Diffusivity by Surface Renewal Theory Calculator

✖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.ⓘ Convective Mass Transfer Coefficient [k_L]			+10% -10%
✖Surface Renewal Rate is the fractional rate or frequency of surface renewal.ⓘ Surface Renewal Rate [s]			+10% -10%

✖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.ⓘ Diffusivity by Surface Renewal Theory [D_AB]

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Diffusivity by Surface Renewal Theory Solution

STEP 0: Pre-Calculation Summary

Formula Used

Diffusion Coefficient (DAB) = (Convective Mass Transfer Coefficient^2)/Surface Renewal Rate
D_AB = (k_L^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

D_AB = (k_L^2)/s --> (0.0095^2)/0.012

Evaluating ... ...

D_AB = 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 00.020 seconds)

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DJ Sanghvi College of Engineering (DJSCE), Mumbai

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< Mass Transfer Theories Calculators

Liquid Phase Mass Transfer Coefficient by Two Film Theory

LaTeX Go Overall Liquid Phase Mass Transfer Coefficient = 1/((1/(Gas Phase Mass Transfer Coefficient*Henry's Constant))+(1/Liquid Phase Mass Transfer Coefficient))

Average Mass Transfer Coefficient by Penetration Theory

LaTeX Go Average Convective Mass Transfer Coefficient = 2*sqrt(Diffusion Coefficient (DAB)/(pi*Average Contact Time))

Mass Transfer Coefficient by Surface Renewal Theory

LaTeX Go Convective Mass Transfer Coefficient = sqrt(Diffusion Coefficient (DAB)*Surface Renewal Rate)

Mass Transfer Coefficient by Film Theory

LaTeX Go Convective Mass Transfer Coefficient = Diffusion Coefficient (DAB)/Film Thickness

Diffusivity by Surface Renewal Theory Formula

LaTeX Go

Diffusion Coefficient (DAB) = (Convective Mass Transfer Coefficient^2)/Surface Renewal Rate
D_AB = (k_L^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 D_AB 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 (k_L) & 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 D_AB = (k_L^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 (k_L) & 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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