Instantaneous 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 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.ⓘ Instantaneous Convective Mass Transfer Coefficient [k_L(Inst)]			+10% -10%

✖Instantaneous Contact Time is the variable used to define the time for contact between liquid and vapour phases.ⓘ Instantaneous Contact Time by Penetration Theory [t]

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Formula

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Instantaneous Contact Time by Penetration Theory

Formula

`"t" = ("D"_{"AB"})/(("k"_{"L(Inst)"}^2)*pi)`

Example

`"27.50826s"=("0.007m²/s")/((("9e-3m/s")^2)*pi)`

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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 = (D_AB)/((k_L(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 = (D_AB)/((k_L(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

FINAL ANSWER

27.5082617689696 ≈ 27.50826 Second <-- Instantaneous Contact Time

(Calculation completed in 00.004 seconds)

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Created by Vaibhav Mishra

DJ Sanghvi College of Engineering (DJSCE), Mumbai

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University of Hawaiʻi at Mānoa (UH Manoa), Hawaii, USA

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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))

Instantaneous Contact Time by Penetration Theory

Go Instantaneous Contact Time = (Diffusion Coefficient (DAB))/((Instantaneous Convective Mass Transfer Coefficient^2)*pi)

Diffusivity by Instanataneous Contact Time in Penetration Theory

Go Diffusion Coefficient (DAB) = (Instantaneous Contact Time*(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)

Average Contact Time by Penetration Theory

Go Average Contact Time = (4*Diffusion Coefficient (DAB))/((Average Convective Mass Transfer Coefficient^2)*pi)

Diffusivity by Average Contact Time in Penetration Theory

Go Diffusion Coefficient (DAB) = (Average Contact Time*(Average Convective Mass Transfer Coefficient^2)*pi)/4

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)

Surface Renewal Rate by Surface Renewal Theory

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

Diffusivity by Surface Renewal Theory

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

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

Instantaneous Contact Time by Penetration Theory Formula

Instantaneous Contact Time = (Diffusion Coefficient (DAB))/((Instantaneous Convective Mass Transfer Coefficient^2)*pi)
t = (D_AB)/((k_L(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) (D_AB) & Instantaneous Convective Mass Transfer Coefficient (k_L(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 = (D_AB)/((k_L(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) (D_AB) & Instantaneous Convective Mass Transfer Coefficient (k_L(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.

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