Diffusivity by Instanataneous Contact Time in Penetration Theory Solution

STEP 0: Pre-Calculation Summary
Formula Used
Diffusion Coefficient = (Instantaneous Contact Time*(Instantaneous Convective Mass Transfer Coefficient^2)*pi)
DAB = (t*(kL(Inst)^2)*pi)
This formula uses 1 Constants, 3 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Diffusion Coefficient - (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.
Instantaneous Contact Time - (Measured in Second) - Instantaneous Contact Time is the variable used to define the time for contact between liquid and vapour phases.
Instantaneous Convective Mass Transfer Coefficient - (Measured in Meter per Second) - The Instantaneous 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.
STEP 1: Convert Input(s) to Base Unit
Instantaneous Contact Time: 9.86 Second --> 9.86 Second No Conversion Required
Instantaneous Convective Mass Transfer Coefficient: 0.009 Meter per Second --> 0.009 Meter per Second No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
DAB = (t*(kL(Inst)^2)*pi) --> (9.86*(0.009^2)*pi)
Evaluating ... ...
DAB = 0.00250906438871602
STEP 3: Convert Result to Output's Unit
0.00250906438871602 Square Meter Per Second --> No Conversion Required
FINAL ANSWER
0.00250906438871602 Square Meter Per Second <-- Diffusion Coefficient
(Calculation completed in 00.012 seconds)

Credits

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DJ Sanghvi College of Engineering (DJSCE), Mumbai
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Gas Phase Mass Transfer Coefficient by Two Film Theory
Overall Gas Phase Mass Transfer Coefficient = 1/((1/Gas Phase Mass Transfer Coefficient)+(Henry's Constant/Liquid Phase Mass Transfer Coefficient)) Go
Average Mass Transfer Coefficient by Penetration Theory
Average Convective Mass Transfer Coefficient = 2*sqrt(Diffusion Coefficient/(pi*Average Contact Time)) Go
Diffusivity by Average Contact Time in Penetration Theory
Diffusion Coefficient = (Average Contact Time*(Average Convective Mass Transfer Coefficient^2)*pi)/4 Go
Average Contact Time by Penetration Theory
Average Contact Time = (4*Diffusion Coefficient)/((Average Convective Mass Transfer Coefficient^2)*pi) Go
Mass Transfer Coefficient by Surface Renewal Theory
Convective Mass Transfer Coefficient = sqrt(Diffusion Coefficient*Surface Renewal Rate) Go
Surface Renewal Rate by Surface Renewal Theory
Surface Renewal Rate = (Convective Mass Transfer Coefficient^2)/Diffusion Coefficient Go
Mass Transfer Coefficient by Film Theory
Convective Mass Transfer Coefficient = Diffusion Coefficient/Film Thickness Go
Film Thickness by Film Theory
Film Thickness = Diffusion Coefficient/Convective Mass Transfer Coefficient Go
Diffusivity by Film Theory
Diffusion Coefficient = Convective Mass Transfer Coefficient*Film Thickness Go

Diffusivity by Instanataneous Contact Time in Penetration Theory Formula

Diffusion Coefficient = (Instantaneous Contact Time*(Instantaneous Convective Mass Transfer Coefficient^2)*pi)
DAB = (t*(kL(Inst)^2)*pi)

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 (tc) and the molecular diffusivity of the gas in the liquid.

How to Calculate Diffusivity by Instanataneous Contact Time in Penetration Theory?

Diffusivity by Instanataneous Contact Time in Penetration Theory calculator uses Diffusion Coefficient = (Instantaneous Contact Time*(Instantaneous Convective Mass Transfer Coefficient^2)*pi) to calculate the Diffusion Coefficient, The Diffusivity by Instanataneous Contact Time in Penetration Theory formula is used to calculate the diffusivity for the liquid phase in contact with the other phase based on penetration theory when instantaneous contact time and mass transfer coefficient are known. Diffusion Coefficient is denoted by DAB symbol.

How to calculate Diffusivity by Instanataneous Contact Time in Penetration Theory using this online calculator? To use this online calculator for Diffusivity by Instanataneous Contact Time in Penetration Theory, enter Instantaneous Contact Time (t) & Instantaneous Convective Mass Transfer Coefficient (kL(Inst)) and hit the calculate button. Here is how the Diffusivity by Instanataneous Contact Time in Penetration Theory calculation can be explained with given input values -> 0.002509 = (9.86*(0.009^2)*pi) .

FAQ

What is Diffusivity by Instanataneous Contact Time in Penetration Theory?
The Diffusivity by Instanataneous Contact Time in Penetration Theory formula is used to calculate the diffusivity for the liquid phase in contact with the other phase based on penetration theory when instantaneous contact time and mass transfer coefficient are known and is represented as DAB = (t*(kL(Inst)^2)*pi) or Diffusion Coefficient = (Instantaneous Contact Time*(Instantaneous Convective Mass Transfer Coefficient^2)*pi) . Instantaneous Contact Time is the variable used to define the time for contact between liquid and vapour phases & The Instantaneous 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.
How to calculate Diffusivity by Instanataneous Contact Time in Penetration Theory?
The Diffusivity by Instanataneous Contact Time in Penetration Theory formula is used to calculate the diffusivity for the liquid phase in contact with the other phase based on penetration theory when instantaneous contact time and mass transfer coefficient are known is calculated using Diffusion Coefficient = (Instantaneous Contact Time*(Instantaneous Convective Mass Transfer Coefficient^2)*pi) . To calculate Diffusivity by Instanataneous Contact Time in Penetration Theory, you need Instantaneous Contact Time (t) & Instantaneous Convective Mass Transfer Coefficient (kL(Inst)). With our tool, you need to enter the respective value for Instantaneous Contact Time & Instantaneous Convective Mass Transfer Coefficient 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?
In this formula, Diffusion Coefficient uses Instantaneous Contact Time & Instantaneous Convective Mass Transfer Coefficient. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Diffusion Coefficient = Convective Mass Transfer Coefficient*Film Thickness
  • Diffusion Coefficient = (Average Contact Time*(Average Convective Mass Transfer Coefficient^2)*pi)/4
  • Diffusion Coefficient = (Convective Mass Transfer Coefficient^2)/ Surface Renewal Rate
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