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Related Concept Videos

Physiological Pharmacokinetic Models: Blood Flow-Limited Versus Diffusion-Limited Models00:57

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

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...
Interference and Diffraction02:18

Interference and Diffraction

Interference is a characteristic phenomenon exhibited by waves. When two electromagnetic waves interact with their peaks and troughs coinciding, a resulting wave with enhanced amplitude is produced. This is known as constructive interference. In this case, the two waves interacting are in phase with each other.
Diffusion01:21

Diffusion

Diffusion is a type of passive transport. In passive transport, a substance tends to move from an area of high concentration to an area of low concentration until the concentration is equal across the space. For example, take the diffusion of substances through the air. When someone opens a perfume bottle in a room filled with people, the perfume is at its highest concentration in the bottle and is at its lowest at the edges of the room. The perfume vapor will diffuse, or spread away, from the...
Diffusion01:12

Diffusion

Diffusion is the passive movement of substances down their concentration gradients—requiring no expenditure of cellular energy. Substances, such as molecules or ions, diffuse from an area of high concentration to an area of low concentration in the cytosol or across membranes. Eventually, the concentration will even out, with the substance moving randomly but causing no net change in concentration. Such a state is called dynamic equilibrium, which is essential for maintaining overall...
Theories of Dissolution: Diffusion Layer Model01:15

Theories of Dissolution: Diffusion Layer Model

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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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 concentration...

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Related Experiment Video

Updated: May 16, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow
08:01

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

Elementary models for turbulent diffusion with complex physical features: eddy diffusivity, spectrum and

Andrew J Majda1, Boris Gershgorin

  • 1Department of Mathematics, Center for Atmosphere Ocean Science, Courant Institute, New York University, 251 Mercer Street, New York, NY 10012, USA. jonjon@cims.nyu.edu

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|November 28, 2012
PubMed
Summary
This summary is machine-generated.

Simple models of turbulent tracers reveal complex statistical behaviors, offering exact formulas for diffusivity and variance spectra. These models aid climate science and filtering turbulent data from noisy observations.

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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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Last Updated: May 16, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow
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The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Area of Science:

  • Turbulence theory
  • Atmospheric science
  • Climate modeling

Background:

  • Turbulent tracers exhibit complex statistical features relevant to atmospheric observations.
  • Existing models often lack the simplicity needed for rigorous testing.

Purpose of the Study:

  • To develop and review elementary models for turbulent tracers with background mean gradients.
  • To demonstrate how simple models can capture complex statistical phenomena.

Main Methods:

  • Development of elementary turbulent tracer models.
  • Derivation of exact formulas for non-local eddy diffusivity.
  • Analysis of tracer variance spectra in statistical steady state.
  • Investigation of transitions to intermittent scalar probability density functions.

Main Results:

  • Models exhibit complex statistical features mirroring laboratory and atmospheric data.
  • Exact formulas for non-local, time- and space-dependent eddy diffusivity were derived.
  • The tracer variance spectrum in statistical steady state was analyzed with simple numerics.
  • Transition to intermittent scalar probability density functions with fat exponential tails was observed.

Conclusions:

  • Simple models with complex statistics serve as valuable test cases for contemporary scientific issues.
  • These models are applicable to climate change science and real-time filtering of turbulent tracers from sparse, noisy data.