Lecture

Flow in Hele-Shaw Cell

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In course

ME-444: Hydrodynamics

Nondimensionalized Navier-Stokes equations result in a great variety of models (Stokes, Lubrication, Euler, Potential) depending on the Reynolds number. The concept of boundary layer enables us then to identify the different components of the hydrodynamic ...

Description

This lecture covers the flow in a Hele-Shaw cell, focusing on the fundamental equations, continuity, Navier-Stokes equations, and the dominant balance principle. It discusses the flow in a rectangular duct and the Hele-Shaw equation.

Instructor

François Gallaire

google scholar https://scholar.google.ch/citations?hl=fr&user=T3OooAcAAAAJ François Gallaire earned his engineering degree from Ecole Polytechnique in 1998 and a master's in Liquids Physics from Université Pierre et Marie Curie in 1999. He completed his PhD in 2002 at LadHyX on swirling flow instabilities and vortex breakdown. After six years at the Mathematics department of Université de Nice, he joined EPFL in 2009, founding the Fluid Mechanics and Instabilities Lab (LFMI). He became an associate professo

Official source

Ontological neighbourhood

Physics

Mechanics: Fluid mechanics

Related concepts (9)

Navier–Stokes equations

The Navier–Stokes equations (nævˈjeː_stəʊks ) are partial differential equations which describe the motion of viscous fluid substances, named after French engineer and physicist Claude-Louis Navier and Irish physicist and mathematician George Gabriel Stokes. They were developed over several decades of progressively building the theories, from 1822 (Navier) to 1842-1850 (Stokes). The Navier–Stokes equations mathematically express momentum balance and conservation of mass for Newtonian fluids.

Fluid dynamics

In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including aerodynamics (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modelling fission weapon detonation.

Stokes flow

Stokes flow (named after George Gabriel Stokes), also named creeping flow or creeping motion, is a type of fluid flow where advective inertial forces are small compared with viscous forces. The Reynolds number is low, i.e. . This is a typical situation in flows where the fluid velocities are very slow, the viscosities are very large, or the length-scales of the flow are very small. Creeping flow was first studied to understand lubrication. In nature, this type of flow occurs in the swimming of microorganisms and sperm.

Fluid mechanics

Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasmas) and the forces on them. It has applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical, and biomedical engineering, as well as geophysics, oceanography, meteorology, astrophysics, and biology. It can be divided into fluid statics, the study of fluids at rest; and fluid dynamics, the study of the effect of forces on fluid motion.

Potential flow

In fluid dynamics, potential flow (or ideal flow) describes the velocity field as the gradient of a scalar function: the velocity potential. As a result, a potential flow is characterized by an irrotational velocity field, which is a valid approximation for several applications. The irrotationality of a potential flow is due to the curl of the gradient of a scalar always being equal to zero. In the case of an incompressible flow the velocity potential satisfies Laplace's equation, and potential theory is applicable.

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