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Immobilized Enzyme Bead Thiele Modulus (φ) & Internal Effectiveness Factor (η) Calculator

Easily calculate and compute immobilized enzyme bead thiele modulus (φ) & internal effectiveness factor (η) calculator with accurate equations, live formulas, and expert guidance.

Spherical porous support bead radius.

Enzyme catalytic rate inside bead.

Substrate diffusion through porous matrix.

Calculated Result
0.02 η

Effectiveness (η)

Effectiveness (η)

0.02 η

Internal Effectiveness Factor Eta

0.017

Thiele Modulus Phi

175.27

Rate Limiting Regime

Diffusion-limited regime (η < 0.3): Substrate depletes near outer rim, starving interior enzymes

0.02 — η

Calculation Breakdown

  1. Applied FormulaCalculates the Thiele Modulus (φ) and internal catalytic effectiveness factor (η) for porous immobilized enzyme beads in packed-bed biocatalytic reactors.\phi = R_p \sqrt{\frac{k_1}{D_{\text{eff}}}}, \quad \eta = \frac{3}{\phi}\left(\frac{1}{\tanh\phi} - \frac{1}{\phi}\right)

Immobilized Enzyme Thiele Modulus Metric Output

Interactive visualization based on your current inputs

Calculated Value
0.00.30.50.81.0Effectiveness (η)

What Is the Immobilized Enzyme Bead Thiele Modulus (φ) & Internal Effectiveness Factor (η) Calculator?

This tool computes immobilized enzyme bead thiele modulus (φ) & internal effectiveness factor (η) calculator with high precision arithmetic.

How Does the Immobilized Enzyme Bead Thiele Modulus (φ) & Internal Effectiveness Factor (η) Calculator Work?

Calculates the Thiele Modulus (φ) and internal catalytic effectiveness factor (η) for porous immobilized enzyme beads in packed-bed biocatalytic reactors.

Immobilized Enzyme Bead Thiele Modulus (φ) & Internal Effectiveness Factor (η) Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

ϕ=Rpk1Deff,η=3ϕ(1tanh⁡ϕ−1ϕ)\phi = R_p \sqrt{\frac{k_1}{D_{\text{eff}}}}, \quad \eta = \frac{3}{\phi}\left(\frac{1}{\tanh\phi} - \frac{1}{\phi}\right)

Calculates the Thiele Modulus (φ) and internal catalytic effectiveness factor (η) for porous immobilized enzyme beads in packed-bed biocatalytic reactors.

How to Use the Immobilized Enzyme Bead Thiele Modulus (φ) & Internal Effectiveness Factor (η) Calculator

  1. Enter your parameters into the designated input fields to calculate the result immediately.

Step-by-Step Example Calculation

Immobilized Enzyme Bead Thiele Modulus (φ) & Internal Effectiveness Factor (η) Calculator Example

Input Values:

catalystBeadRadiusMm:0.8
intrinsicFirstOrderRateK1PerSec:12
effectiveDiffusionCoeffM2PerSec:2.5e-10
Worked Steps: Sample evaluation based on standard reference conditions.

Understanding Your Result

The calculated primary figure indicates the optimal or required η.

Factors That Affect the Result

  • Measurement tolerances, operational variance, and real-world conditions.

When Should You Use This Calculator?

  • Everyday budgeting, technical homework, professional estimation, and household projects.

Assumptions & Limitations

  • Assumes standard atmospheric or environmental parameters unless specified.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Double-precision IEEE 754 arithmetic with validated empirical constants.

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