Diffusivity by Surface Renewal Theory Solution

STEP 0: Pre-Calculation Summary
Formula Used
Diffusion Coefficient (DAB) = (Convective Mass Transfer Coefficient^2)/ Surface Renewal Rate
DAB = (kL^2)/ s
This formula uses 3 Variables
Variables Used
Diffusion Coefficient (DAB) - (Measured in Square Meter Per Second) - The Diffusion Coefficient (DAB) is the amount of a particular substance that diffuses across a unit area in 1 second under the influence of a gradient of one unit.
Convective Mass Transfer Coefficient - (Measured in Meter per Second) - Convective Mass Transfer Coefficient is a function of geometry of the system and the velocity and properties of the fluid similar to the heat transfer coefficient.
Surface Renewal Rate - (Measured in 1 Per Second) - Surface Renewal Rate is the fractional rate or frequency of surface renewal.
STEP 1: Convert Input(s) to Base Unit
Convective Mass Transfer Coefficient: 0.0095 Meter per Second --> 0.0095 Meter per Second No Conversion Required
Surface Renewal Rate: 0.012 1 Per Second --> 0.012 1 Per Second No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
DAB = (kL^2)/ s --> (0.0095^2)/ 0.012
Evaluating ... ...
DAB = 0.00752083333333333
STEP 3: Convert Result to Output's Unit
0.00752083333333333 Square Meter Per Second --> No Conversion Required
FINAL ANSWER
0.00752083333333333 0.007521 Square Meter Per Second <-- Diffusion Coefficient (DAB)
(Calculation completed in 00.004 seconds)

Credits

Created by Vaibhav Mishra
DJ Sanghvi College of Engineering (DJSCE), Mumbai
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20 Mass Transfer Theories Calculators

Liquid Phase Mass Transfer Coefficient by Two Film Theory
Go Overall Liquid Phase Mass Transfer Coefficient = 1/((1/(Gas Phase Mass Transfer Coefficient*Henry's Constant))+(1/Liquid Phase Mass Transfer Coefficient))
Instantaneous Mass Transfer Coefficient by Penetration Theory
Go Instantaneous Convective Mass Transfer Coefficient = sqrt(Diffusion Coefficient (DAB)/(pi*Instantaneous Contact Time))
Gas Phase Mass Transfer Coefficient by Two Film Theory
Go Overall Gas Phase Mass Transfer Coefficient = 1/((1/Gas Phase Mass Transfer Coefficient)+(Henry's Constant/Liquid Phase Mass Transfer Coefficient))
Average Mass Transfer Coefficient by Penetration Theory
Go Average Convective Mass Transfer Coefficient = 2*sqrt(Diffusion Coefficient (DAB)/(pi*Average Contact Time))
Diffusivity by Instanataneous Contact Time in Penetration Theory
Go Diffusion Coefficient (DAB) = (Instantaneous Contact Time*(Instantaneous Convective Mass Transfer Coefficient^2)*pi)
Instantaneous Contact Time by Penetration Theory
Go Instantaneous Contact Time = (Diffusion Coefficient (DAB))/((Instantaneous Convective Mass Transfer Coefficient^2)*pi)
Fractional Resistance Offered by Liquid Phase
Go Fractional Resistance Offered by Liquid Phase = (1/Liquid Phase Mass Transfer Coefficient)/(1/Overall Liquid Phase Mass Transfer Coefficient)
Diffusivity by Average Contact Time in Penetration Theory
Go Diffusion Coefficient (DAB) = (Average Contact Time*(Average Convective Mass Transfer Coefficient^2)*pi)/4
Average Contact Time by Penetration Theory
Go Average Contact Time = (4*Diffusion Coefficient (DAB))/((Average Convective Mass Transfer Coefficient^2)*pi)
Overall Liquid Phase Mass Transfer Coefficient using Fractional Resistance by Liquid Phase
Go Overall Liquid Phase Mass Transfer Coefficient = Liquid Phase Mass Transfer Coefficient*Fractional Resistance Offered by Liquid Phase
Liquid Phase Mass Transfer Coefficient using Fractional Resistance by Liquid Phase
Go Liquid Phase Mass Transfer Coefficient = Overall Liquid Phase Mass Transfer Coefficient/Fractional Resistance Offered by Liquid Phase
Fractional Resistance Offered by Gas Phase
Go Fractional Resistance Offered by Gas Phase = (1/Gas Phase Mass Transfer Coefficient)/(1/Overall Gas Phase Mass Transfer Coefficient)
Overall Gas Phase Mass Transfer Coefficient using Fractional Resistance by Gas Phase
Go Overall Gas Phase Mass Transfer Coefficient = Gas Phase Mass Transfer Coefficient*Fractional Resistance Offered by Gas Phase
Gas Phase Mass Transfer Coefficient using Fractional Resistance by Gas Phase
Go Gas Phase Mass Transfer Coefficient = Overall Gas Phase Mass Transfer Coefficient/Fractional Resistance Offered by Gas Phase
Mass Transfer Coefficient by Surface Renewal Theory
Go Convective Mass Transfer Coefficient = sqrt(Diffusion Coefficient (DAB)*Surface Renewal Rate)
Diffusivity by Surface Renewal Theory
Go Diffusion Coefficient (DAB) = (Convective Mass Transfer Coefficient^2)/ Surface Renewal Rate
Surface Renewal Rate by Surface Renewal Theory
Go Surface Renewal Rate = (Convective Mass Transfer Coefficient^2)/Diffusion Coefficient (DAB)
Mass Transfer Coefficient by Film Theory
Go Convective Mass Transfer Coefficient = Diffusion Coefficient (DAB)/Film Thickness
Film Thickness by Film Theory
Go Film Thickness = Diffusion Coefficient (DAB)/Convective Mass Transfer Coefficient
Diffusivity by Film Theory
Go Diffusion Coefficient (DAB) = Convective Mass Transfer Coefficient*Film Thickness

Diffusivity by Surface Renewal Theory Formula

Diffusion Coefficient (DAB) = (Convective Mass Transfer Coefficient^2)/ Surface Renewal Rate
DAB = (kL^2)/ s

What is Surface Renewal Theory ?

The surface renewal theory, developed by Danckwerts, applies mathematics of the penetration theory to a more plausible situation, where the liquid is pictured as two regions, a large well mixed bulk region and an interfacial region, which is renewed so fast that it behaves as a thick film.

Assumptions of Surface Renewal Theory

The basic assumptions of the theory are (1) liquid elements at the interface are being randomly swapped by fresh elements from the bulk; (2) at any moment, each of the liquid elements at the interface has the same probability of being substituted by a fresh element; and (3) mass transfer from the gas into the liquid element during its stay at the interface takes place under unsteady-state conditions.

How to Calculate Diffusivity by Surface Renewal Theory?

Diffusivity by Surface Renewal Theory calculator uses Diffusion Coefficient (DAB) = (Convective Mass Transfer Coefficient^2)/ Surface Renewal Rate to calculate the Diffusion Coefficient (DAB), The Diffusivity by Surface Renewal Theory formula is used to calculate the diffusivity in mass transfer based on surface renewal theory using surface renewal rate and mass transfer coefficient. Diffusion Coefficient (DAB) is denoted by DAB symbol.

How to calculate Diffusivity by Surface Renewal Theory using this online calculator? To use this online calculator for Diffusivity by Surface Renewal Theory, enter Convective Mass Transfer Coefficient (kL) & Surface Renewal Rate (s) and hit the calculate button. Here is how the Diffusivity by Surface Renewal Theory calculation can be explained with given input values -> 0.007521 = (0.0095^2)/ 0.012.

FAQ

What is Diffusivity by Surface Renewal Theory?
The Diffusivity by Surface Renewal Theory formula is used to calculate the diffusivity in mass transfer based on surface renewal theory using surface renewal rate and mass transfer coefficient and is represented as DAB = (kL^2)/ s or Diffusion Coefficient (DAB) = (Convective Mass Transfer Coefficient^2)/ Surface Renewal Rate. Convective Mass Transfer Coefficient is a function of geometry of the system and the velocity and properties of the fluid similar to the heat transfer coefficient & Surface Renewal Rate is the fractional rate or frequency of surface renewal.
How to calculate Diffusivity by Surface Renewal Theory?
The Diffusivity by Surface Renewal Theory formula is used to calculate the diffusivity in mass transfer based on surface renewal theory using surface renewal rate and mass transfer coefficient is calculated using Diffusion Coefficient (DAB) = (Convective Mass Transfer Coefficient^2)/ Surface Renewal Rate. To calculate Diffusivity by Surface Renewal Theory, you need Convective Mass Transfer Coefficient (kL) & Surface Renewal Rate (s). With our tool, you need to enter the respective value for Convective Mass Transfer Coefficient & Surface Renewal Rate 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 Diffusion Coefficient (DAB)?
In this formula, Diffusion Coefficient (DAB) uses Convective Mass Transfer Coefficient & Surface Renewal Rate. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Diffusion Coefficient (DAB) = Convective Mass Transfer Coefficient*Film Thickness
  • Diffusion Coefficient (DAB) = (Average Contact Time*(Average Convective Mass Transfer Coefficient^2)*pi)/4
  • Diffusion Coefficient (DAB) = (Instantaneous Contact Time*(Instantaneous Convective Mass Transfer Coefficient^2)*pi)
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