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Eulerian and Lagrangian Flow Descriptions

Eulerian and Lagrangian Flow Descriptions

Fluid flow analysis is critical in many scientific and engineering disciplines, and two principal approaches are used to describe this flow: the Eulerian and Lagrangian methods. These methods offer different perspectives on monitoring and analyzing the motion of fluids, each with distinct advantages depending on the scenario.
The Eulerian method focuses on fixed points in space where fluid properties, such as velocity, pressure, and temperature, are observed as the fluid moves between these...

Reynolds Transport Theorem

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.

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Plane potential flows simplify fluid motion by assuming the fluid to be irrotational and incompressible. These characteristics allow these flows to be described by a velocity potential function, ϕ, representing the flow speed in a given direction, and a stream function, ψ, that visualizes the flow path, both governed by Laplace's equation. These parameters help in estimating flow patterns, velocity distributions, and pressure fields around various hydraulic structures.
Uniform Flow
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Navier–Stokes Equations

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For incompressible Newtonian fluids, where density remains constant, stresses show a linear relationship with the deformation rate, defined by normal and shear stresses. Normal stresses depend on the pressure exerted on the fluid and the rate of deformation in specific directions, which determines how fluid flows under varying pressures. Shear stresses, on the other hand, act tangentially across fluid layers. They explain how adjacent fluid layers slide relative to one another, connecting...

Couette Flow

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Related Experiment Video

Updated: Jul 22, 2026

BioMEMS: Forging New Collaborations Between Biologists and Engineers

BioMEMS: Forging New Collaborations Between Biologists and Engineers

Published on: November 1, 2007

Microfluidic and Computational Tools for Neurodegeneration Studies.

Kin Gomez¹, Victoria R Yarmey^1,2, Hrishikesh Mane¹

¹Department of Chemical and Biomolecular Engineering, North Carolina State University, Raleigh, North Carolina, USA;

Annual Review of Chemical and Biomolecular Engineering

|January 15, 2025

Summary

Microfluidic technology and advanced computational tools accelerate neurodegenerative disease (ND) research by enhancing biomarker analysis and data interpretation for better diagnostics and treatments.

Keywords:

biomarkers brain-on-a-chip computational tools disease modeling microfluidics neurodegeneration

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Published on: November 17, 2021

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Last Updated: Jul 22, 2026

BioMEMS: Forging New Collaborations Between Biologists and Engineers

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Published on: November 1, 2007

Preparation of Neuronal Co-cultures with Single Cell Precision

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Co-culture of Glutamatergic Neurons and Pediatric High-Grade Glioma Cells Into Microfluidic Devices to Assess Electrical Interactions

Co-culture of Glutamatergic Neurons and Pediatric High-Grade Glioma Cells Into Microfluidic Devices to Assess Electrical Interactions

Published on: November 17, 2021

Area of Science:

Neuroscience
Biotechnology
Computational Biology

Background:

Neurodegenerative diseases (NDs) present complex pathologies challenging conventional research methods.
Limitations in current analytical techniques hinder the development of accurate diagnostics and effective therapies for NDs.

Purpose of the Study:

To explore the role of microfluidic technology in advancing neurodegenerative disease research.
To highlight the necessity of sophisticated computational tools for analyzing complex biological data.

Main Methods:

Utilizing microfluidic devices for improved biomarker quantification, brain organoid culture, and small animal model manipulation.
Applying advanced analytical algorithms and machine learning platforms to process and analyze data from microfluidic systems and other biological datasets (genomic, proteomic, anatomical, cognitive).

Main Results:

Microfluidic technology enhances experimental throughput and the number of measurable metrics.
Computational tools are essential for managing and interpreting the large, complex datasets generated by microfluidic systems and other high-throughput methods.
These integrated approaches show potential for discerning patterns across diverse data types.

Conclusions:

Microfluidics and advanced computation offer powerful synergistic approaches to accelerate discoveries in neurodegenerative disease research.
These technologies can significantly improve the characterization, diagnosis, and treatment platforms for neurodegenerative diseases, leading to better clinical outcomes.