Instantaneous Mass Transfer Coefficient 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%
✖Instantaneous Contact Time is the variable used to define the time for contact between liquid and vapour phases.ⓘ Instantaneous Contact Time [t]			+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 Mass Transfer Coefficient by Penetration Theory [k_L(Inst)]

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Instantaneous Mass Transfer Coefficient by Penetration Theory Solution

STEP 0: Pre-Calculation Summary

Formula Used

Instantaneous Convective Mass Transfer Coefficient = sqrt(Diffusion Coefficient (DAB)/(pi*Instantaneous Contact Time))
k_L(Inst) = sqrt(D_AB/(pi*t))
This formula uses 1 Constants, 1 Functions, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

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.
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 Contact Time - (Measured in Second) - Instantaneous Contact Time is the variable used to define the time for contact between liquid and vapour phases.

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 Contact Time: 9.86 Second --> 9.86 Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

k_L(Inst) = sqrt(D_AB/(pi*t)) --> sqrt(0.007/(pi*9.86))

Evaluating ... ...

k_L(Inst) = 0.0150326527738966

STEP 3: Convert Result to Output's Unit

0.0150326527738966 Meter per Second --> No Conversion Required

FINAL ANSWER

0.0150326527738966 ≈ 0.015033 Meter per Second <-- Instantaneous Convective Mass Transfer Coefficient

(Calculation completed in 00.004 seconds)

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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

Instantaneous Mass Transfer Coefficient by Penetration Theory Formula

LaTeX Go

Instantaneous Convective Mass Transfer Coefficient = sqrt(Diffusion Coefficient (DAB)/(pi*Instantaneous Contact Time))
k_L(Inst) = sqrt(D_AB/(pi*t))

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 and the molecular diffusivity of the gas in the liquid.

How to Calculate Instantaneous Mass Transfer Coefficient by Penetration Theory?

Instantaneous Mass Transfer Coefficient by Penetration Theory calculator uses Instantaneous Convective Mass Transfer Coefficient = sqrt(Diffusion Coefficient (DAB)/(pi*Instantaneous Contact Time)) to calculate the Instantaneous Convective Mass Transfer Coefficient, The Instantaneous Mass Transfer Coefficient by Penetration Theory formula is used to calculate the instantaneous mass transfer coefficient for the liquid phase in contact with the other phase based on penetration theory. Instantaneous Convective Mass Transfer Coefficient is denoted by k_L(Inst) symbol.

How to calculate Instantaneous Mass Transfer Coefficient by Penetration Theory using this online calculator? To use this online calculator for Instantaneous Mass Transfer Coefficient by Penetration Theory, enter Diffusion Coefficient (DAB) (D_AB) & Instantaneous Contact Time (t) and hit the calculate button. Here is how the Instantaneous Mass Transfer Coefficient by Penetration Theory calculation can be explained with given input values -> 0.015033 = sqrt(0.007/(pi*9.86)).

FAQ

What is Instantaneous Mass Transfer Coefficient by Penetration Theory?

The Instantaneous Mass Transfer Coefficient by Penetration Theory formula is used to calculate the instantaneous mass transfer coefficient for the liquid phase in contact with the other phase based on penetration theory and is represented as k_L(Inst) = sqrt(D_AB/(pi*t)) or Instantaneous Convective Mass Transfer Coefficient = sqrt(Diffusion Coefficient (DAB)/(pi*Instantaneous Contact Time)). 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 is the variable used to define the time for contact between liquid and vapour phases.

How to calculate Instantaneous Mass Transfer Coefficient by Penetration Theory?

The Instantaneous Mass Transfer Coefficient by Penetration Theory formula is used to calculate the instantaneous mass transfer coefficient for the liquid phase in contact with the other phase based on penetration theory is calculated using Instantaneous Convective Mass Transfer Coefficient = sqrt(Diffusion Coefficient (DAB)/(pi*Instantaneous Contact Time)). To calculate Instantaneous Mass Transfer Coefficient by Penetration Theory, you need Diffusion Coefficient (DAB) (D_AB) & Instantaneous Contact Time (t). With our tool, you need to enter the respective value for Diffusion Coefficient (DAB) & Instantaneous Contact Time 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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