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Theories of Dissolution: The Danckwerts' Model and Interfacial Barrier Model01:09

Theories of Dissolution: The Danckwerts' Model and Interfacial Barrier Model

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Various dissolution theories provide insight into the factors that influence the dissolution rate. Danckwerts' Model suggests that turbulence, rather than a stagnant layer, characterizes the dissolution medium at the solid-liquid interface. In this model, the agitated solvent contains macroscopic packets that move to the interface via eddy currents, facilitating the absorption and delivery of the drug to the bulk solution. The regular replenishment of solvent packets maintains the...
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Theories of Dissolution: Diffusion Layer Model01:15

Theories of Dissolution: Diffusion Layer Model

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Dissolution, the process by which drug particles dissolve in a solvent, is explained by the diffusion layer model, a theoretical framework that simulates the absorption of oral drugs and allows us to analyze experimental data.
This process starts with a thin layer, saturated with the drug, forming at the interface between the solid and liquid. The solute then diffuses from this layer into the main solution. The Noyes-Whitney equation suggests that the rate of dissolution relies on the diffusion...
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Passive Diffusion: Overview and Kinetics01:17

Passive Diffusion: Overview and Kinetics

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Passive diffusion is a critical process that allows small lipophilic drugs to cross the cell membrane along a concentration gradient. This mechanism's efficiency depends on four primary factors: the membrane's surface area, the drug's lipid-water partition coefficient, the concentration gradient, and the membrane's thickness.
When administered orally, drugs establish a substantial concentration gradient between the gastrointestinal (GI) lumen and the bloodstream, expediting...
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Facilitated Diffusion01:16

Facilitated Diffusion

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The plasma membrane, a critical structure in cellular biology, houses an array of transporters, or carrier proteins, interspersed within its lipid bilayer. These proteins play a crucial role in solute transport through facilitated diffusion, a form of passive diffusion that uses transporters to move the molecules across the membrane.
In this process, substrates such as organic compounds and ions interact with a transporter on one side, triggering conformational changes in proteins that enable...
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Physiological Pharmacokinetic Models: Blood Flow-Limited Versus Diffusion-Limited Models00:57

Physiological Pharmacokinetic Models: Blood Flow-Limited Versus Diffusion-Limited Models

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Physiological pharmacokinetic models, often called flow-limited or perfusion models, typically assume a swift drug distribution between tissue and venous blood, creating a rapid drug equilibrium. This premise is based on the idea that drug diffusion is extremely fast, and the cell membrane presents no barrier to drug permeation. In this scenario, where no drug binding occurs, the drug concentration in the tissue equals that of the venous blood leaving the tissue. This greatly simplifies the...
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Behavior of Gas Molecules: Molecular Diffusion, Mean Free Path, and Effusion03:48

Behavior of Gas Molecules: Molecular Diffusion, Mean Free Path, and Effusion

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Although gaseous molecules travel at tremendous speeds (hundreds of meters per second), they collide with other gaseous molecules and travel in many different directions before reaching the desired target. At room temperature, a gaseous molecule will experience billions of collisions per second. The mean free path is the average distance a molecule travels between collisions. The mean free path increases with decreasing pressure; in general, the mean free path for a gaseous molecule will be...
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Related Experiment Video

Updated: Jul 11, 2025

A Method for Determination and Simulation of Permeability and Diffusion in a 3D Tissue Model in a Membrane Insert System for Multi-well Plates
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A Method for Determination and Simulation of Permeability and Diffusion in a 3D Tissue Model in a Membrane Insert System for Multi-well Plates

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Modelling of surface reactions and diffusion mediated by bulk diffusion.

Fernando P Duda1, Francisco S Forte Neto1, Eliot Fried2

  • 1Programa de Engenharia Mecânica, COPPE, Universidade Federal do Rio de Janeiro, Cidade Universitária, Rio de Janeiro, CEP 21941-972, RJ, Brazil.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|November 5, 2023
PubMed
Summary
This summary is machine-generated.

We present a new continuum framework for diffusion coupled with surface reactions, applicable to hydrogen storage and cell biology. This model predicts pattern formation and oscillations driven by surface diffusion, with implications for material science and biological systems.

Keywords:
bulk-surface partial-differential equationsdiffusioninternal constraintspattern formationreaction kineticsstability

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Last Updated: Jul 11, 2025

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Area of Science:

  • Continuum mechanics
  • Chemical kinetics
  • Mathematical modeling

Background:

  • Coupled diffusion and reaction processes are crucial in fields like solid-state hydrogen storage and cell biology.
  • Existing models often simplify the complex interplay between bulk diffusion and boundary reactions.

Purpose of the Study:

  • To develop a unified continuum framework for systems with coupled bulk diffusion and surface reaction-diffusion dynamics.
  • To investigate the role of surface diffusion in driving instabilities and pattern formation.
  • To extend the framework to include mechanochemical coupling in deformable media.

Main Methods:

  • Formulation of continuum balances for all constituents.
  • Development of thermodynamically consistent constitutive equations, including Marcelin-De Donder and mass action kinetics.
  • Derivation of a coupled bulk diffusion and surface reaction-diffusion system (FitzHugh-Nagumo type).
  • Linear stability analysis and numerical simulations.

Main Results:

  • The framework successfully models diffusion coupled with surface adsorption/desorption and reactions.
  • Surface diffusion can drive instabilities, leading to steady-state spatial patterns.
  • Bulk diffusion can suppress spatial patterns, potentially leading to temporal oscillations.
  • The framework is extended to include mechanochemical coupling in deformable solids.

Conclusions:

  • The developed continuum framework provides a robust approach for analyzing complex coupled phenomena in various scientific domains.
  • Surface diffusion is identified as a key driver for pattern formation and instability in these systems.
  • The findings offer insights into phenomena relevant to materials science, cell biology, and chemical engineering.