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Irrotational Flow

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Irrotational flow is characterized by fluid motion where particles do not rotate around their axes, resulting in zero vorticity. For a flow to be irrotational, the curl of the velocity field must be zero. This imposes specific conditions on velocity gradients. For instance, to maintain zero rotation about the z-axis, the gradient condition:

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Deformation in a Circular Shaft

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Related Experiment Video

Updated: May 14, 2026

Mechano-Node-Pore Sensing: A Rapid, Label-Free Platform for Multi-Parameter Single-Cell Viscoelastic Measurements

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Published on: December 2, 2022

Elastic capsule deformation in general irrotational linear flows.

Alex C Szatmary¹, Charles D Eggleton

¹Department of Mechanical Engineering, University of Maryland, Baltimore County, Baltimore, MD 21250, USA.

Fluid Dynamics Research

|February 22, 2013

Summary

Understanding capsule deformation in fluid flow is key for cell motion prediction. This study introduces a new flow characterization and models capsule responses to various flows, revealing planar flows cause greater deformation.

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Area of Science:

Fluid Dynamics
Biophysics
Computational Mechanics

Background:

Predicting biological cell and synthetic capsule deformation in fluid flow is crucial for microfluidics and microcirculation.
Previous studies analyzed capsule behavior in shear and extensional flows.

Purpose of the Study:

To characterize general irrotational linear flows using strain rate and a new parameter 'q'.
To model the deformation of spherical and spheroidal capsules in various extensional flows.
To analyze the effect of flow type on capsule deformation and energy.

Main Methods:

Characterization of flow gradient matrix using strain rate and parameter 'q'.
Modeling capsule deformation (sphere, prolate, oblate spheroids) using the immersed boundary method.
Analysis of time response, steady-state deformation, strain energy, and surface area.

Main Results:

Deformable non-spherical particles align with irrotational flow axes.
A new flow characterization is effective for ellipsoids and spheres at low capillary numbers.
Planar flows induce greater capsule deformation than uniaxial or biaxial flows at a given capillary number.

Conclusions:

The study provides a practical approach to modeling non-spherical particle deformation by aligning them with flow axes.
Capsule behavior is bounded by responses to uniaxial, biaxial, and planar extensional flows.
The findings advance the understanding of capsule dynamics in microfluidic environments.