## Instantaneous Contact Time by Penetration Theory Solution

STEP 0: Pre-Calculation Summary
Formula Used
Instantaneous Contact Time = (Diffusion Coefficient (DAB))/((Instantaneous Convective Mass Transfer Coefficient^2)*pi)
t = (DAB)/((kL(Inst)^2)*pi)
This formula uses 1 Constants, 3 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Instantaneous Contact Time - (Measured in Second) - Instantaneous Contact Time is the variable used to define the time for contact between liquid and vapour 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.
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
Diffusion Coefficient (DAB): 0.007 Square Meter Per Second --> 0.007 Square Meter Per 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
t = (DAB)/((kL(Inst)^2)*pi) --> (0.007)/((0.009^2)*pi)
Evaluating ... ...
t = 27.5082617689696
STEP 3: Convert Result to Output's Unit
27.5082617689696 Second --> No Conversion Required
27.5082617689696 27.50826 Second <-- Instantaneous Contact Time
(Calculation completed in 00.004 seconds)
You are here -
Home »

## Credits

Created by Vaibhav Mishra
DJ Sanghvi College of Engineering (DJSCE), Mumbai
Vaibhav Mishra has created this Calculator and 300+ more calculators!
Verified by Prerana Bakli
National Institute of Technology (NIT), Meghalaya
Prerana Bakli has verified this Calculator and 1500+ more calculators!

## < 20 Mass Transfer Theories Calculators

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

## Instantaneous Contact Time by Penetration Theory Formula

Instantaneous Contact Time = (Diffusion Coefficient (DAB))/((Instantaneous Convective Mass Transfer Coefficient^2)*pi)
t = (DAB)/((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 Instantaneous Contact Time by Penetration Theory?

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

How to calculate Instantaneous Contact Time by Penetration Theory using this online calculator? To use this online calculator for Instantaneous Contact Time by Penetration Theory, enter Diffusion Coefficient (DAB) (DAB) & Instantaneous Convective Mass Transfer Coefficient (kL(Inst)) and hit the calculate button. Here is how the Instantaneous Contact Time by Penetration Theory calculation can be explained with given input values -> 27.50826 = (0.007)/((0.009^2)*pi).

### FAQ

What is Instantaneous Contact Time by Penetration Theory?
The Instantaneous Contact Time by Penetration Theory formula is used to calculate the instantaneous 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 = (DAB)/((kL(Inst)^2)*pi) or Instantaneous Contact Time = (Diffusion Coefficient (DAB))/((Instantaneous 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 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 Instantaneous Contact Time by Penetration Theory?
The Instantaneous Contact Time by Penetration Theory formula is used to calculate the instantaneous 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 Instantaneous Contact Time = (Diffusion Coefficient (DAB))/((Instantaneous Convective Mass Transfer Coefficient^2)*pi). To calculate Instantaneous Contact Time by Penetration Theory, you need Diffusion Coefficient (DAB) (DAB) & Instantaneous Convective Mass Transfer Coefficient (kL(Inst)). With our tool, you need to enter the respective value for Diffusion Coefficient (DAB) & 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. Let Others Know