Distributed Model Assumptions for Immobilized Enzymes — Which set of assumptions underlies diffusion–reaction modeling inside spherical biocatalyst particles?

Introduction:
Distributed (diffusion–reaction) models for immobilized enzymes treat concentration and reaction rate as spatially varying within a particle. To make the problem tractable and comparable with intrinsic kinetics, several simplifying assumptions are adopted. This question asks you to identify those standard assumptions.

Given Data / Assumptions:

• Spherical particles with uniform properties.
• Effective kinetics mimic free-enzyme forms with modified parameters (e.g., Km, Vmax).
• Transport within the particle is diffusion-dominated.
• External film resistance is minimized by adequate mixing.

Concept / Approach:

Under these assumptions, the governing equation becomes a diffusion–reaction differential equation with boundary conditions at the particle surface. Treating kinetics as locally similar to free enzyme permits using familiar rate laws while acknowledging reduced effective values due to immobilization. Assuming negligible external resistance allows focus on internal gradients without additional coupling to bulk mass transfer limitations.

Step-by-Step Solution:

Verification / Alternative check:

Effectiveness-factor solutions and Thiele-modulus analyses use these assumptions to predict observed rates and to diagnose internal diffusion limitations.

Why Other Options Are Wrong:

E contradicts standard modeling practices; A–C are each valid components and collectively form the modeling framework.

Common Pitfalls:

Ignoring external films in poorly mixed systems or applying free-enzyme parameters directly without accounting for reduced effectiveness; always verify with experiments.

Final Answer:

All of the above