Rate Constant of Phase between Bubble and Cloud Calculator

✖Minimum Fluidization Velocity is the Velocity of the Fluid in the Reactor when the pressure drop exceeds the weight of solids.ⓘ Minimum Fluidization Velocity [u_mf]			+10% -10%
✖Diameter of Bubble is the Bubble Diameter passing through Fluid.ⓘ Diameter of Bubble [d_b]			+10% -10%
✖Diffusion Coefficient for Fluidized Reactors is Diffusion of respective Fluid into the Stream, where the fluid is subjected to flow, in the Fluidized Reactors.ⓘ Diffusion Coefficient for Fluidized Reactors [D_{f R}]			+10% -10%

✖Rate Constant for Bubble Cloud Circulation is Calculated when there is an interchange of Phase from Liquid to Gas.ⓘ Rate Constant of Phase between Bubble and Cloud [K_bc]

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Formula

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Rate Constant of Phase between Bubble and Cloud

Formula

`"K"_{"bc"} = 4.50*("u"_{"mf"}/"d"_{"b"})+5.85*(("D"_{"f R"})^(1/2)*("[g]")^(1/4))/"d"_{"b"}^(5/4)`

Example

`"613.2507s⁻¹"=4.50*("1.941m/s"/"0.048m")+5.85*(("0.8761m²/s")^(1/2)*("[g]")^(1/4))/("0.048m")^(5/4)`

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Rate Constant of Phase between Bubble and Cloud Solution

STEP 0: Pre-Calculation Summary

Formula Used

Rate Constant for Bubble Cloud Circulation = 4.50*(Minimum Fluidization Velocity/Diameter of Bubble)+5.85*((Diffusion Coefficient for Fluidized Reactors)^(1/2)*([g])^(1/4))/Diameter of Bubble^(5/4)
K_bc = 4.50*(u_mf/d_b)+5.85*((D_{f R})^(1/2)*([g])^(1/4))/d_b^(5/4)
This formula uses 1 Constants, 4 Variables

Constants Used

[g] - Gravitational acceleration on Earth Value Taken As 9.80665

Variables Used

Rate Constant for Bubble Cloud Circulation - (Measured in 1 Per Second) - Rate Constant for Bubble Cloud Circulation is Calculated when there is an interchange of Phase from Liquid to Gas.
Minimum Fluidization Velocity - (Measured in Meter per Second) - Minimum Fluidization Velocity is the Velocity of the Fluid in the Reactor when the pressure drop exceeds the weight of solids.
Diameter of Bubble - (Measured in Meter) - Diameter of Bubble is the Bubble Diameter passing through Fluid.
Diffusion Coefficient for Fluidized Reactors - (Measured in Square Meter Per Second) - Diffusion Coefficient for Fluidized Reactors is Diffusion of respective Fluid into the Stream, where the fluid is subjected to flow, in the Fluidized Reactors.

STEP 1: Convert Input(s) to Base Unit

Minimum Fluidization Velocity: 1.941 Meter per Second --> 1.941 Meter per Second No Conversion Required
Diameter of Bubble: 0.048 Meter --> 0.048 Meter No Conversion Required
Diffusion Coefficient for Fluidized Reactors: 0.8761 Square Meter Per Second --> 0.8761 Square Meter Per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

K_bc = 4.50*(u_mf/d_b)+5.85*((D_{f R})^(1/2)*([g])^(1/4))/d_b^(5/4) --> 4.50*(1.941/0.048)+5.85*((0.8761)^(1/2)*([g])^(1/4))/0.048^(5/4)

Evaluating ... ...

K_bc = 613.250745659295

STEP 3: Convert Result to Output's Unit

613.250745659295 1 Per Second --> No Conversion Required

FINAL ANSWER

613.250745659295 ≈ 613.2507 1 Per Second <-- Rate Constant for Bubble Cloud Circulation

(Calculation completed in 00.004 seconds)

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Created by Pavan Kumar

Anurag Group of Institutions (AGI), Hyderabad

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< 10+ Various Fluidized Reactors Calculators

Rate Constant of Phase between Bubble and Cloud

Go Rate Constant for Bubble Cloud Circulation = 4.50*(Minimum Fluidization Velocity/Diameter of Bubble)+5.85*((Diffusion Coefficient for Fluidized Reactors)^(1/2)*([g])^(1/4))/Diameter of Bubble^(5/4)

Velocity in Pneumatic Conveying

Go Velocity in Pneumatic Conveying = ((21.6*((Gas Flow Rate/Density of Gas)^0.542)*(Dimensionless Diameter^0.315))*sqrt([g]*Diameter of Particle))^(1/1.542)

Dimensionless Diameter for Fluidized Reactors at G/S Contacting Regime

Go Dimensionless Diameter = Diameter of Particle*(((Density of Gas*(Density of Solids-Density of Gas)*[g])/(Viscosity of Liquid)^2)^(1/3))

Velocity in Fast Fluidized Bed

Go Velocity in Turbulent Fast Fluidized Bed = 1.53*sqrt(((Density of Solids-Density of Gas)*[g]*Diameter of Particle)/Density of Gas)

Dimensionless Velocity for Fluidized Reactors at G/S Contacting Regime

Go Dimensionless Velocity = Velocity in Tube*((Density of Gas^2)/(Viscosity of Liquid*(Density of Solids-Density of Gas)*[g]))^(1/3)

Rate Constant of Phase between Cloud-Wake and Emulsion

Go Rate Constant for Cloud-Wake and Emulsion = 6.77*((Void Fraction at Minimum Fluidization*Diffusion Coefficient for Fluidized Reactors*Rise Velocity of Bubble)/Diameter of Bubble^3)^(1/2)

Terminal Velocity of Fluids for Irregular Shaped Particles

Go Terminal Velocity of Fluid = ((18/(Dimensionless Diameter)^2)+((2.335-(1.744*Sphericity of Particle))/sqrt(Dimensionless Diameter)))^(-1)

Rise Velocity of Bubble in Bubbling Bed

Go Velocity in Bubbling Bed = Initial Velocity of Fluid-Minimum Fluidization Velocity+Rise Velocity of Bubble

Terminal Velocity of Fluid for Spherical Particles

Go Terminal Velocity of Fluid = ((18/(Dimensionless Diameter)^2)+(0.591/sqrt(Dimensionless Diameter)))^(-1)

Rise Velocity of Bubble

Go Rise Velocity of Bubble = 0.711*sqrt([g]*Diameter of Bubble)

Rate Constant of Phase between Bubble and Cloud Formula

What is Bubble and Cloud ?

In the Bubbling phase of a Fluidized Bed Reactor, the Fluidizing Gas flows through the bed, causing the solid particles to behave like a boiling liquid, which is known as formation of Bubble .The cloud phase occurs when the upward gas velocity is increased beyond a certain point. In this phase, the bed loses its definition, and the solid particles are lifted out of the bed, creating a cloud of particles above the bed.

What are Fluidized Reactors ?

Fluidized reactors are a type of chemical reactor that use a fluidized bed as a key component for carrying out various chemical processes. In a fluidized bed reactor, a solid material is suspended and behaves like a fluid when a gas or liquid flows through it. This creates a dynamic system with characteristics of both a solid and a fluid.

How to Calculate Rate Constant of Phase between Bubble and Cloud?

Rate Constant of Phase between Bubble and Cloud calculator uses Rate Constant for Bubble Cloud Circulation = 4.50*(Minimum Fluidization Velocity/Diameter of Bubble)+5.85*((Diffusion Coefficient for Fluidized Reactors)^(1/2)*([g])^(1/4))/Diameter of Bubble^(5/4) to calculate the Rate Constant for Bubble Cloud Circulation, Rate Constant of Phase between Bubble and Cloud formula is defined as Rate Constant Calculated, when Bubbling occurs in the Fluidized Reactor. Rate Constant for Bubble Cloud Circulation is denoted by K_bc symbol.

How to calculate Rate Constant of Phase between Bubble and Cloud using this online calculator? To use this online calculator for Rate Constant of Phase between Bubble and Cloud, enter Minimum Fluidization Velocity (u_mf), Diameter of Bubble (d_b) & Diffusion Coefficient for Fluidized Reactors (D_{f R}) and hit the calculate button. Here is how the Rate Constant of Phase between Bubble and Cloud calculation can be explained with given input values -> 613.2261 = 4.50*(1.941/0.048)+5.85*((0.8761)^(1/2)*([g])^(1/4))/0.048^(5/4).

FAQ

What is Rate Constant of Phase between Bubble and Cloud?

Rate Constant of Phase between Bubble and Cloud formula is defined as Rate Constant Calculated, when Bubbling occurs in the Fluidized Reactor and is represented as K_bc = 4.50*(u_mf/d_b)+5.85*((D_{f R})^(1/2)*([g])^(1/4))/d_b^(5/4) or Rate Constant for Bubble Cloud Circulation = 4.50*(Minimum Fluidization Velocity/Diameter of Bubble)+5.85*((Diffusion Coefficient for Fluidized Reactors)^(1/2)*([g])^(1/4))/Diameter of Bubble^(5/4). Minimum Fluidization Velocity is the Velocity of the Fluid in the Reactor when the pressure drop exceeds the weight of solids, Diameter of Bubble is the Bubble Diameter passing through Fluid & Diffusion Coefficient for Fluidized Reactors is Diffusion of respective Fluid into the Stream, where the fluid is subjected to flow, in the Fluidized Reactors.

How to calculate Rate Constant of Phase between Bubble and Cloud?

Rate Constant of Phase between Bubble and Cloud formula is defined as Rate Constant Calculated, when Bubbling occurs in the Fluidized Reactor is calculated using Rate Constant for Bubble Cloud Circulation = 4.50*(Minimum Fluidization Velocity/Diameter of Bubble)+5.85*((Diffusion Coefficient for Fluidized Reactors)^(1/2)*([g])^(1/4))/Diameter of Bubble^(5/4). To calculate Rate Constant of Phase between Bubble and Cloud, you need Minimum Fluidization Velocity (u_mf), Diameter of Bubble (d_b) & Diffusion Coefficient for Fluidized Reactors (D_{f R}). With our tool, you need to enter the respective value for Minimum Fluidization Velocity, Diameter of Bubble & Diffusion Coefficient for Fluidized Reactors 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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