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...

The development of flow cytometry techniques began in 1934 with initial attempts by Andrew Moldavan, a bacteriologist who counted the cells in a flowing capillary system. Moldavan pumped cells through a capillary tube focused under a microscope for visualization. The invention of photometry allowed the measurement of differentially-stained cells, and Louis Kamentsky developed the first multiparameter flow cytometer in 1965 to identify and count the cancer cells in cervical tissue specimens.
In...

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...

Cell separation was first achieved in 1964 by S. H. Seal, who separated large tumor cells from the smaller blood cells using filtration. Two years later, Pohl and Hawk performed experiments on how cells respond differently to a nonuniform electric field based on the cell type. Such observations were the inception of cell separation methods, which allow isolating a single cell type from a heterogeneous sample.

Electrophoresis is a powerful analytical separation technique that relies on the differential migration of charged species when subjected to an electric field. The core strength of electrophoresis lies in its ability to separate high-molecular-weight species in complex mixtures. It has found widespread use in biochemistry, molecular biology, and analytical chemistry, allowing the separation of compounds like amino acids, nucleotides, carbohydrates, and proteins with excellent resolution.
There...

Fluid flows are categorized by dimensionality and behavior, with one-dimensional flow being the simplest form, where properties like velocity and pressure change only along a single axis. Water moving through straight pipes exemplifies this flow type, as variations in other directions are minimal. One-dimensional analysis helps simplify understanding such flows, focusing solely on changes along the pipe's length.
Two-dimensional flow involves changes in both length and height, as seen in...