ratio factor distinguishing Scheibel from continuum Stokes-Einstein.
=IF(OR(B4 <= 0, B5 <= 0), "Invalid Scheibel Inputs", ROUND(1 + ((3 * B5 / B4) ^ (2 / 3)), 4))Try the example
Use the original values or change them to test your understanding.