Oseen equations

Oseen equations

The Oseen equations refer to equations (1.108) and (1.109) that describe the evolution of small perturbations of velocity components for a viscous incompressible fluid near the unperturbed flow with constant velocity vector and pressure. These equations are used in fluid dynamics to describe the flow of an incompressible and viscous fluid in low Reynolds number.From: Multiphase Flow Handbook [2019], Handbook of Linear Partial Differential Equations for Engineers and Scientists [2019], Development of 3D manipulation of viscoelastic biological cells by AFM based on contact models and oscillatory drag [2021]

Fundamentals of Multiphase Flow

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Published in Efstathios E. Michaelides, Clayton T. Crowe, John D. Schwarzkopf, Multiphase Flow Handbook, 2016

Efstathios E. Michaelides, Zhi-Gang Feng

When applied to particulate ows, Equations 1.87 and 1.88 are sometimes referred to as the "Oseen equations." ey contain the velocity at the surface of the sphere and the nonlinear advection term of the uid ow, which is the last term in the two equations (Oseen, 1913). When Re 1, the nonlinear advection term may be neglected in comparison to the viscous term. en the momentum equation becomes linear and reads as follows: rf or in dimensionless form - * p * + *2u * = u * . t * (1.91) u = -p + m f 2u t (1.90)

Development of 3D manipulation of viscoelastic biological cells by AFM based on contact models and oscillatory drag

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Journal Information

Published in Mechanics of Advanced Materials and Structures, 2021

Moharam Habibnejad Korayem, Zahra Rastegar

In fluid dynamics, Oseen equations describe the flow of an incompressible and viscose fluid in low Reynold’s number. The Oseen flow is a modified description of these flows in comparison with stokes flow. Since conditions of the cantilever movement in the liquid environment are near the defined conditions in Oseen equations, therefore, the drag force equation of Oseen is applicable.

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Fundamentals of Multiphase Flow

Development of 3D manipulation of viscoelastic biological cells by AFM based on contact models and oscillatory drag