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Related Concept Videos

Density00:56

Density

Density is an important characteristic of substances, crucial in determining whether an object sinks or floats in a fluid. Its SI unit is kg/m3, and its cgs unit is g/cm3. The density of an object helps in identifying its composition, and also reveals information about the phase of the matter and its substructure. The densities of liquids and solids are roughly comparable, consistent with the fact that their atoms are in close contact. However, gases have much lower densities than liquids and...
The Kinetic Model of Gases01:24

The Kinetic Model of Gases

The kinetic model of gases explains the properties of a perfect gas using three main assumptions: molecules move in ceaseless random motion, their size is negligible compared to the distances between them, and they do not interact except during perfectly elastic collisions. The total energy of a gas is the sum of the kinetic energies of all its constituent molecules. The pressure exerted by the gas arises from the continual bombardment of the container walls by billions of colliding molecules.
Real Gases: Effects of Intermolecular Forces and Molecular Volume Deriving Van der Waals Equation04:01

Real Gases: Effects of Intermolecular Forces and Molecular Volume Deriving Van der Waals Equation

Thus far, the ideal gas law, PV = nRT, has been applied to a variety of different types of problems, ranging from reaction stoichiometry and empirical and molecular formula problems to determining the density and molar mass of a gas. However, the behavior of a gas is often non-ideal, meaning that the observed relationships between its pressure, volume, and temperature are not accurately described by the gas laws.
Characteristics of Fluids01:20

Characteristics of Fluids

When a force is applied parallel to the top surface of a solid, it resists the applied force due to the internal frictional forces between the layers of the solid known as shearing resistance. However, when the force is removed, the shearing forces restore the original shape of the solid. Other deformation forces also cause temporary changes in shape if the forces are not beyond a threshold magnitude. Solids tend to retain their shape, making the study of their rest and motion easier. Beyond...
Characteristics of Fluids01:31

Characteristics of Fluids

Fluids differ from solids primarily in their molecular structure and stress response. Solids have tightly packed molecules with strong intermolecular forces, maintaining their shape and resisting deformation. In contrast, fluids have molecules spaced farther apart with weaker forces, allowing them to flow and deform easily.
Fluids, which include both liquids and gases, are substances that deform continuously under shearing stress. For example, water and oil are liquids with molecules that can...
Basic Postulates of Kinetic Molecular Theory: Particle Size, Energy, and Collision02:43

Basic Postulates of Kinetic Molecular Theory: Particle Size, Energy, and Collision

The ideal-gas equation, which is empirical, describes the behavior of gases by establishing relationships between their macroscopic properties. For example, Charles’ law states that volume and temperature are directly related. Gases, therefore, expand when heated at constant pressure. Although gas laws explain how the macroscopic properties change relative to one another, it does not explain the rationale behind it.

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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

General dynamical density functional theory for classical fluids.

Benjamin D Goddard1, Andreas Nold, Nikos Savva

  • 1Department of Chemical Engineering, Imperial College London, United Kingdom.

Physical Review Letters
|September 26, 2012
PubMed
Summary
This summary is machine-generated.

We developed a new dynamical density functional theory for colloidal fluids that accurately models inertia and hydrodynamic interactions. This approach aligns well with Langevin dynamics simulations.

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Area of Science:

  • Soft Matter Physics
  • Fluid Dynamics
  • Statistical Mechanics

Background:

  • Colloidal fluids exhibit complex dynamics influenced by inertia and hydrodynamic interactions.
  • Understanding nonequilibrium properties is crucial for soft matter systems.
  • Existing theories may not fully capture these dynamic effects.

Purpose of the Study:

  • To derive a general dynamical density functional theory (DDFT) for colloidal fluids.
  • To incorporate inertia and hydrodynamic interactions into the DDFT framework.
  • To validate the new DDFT against established simulation methods.

Main Methods:

  • Derivation of a general dynamical density functional theory.
  • Inclusion of inertial effects and hydrodynamic interactions.
  • Comparison with full Langevin dynamics simulations.

Main Results:

  • The derived DDFT shows excellent agreement with full Langevin dynamics.
  • The theory successfully captures the influence of inertia and hydrodynamic interactions.
  • In specific limits, the theory recovers known DDFT and Navier-Stokes-like equations.

Conclusions:

  • The new DDFT provides a robust framework for studying colloidal fluid dynamics.
  • Inertia and hydrodynamic interactions are essential for accurately describing nonequilibrium properties.
  • The derived theory offers a valuable tool for both theoretical and computational research.