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Related Concept Videos

Diffusion01:21

Diffusion

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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...
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Diffusion01:12

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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...
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Proteins show rotational as well as lateral diffusion across the membrane. The lateral diffusion of proteins was confirmed through the cell fusion experiment where mouse and human cells were fused, resulting in hybrid cells. When the human and mouse cells fused, the specific membrane proteins on human and mouse cells were marked with the red and green-fluorescent markers, respectively. Initially, the red and green fluorescence was located on the respective hemisphere of the cell. As time...
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Passive Diffusion: Overview and Kinetics01:17

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

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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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Steady, Laminar Flow Between Parallel Plates01:17

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Understanding steady, laminar flow between parallel plates is essential for analyzing and designing flow in narrow rectangular channels, commonly found in various water conveyance and drainage systems. The Navier-Stokes equations govern fluid motion and are generally challenging to solve due to their nonlinearity. However, simplifications are possible in certain cases, like the steady laminar flow between parallel plates. For this scenario, we assume steady, incompressible, laminar flow.
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The Diffusion of Passive Tracers in Laminar Shear Flow
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Front propagation in cellular flows for fast reaction and small diffusivity.

Alexandra Tzella1, Jacques Vanneste2

  • 1School of Mathematics, University of Birmingham, Birmingham, United Kingdom.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
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Fluid flows significantly impact chemical front propagation in Fisher-Kolmogorov-Petrovsky-Piskunov models. An asymptotic theory reveals front speed depends on a minimized path, providing efficient calculations for various Péclet (Pe) and Damköhler (Da) number regimes.

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Area of Science:

  • Chemical kinetics
  • Fluid dynamics
  • Mathematical modeling

Background:

  • Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) models describe phenomena like population dynamics and chemical reactions.
  • Understanding the influence of external forces, such as fluid flow, is crucial for accurately predicting front propagation.
  • Previous studies often simplified flow conditions or focused on different parameter regimes.

Purpose of the Study:

  • To investigate how fluid flows affect chemical front speeds in FKPP models.
  • To develop an asymptotic theory for front propagation in cellular flows.
  • To derive efficient methods for calculating front speeds under specific limiting conditions.

Main Methods:

  • Development of an asymptotic theory for front speed in cellular flow.
  • Analysis in the limit of small molecular diffusivity and large Péclet (Pe) and Damköhler (Da) numbers.
  • Utilizing instanton theory to identify paths minimizing a specific functional for front speed calculation.

Main Results:

  • The front speed is determined by a periodic path (instanton) that minimizes a functional.
  • Efficient procedures for calculating front speed were established.
  • Closed-form expressions for front speed were derived for two distinct parameter regimes: (logPe)(-1) ≪ Da ≪ Pe and Da ≫ Pe.

Conclusions:

  • The study provides a robust theoretical framework for understanding advection-dominated chemical front propagation.
  • Theoretical predictions align well with numerical solutions and simulations.
  • The findings offer insights into optimizing reaction-diffusion processes in flowing systems.