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Penetration Theory of Mass Transfer Solution

STEP 0: Pre-Calculation Summary
Formula Used
Convective Mass Transfer Coefficient = 2*sqrt(Diffusion Coefficient/(pi*Contact Time))
kL = 2*sqrt(DAB/(pi*tc))
This formula uses 1 Constants, 1 Functions, 2 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
Diffusion Coefficient - The Diffusion Coefficient (DAB) is the amount of a particular substance that diffuses across a unit area in 1 s under the influence of a gradient of one unit. (Measured in Square Meter Per Second)
Contact Time - Contact Time means the time for contact between the vapor and liquid phases. (Measured in Second)
STEP 1: Convert Input(s) to Base Unit
Diffusion Coefficient: 0.005 Square Meter Per Second --> 0.005 Square Meter Per Second No Conversion Required
Contact Time: 10 Second --> 10 Second No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
kL = 2*sqrt(DAB/(pi*tc)) --> 2*sqrt(0.005/(pi*10))
Evaluating ... ...
kL = 0.0252313252202016
STEP 3: Convert Result to Output's Unit
0.0252313252202016 Meter per Second --> No Conversion Required
FINAL ANSWER
0.0252313252202016 Meter per Second <-- Convective Mass Transfer Coefficient
(Calculation completed in 00.000 seconds)

7 Mass Transfer Theories Calculators

Penetration Theory of Mass Transfer
Convective Mass Transfer Coefficient = 2*sqrt(Diffusion Coefficient/(pi*Contact Time)) Go
Contact Time based on Penetration Theory
Contact Time = (4*Diffusion Coefficient)/((Convective Mass Transfer Coefficient^2)*pi) Go
Mass Transfer Coefficient based on Surface Renewal Theory
Convective Mass Transfer Coefficient = sqrt(Diffusion Coefficient*Surface Renewal Rate) Go
Surface Renewal Rate based on Surface Renewal Theory
Surface Renewal Rate = (Convective Mass Transfer Coefficient^2)/Diffusion Coefficient Go
Mass Transfer Coefficient based on Film Theory
Convective Mass Transfer Coefficient = Diffusion Coefficient/Film Thickness Go
Film Thickness based on Film Theory
Film Thickness = Diffusion Coefficient/Convective Mass Transfer Coefficient Go
Diffusivity Based on Film Theory
Diffusion Coefficient = Convective Mass Transfer Coefficient*Film Thickness Go

Penetration Theory of Mass Transfer Formula

Convective Mass Transfer Coefficient = 2*sqrt(Diffusion Coefficient/(pi*Contact Time))
kL = 2*sqrt(DAB/(pi*tc))

What is Penetration Theory ?

The “Penetration Theory” or “Higbie’s model” assumes that each liquid element at the gas-liquid interface is exposed to the gas for a short time. The basic assumptions of the theory are: (1) Mass transfer from the gas into a liquid element occurs under unsteady-state conditions once they are in contact; (2) Each of the liquid elements stays in contact with the gas for same time period; and (3) Equilibrium exists at the gas-liquid interface. This theory was considered an improvement from the two-film theory since mass transfer occurs under unsteady-state conditions in many industrial processes. The Penetration Theory expresses the liquid-side mass transfer coefficient in terms of the contact time and the molecular diffusivity of the gas in the liquid.

How to Calculate Penetration Theory of Mass Transfer?

Penetration Theory of Mass Transfer calculator uses Convective Mass Transfer Coefficient = 2*sqrt(Diffusion Coefficient/(pi*Contact Time)) to calculate the Convective Mass Transfer Coefficient, The Penetration Theory of Mass Transfer formula is used to calculate the mass transfer coefficient for the liquid phase in contact with the other phase based on penetration theory. Convective Mass Transfer Coefficient is denoted by kL symbol.

How to calculate Penetration Theory of Mass Transfer using this online calculator? To use this online calculator for Penetration Theory of Mass Transfer, enter Diffusion Coefficient (DAB) & Contact Time (tc) and hit the calculate button. Here is how the Penetration Theory of Mass Transfer calculation can be explained with given input values -> 0.025231 = 2*sqrt(0.005/(pi*10)).

FAQ

What is Penetration Theory of Mass Transfer?
The Penetration Theory of Mass Transfer formula is used to calculate the mass transfer coefficient for the liquid phase in contact with the other phase based on penetration theory and is represented as kL = 2*sqrt(DAB/(pi*tc)) or Convective Mass Transfer Coefficient = 2*sqrt(Diffusion Coefficient/(pi*Contact Time)). The Diffusion Coefficient (DAB) is the amount of a particular substance that diffuses across a unit area in 1 s under the influence of a gradient of one unit & Contact Time means the time for contact between the vapor and liquid phases.
How to calculate Penetration Theory of Mass Transfer?
The Penetration Theory of Mass Transfer formula is used to calculate the mass transfer coefficient for the liquid phase in contact with the other phase based on penetration theory is calculated using Convective Mass Transfer Coefficient = 2*sqrt(Diffusion Coefficient/(pi*Contact Time)). To calculate Penetration Theory of Mass Transfer, you need Diffusion Coefficient (DAB) & Contact Time (tc). With our tool, you need to enter the respective value for Diffusion Coefficient & Contact Time and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Convective Mass Transfer Coefficient?
In this formula, Convective Mass Transfer Coefficient uses Diffusion Coefficient & Contact Time. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Convective Mass Transfer Coefficient = Diffusion Coefficient/Film Thickness
  • Convective Mass Transfer Coefficient = sqrt(Diffusion Coefficient*Surface Renewal Rate)
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