Mass Transfer Coefficient Calculator
Compute the convective mass transfer coefficient k from Reynolds- and Schmidt-number correlations for turbulent pipe flow, a flat plate, or a single sphere (droplet, bubble or particle). Used by chemical engineers for preliminary contactor and reactor sizing.
Last updated: September 2026
Formula below · 2 sources (aiche.org, Wikipedia) · Updated Sep 2026
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About this calculator
The mass transfer coefficient k (m/s) follows from a Sherwood-number correlation: k = Sh × D / L, where Re = v·L/ν is the Reynolds number, Sc = ν/D is the Schmidt number, D is molecular diffusivity (m²/s), L is the characteristic length (m), ν is kinematic viscosity (m²/s), and v is fluid velocity (m/s). Three published correlations are offered: turbulent flow inside a pipe (Linton–Sherwood, Sh = 0.023·Re^0.83·Sc^(1/3), Re > 2,000, L = pipe diameter); a flat plate with a turbulent boundary layer (Sh = 0.037·Re^0.8·Sc^(1/3), average over length L, Re > 5×10⁵); and a single sphere such as a droplet, bubble or particle (Ranz–Marshall, Sh = 2 + 0.6·Re^0.5·Sc^(1/3), L = sphere diameter). Packed beds, bubble columns and stirred tanks need their own geometry-specific correlations (e.g. Wilson–Geankoplis, Calderbank) with additional inputs such as bed voidage or power per volume, so they are not approximated here.
How to use
Consider liquid flowing in a 1 cm pipe with D = 2×10⁻⁹ m²/s, v = 0.5 m/s, L = 0.01 m, ν = 1×10⁻⁶ m²/s, geometry = Turbulent pipe flow. Step 1 — Re = (0.5 × 0.01) / 1×10⁻⁶ = 5,000. Step 2 — Sc = 1×10⁻⁶ / 2×10⁻⁹ = 500, Sc^(1/3) = 7.94. Step 3 — Sh = 0.023 × 5000^0.83 × 7.94 = 0.023 × 1,179 × 7.94 = 215. Step 4 — k = 215 × 2×10⁻⁹ / 0.01 = 4.3×10⁻⁵ m/s. For a 2 mm droplet moving at 0.05 m/s in the same liquid (Sphere, L = 0.002): Re = 100, Sh = 2 + 0.6 × 10 × 7.94 = 49.6, k = 49.6 × 2×10⁻⁹ / 0.002 = 5.0×10⁻⁵ m/s.
Frequently asked questions
Which correlation should I choose?
Pick the one whose geometry and flow regime match yours. Linton–Sherwood is for fully turbulent flow inside a pipe or tube (Re above ~2,000, Sc 0.6–3,000), with L the pipe diameter. The flat-plate correlation is the length-averaged turbulent boundary-layer result, with L the plate length. Ranz–Marshall applies to an isolated sphere (drop, bubble, particle), with L the diameter; its constant 2 is the pure-diffusion limit in a stagnant fluid. Packed and bubble columns have their own correlations with extra inputs (packing area, voidage, gas holdup), which this calculator does not model.
How does molecular diffusivity affect the mass transfer coefficient?
Diffusivity D appears twice: through the Schmidt number Sc = ν/D (raised to 1/3) and directly in k = Sh·D/L. The net effect in the turbulent correlations is k ∝ D^(2/3), so a higher diffusivity raises the mass transfer coefficient. Gases have diffusivities around 10⁻⁵ m²/s, roughly 10,000 times larger than liquids (10⁻⁹ m²/s), which is why gas-phase mass transfer coefficients are much larger than liquid-phase ones.
When should I use a more detailed model instead of this dimensionless correlation?
This correlation is suitable for preliminary design and order-of-magnitude estimates in turbulent flow regimes (Re > 1,000). For laminar flow, non-Newtonian fluids, or highly concentrated systems where the driving force is not dilute, more rigorous models such as penetration theory or surface renewal theory are recommended. Reactive absorption systems also require incorporating enhancement factors. Experimental validation with pilot data is always advisable before finalizing column specifications for production-scale equipment.