Average Contact Time by Penetration Theory Calculator

✖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.ⓘ Diffusion Coefficient (DAB) [D_AB]			+10% -10%
✖The Average 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.ⓘ Average Convective Mass Transfer Coefficient [k_{L (Avg)}]			+10% -10%

✖Average Contact Time is the variable used to define the time for contacting between liquid and vapor phases.ⓘ Average Contact Time by Penetration Theory [t_c]

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Average Contact Time by Penetration Theory Solution

STEP 0: Pre-Calculation Summary

Formula Used

Average Contact Time = (4*Diffusion Coefficient (DAB))/((Average Convective Mass Transfer Coefficient^2)*pi)
t_c = (4*D_AB)/((k_{L (Avg)}^2)*pi)
This formula uses 1 Constants, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Average Contact Time - (Measured in Second) - Average Contact Time is the variable used to define the time for contacting between liquid and vapor phases.
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.
Average Convective Mass Transfer Coefficient - (Measured in Meter per Second) - The Average 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

Diffusion Coefficient (DAB): 0.007 Square Meter Per Second --> 0.007 Square Meter Per Second No Conversion Required
Average Convective Mass Transfer Coefficient: 0.028465 Meter per Second --> 0.028465 Meter per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

t_c = (4*D_AB)/((k_{L (Avg)}^2)*pi) --> (4*0.007)/((0.028465^2)*pi)

Evaluating ... ...

t_c = 10.9998251641277

STEP 3: Convert Result to Output's Unit

10.9998251641277 Second --> No Conversion Required

FINAL ANSWER

10.9998251641277 ≈ 10.99983 Second <-- Average Contact Time

(Calculation completed in 00.008 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

Average Contact Time by Penetration Theory Formula

LaTeX Go

Average Contact Time = (4*Diffusion Coefficient (DAB))/((Average Convective Mass Transfer Coefficient^2)*pi)
t_c = (4*D_AB)/((k_{L (Avg)}^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 Average Contact Time by Penetration Theory?

Average Contact Time by Penetration Theory calculator uses Average Contact Time = (4*Diffusion Coefficient (DAB))/((Average Convective Mass Transfer Coefficient^2)*pi) to calculate the Average Contact Time, The Average Contact Time by Penetration Theory formula is used to calculate the average contact time for the liquid phase in contact with the other phase based on penetration theory when diffusivity and mass transfer coefficient are known. Average Contact Time is denoted by t_c symbol.

How to calculate Average Contact Time by Penetration Theory using this online calculator? To use this online calculator for Average Contact Time by Penetration Theory, enter Diffusion Coefficient (DAB) (D_AB) & Average Convective Mass Transfer Coefficient (k_{L (Avg)}) and hit the calculate button. Here is how the Average Contact Time by Penetration Theory calculation can be explained with given input values -> 10.99983 = (4*0.007)/((0.028465^2)*pi).

FAQ

What is Average Contact Time by Penetration Theory?

The Average Contact Time by Penetration Theory formula is used to calculate the average contact time for the liquid phase in contact with the other phase based on penetration theory when diffusivity and mass transfer coefficient are known and is represented as t_c = (4*D_AB)/((k_{L (Avg)}^2)*pi) or Average Contact Time = (4*Diffusion Coefficient (DAB))/((Average Convective Mass Transfer Coefficient^2)*pi). 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 & The Average 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 Average Contact Time by Penetration Theory?

The Average Contact Time by Penetration Theory formula is used to calculate the average contact time for the liquid phase in contact with the other phase based on penetration theory when diffusivity and mass transfer coefficient are known is calculated using Average Contact Time = (4*Diffusion Coefficient (DAB))/((Average Convective Mass Transfer Coefficient^2)*pi). To calculate Average Contact Time by Penetration Theory, you need Diffusion Coefficient (DAB) (D_AB) & Average Convective Mass Transfer Coefficient (k_{L (Avg)}). With our tool, you need to enter the respective value for Diffusion Coefficient (DAB) & Average 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.

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