Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Reynolds Transport Theorem01:24

Reynolds Transport Theorem

The Reynolds transport theorem provides a framework to relate the time rate of change of an extensive property within a system to that in a control volume, which is crucial for analyzing fluid dynamics. Extensive properties, such as mass, velocity, acceleration, temperature, and momentum, can be expressed in terms of the mass of a fluid portion. These properties are called extensive because they depend on the system's size, while intensive properties are their corresponding values per unit mass.
Equation of Continuity01:12

Equation of Continuity

Fluid motion is represented by either velocity vectors or streamlines. The volume of a fluid flowing past a given location through an area during a period of time is called the flow rate Q, or more precisely, the volume flow rate. Flow rate and velocity are related—for instance, a river has a greater flow rate if the velocity of the water in it is greater. However, the flow rate also depends on the size and shape of the river. The relationship between flow rate (Q) and average speed (v)...
Conservation of Mass in Finite Cotrol Volume01:16

Conservation of Mass in Finite Cotrol Volume

The principle of conservation of mass is a fundamental law in fluid mechanics and is applied using the continuity equation. We apply the concept to a finite control volume to derive the continuity equation.
A system is defined as a collection of unchanging contents, and the conservation of mass states that a system's mass is constant.
Turbulent Flow: Problem Solving01:09

Turbulent Flow: Problem Solving

Carbonation is a process used to dissolve carbon dioxide gas in a liquid, commonly used in the production of carbonated beverages. Achieving efficient carbonation requires careful control of temperature, pressure, and flow conditions. By adjusting these parameters, carbonation efficiency can be maximized, producing a higher concentration of CO2 in the liquid.
Temperature is a key factor in CO2 solubility. In this case, the CO2 gas and the liquid are cooled to 20°C. Lower temperatures enhance...
Bernoulli's Equation for Flow Along a Streamline01:30

Bernoulli's Equation for Flow Along a Streamline

Bernoulli's equation relates the energy conservation in a fluid moving along a streamline. The equation applies to incompressible and inviscid fluids under steady flow. For such a flow, Newton's second law is applied to a small fluid element, which experiences forces due to pressure differences, gravity, and velocity variations. The force balance leads to the following form of Bernoulli's equation:
Steady, Laminar Flow in Circular Tubes01:23

Steady, Laminar Flow in Circular Tubes

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 purely axial,...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Universality Class of Ion-Intercalation Models.

The journal of physical chemistry letters·2026
Same author

Two-Stage Wildlife Event Classification for Edge Deployment.

Sensors (Basel, Switzerland)·2026
Same author

Multipoint Correlations in Poisson Media.

Physical review letters·2025
Same author

Data-aware forecast of harmful algal blooms with model error.

Water research·2025
Same author

Mechanisms of interface jumps, pinning and hysteresis during cyclic fluid displacements in an isolated pore.

Journal of colloid and interface science·2025
Same author

Unified approach to reset processes and application to coupling between process and reset.

Physical review. E·2024

Related Experiment Video

Updated: Jul 3, 2026

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
11:00

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

Self-consistent four-point closure for transport in steady random flows.

Marco Dentz1, Daniel M Tartakovsky

  • 1Department of Geotechnical Engineering and Geosciences, Technical University of Catalonia (UPC), Barcelona, Spain. marco.dentz@upc.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 23, 2008
PubMed
Summary
This summary is machine-generated.

This study introduces a novel four-point closure approximation for modeling passive scalar transport in random velocity fields. This new method accurately predicts dispersion properties, overcoming limitations of existing two-point closures in steady, biased flows.

More Related Videos

Isolation and Time-Lapse Imaging of Primary Mouse Embryonic Palatal Mesenchyme Cells to Analyze Collective Movement Attributes
07:13

Isolation and Time-Lapse Imaging of Primary Mouse Embryonic Palatal Mesenchyme Cells to Analyze Collective Movement Attributes

Published on: February 13, 2021

Related Experiment Videos

Last Updated: Jul 3, 2026

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
11:00

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

Isolation and Time-Lapse Imaging of Primary Mouse Embryonic Palatal Mesenchyme Cells to Analyze Collective Movement Attributes
07:13

Isolation and Time-Lapse Imaging of Primary Mouse Embryonic Palatal Mesenchyme Cells to Analyze Collective Movement Attributes

Published on: February 13, 2021

Area of Science:

  • Fluid dynamics
  • Transport phenomena
  • Statistical mechanics

Background:

  • Ensemble averaging of advection-dispersion equations for passive scalar transport in random velocity fields necessitates closure approximations.
  • Current two-point (one-loop) closures, including direct interaction approximation and large-eddy simulations, are effective for unbiased, time-dependent fields but fail for steady, biased fields.
  • Existing methods exhibit inconsistencies, predicting non-zero transverse dispersion and underestimating longitudinal dispersion in steady, biased flows.

Purpose of the Study:

  • To develop an improved closure approximation that accurately describes passive scalar transport in steady, biased random velocity fields.
  • To address the quantitative and qualitative failures of existing two-point closures in predicting effective transport properties, particularly transverse dispersion.

Main Methods:

  • Derivation of a novel four-point closure approximation for stochastically averaged transport equations.
  • Comparison of the four-point closure predictions with rigorous theoretical results and Monte Carlo random walk simulations.
  • Analysis of the closure's performance in predicting both transverse and longitudinal dispersion coefficients.

Main Results:

  • The derived four-point closure is exact for transverse dispersion in two spatial dimensions for purely advective transport, correctly predicting no disorder-induced contribution.
  • It accurately predicts a quadratic increase in longitudinal disorder-induced dispersion coefficient with the variance of strong disorder.
  • Asymptotic longitudinal dispersion coefficients align with results from Monte Carlo random walk simulations.

Conclusions:

  • The four-point closure significantly advances the modeling of passive scalar transport in complex, steady, biased random velocity fields.
  • This improved closure resolves inconsistencies of classical one-loop schemes, offering accurate predictions for both longitudinal and transverse dispersion.
  • The findings provide a more robust theoretical framework for understanding and simulating transport phenomena in disordered media.