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Related Concept Videos

Distribution of Molecular Speeds01:27

Distribution of Molecular Speeds

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The motion of molecules in a gas is random in magnitude and direction for individual molecules, but a gas of many molecules has a predictable distribution of molecular speeds. This predictable distribution of molecular speeds is known as the Maxwell-Boltzmann distribution. The distribution of molecular speeds in liquids is comparable to that of gases but not identical and can help to understand the phenomenon of the boiling and vapor pressure of a liquid. Consider that a molecule requires a...
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Steady, Laminar Flow in Circular Tubes01:23

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Hagen-Poiseuille flow describes a viscous fluid's steady, incompressible flow through a cylindrical tube with a constant radius R. This flow profile is often applied to understand fluid transport in narrow channels, such as capillaries. It serves as a foundational example of laminar flow. In this model, cylindrical coordinates (r,θ,z) are used to describe the radial (r), angular (θ), and axial (z) dimensions within the tube. For Hagen-Poiseuille flow, the velocity profile is...
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Newtonian Fluid: Problem Solving01:18

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Newtonian fluids exhibit a constant viscosity, meaning their shear stress and shear strain rate are directly proportional. This property ensures a predictable and stable response to applied forces, maintaining a linear relationship between force and flow. Examples include water, air, and light oils, consistently demonstrating this proportional behavior regardless of external conditions.
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Viscosity01:17

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When water is poured into a glass, it falls freely and quickly, whereas if honey or maple syrup is poured over a pancake, it flows slowly and sticks to the surface of the container. This difference in the flow of different kinds of liquids arises due to the fluid friction between the liquid layers and the liquid and the surrounding material. This property of fluids is called fluid viscosity. In this example, water has a lower viscosity than honey and maple syrup.
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Molecular Weight of Step-Growth Polymers01:08

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Step growth polymerization involves bi or multifunctional monomers. Bifunctional monomers react to form linear step growth polymers, whereas multifunctional monomers react to form non-linear or branched polymers.
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Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
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Updated: Aug 22, 2025

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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Distributed medium viscosity yields quasi-exponential step-size probability distributions in heterogeneous media.

Nicole A Bustos1, Chadi M Saad-Roy2,3,4, Andrey G Cherstvy5

  • 1Department of Mechanical Engineering, MIT, Cambridge, MA 02139, USA.

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|November 14, 2022
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Analyzing random walks in complex media reveals that particle step-size distributions in heterogeneous environments may not be exponential. This finding impacts understanding pathogen transport and drug delivery.

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Area of Science:

  • Biophysics
  • Statistical Mechanics

Background:

  • Random walk analysis is crucial for understanding particle movement in complex media.
  • Heterogeneous environments often exhibit exponential step-size distributions, differing from Brownian motion's Gaussian model.

Purpose of the Study:

  • To develop a theoretical framework for passive tracer motion in environments with varying viscosity.
  • To derive an analytical expression for particle step-size distribution in a multi-viscosity system.

Main Methods:

  • Theoretical modeling of passive tracer movement across diverse viscosity sub-environments.
  • Experimental validation using glycerol-water mixtures with systematically varied glycerol concentrations.

Main Results:

  • An exact analytical expression for particle step-size distribution was derived in the limit of many equi-distributed sub-environments.
  • The derived distribution approaches an exponential form for small step sizes.
  • Experimental results validated the theoretical framework.

Conclusions:

  • The assumption of exponential step-size distributions may overestimate large steps in heterogeneous systems.
  • Findings have significant implications for analyzing biophysical processes like pathogen transport and drug delivery.