Related Experiment Video
Updated: Apr 15, 2026
11:00
Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
Published on: July 19, 2016
12.0K
Interface deformations due to counter-rotating vortices: Viscous versus elastic media
Jacco H Snoeijer1,2, Leen van Wijngaarden1
1Physics of Fluids Group and J. M. Burgers Centre for Fluid Dynamics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands.
Summary
Surface forces shape liquid interfaces and elastic solids. This study reveals that while viscous flow and elastic deformation share identical equations, their resulting surface deflections exhibit opposite signs due to differing kinematics.
Area of Science:
- Physics
- Fluid Mechanics
- Solid Mechanics
- Surface Science
Background:
- Capillary forces govern liquid interface shapes.
- Surface forces also affect elastic solids, particularly those with low Young's modulus.
- Vortices can induce deformation in both viscous fluids and elastic media.
Purpose of the Study:
- To compare the free surface deformation caused by vortices in a viscous fluid versus an elastic medium.
- To analyze the kinematic differences between viscous flow and elastic deformation.
- To investigate the resulting surface deflection signs and field topologies.
Main Methods:
- Utilized complex variable methods to solve two-dimensional problems.
- Leveraged the mathematical identity between linear incompressible elasticity and viscous flow equations.
- Compared the kinematics of free surface deformation in both systems.
Main Results:
- Identified strict mathematical equivalence between viscous flow and elastic deformation equations.
- Demonstrated significantly different free surface kinematics between the two cases.
- Observed displacement and velocity fields with distinct topologies.
- Found that surface deflections were unexpectedly of opposite signs for viscous and elastic scenarios.
Conclusions:
- Despite identical governing equations, viscous and elastic free surface deformations exhibit contrasting kinematics.
- The topological differences in fields lead to opposite surface deflection signs.
- This highlights the importance of considering elastic surface forces in materials with low Young's modulus.
Related Concept Videos
01:28Navier–Stokes Equations
2.9K
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...
2.9K
01:21Deformations in a Transverse Cross Section
752
When a material is subjected to uniaxial stress, it elongates or contracts in the direction of the applied force, and also undergoes changes in the perpendicular directions. This behavior is crucial for understanding how materials behave under stress and is governed by mechanical properties such as Poisson's ratio v, which measures the ratio of transverse strain to axial strain.
As the material stretches, it expands or contracts in orthogonal directions to the load. This phenomenon varies...
As the material stretches, it expands or contracts in orthogonal directions to the load. This phenomenon varies...
752
01:28Euler's Equations of Motion
1.1K
In fluid mechanics, shear stresses arise from viscosity, which represents a fluid's internal resistance to deformation. For low-viscosity fluids, like water, these stresses are minimal, simplifying flow analysis by allowing the fluid to be treated as inviscid, or frictionless. In an inviscid fluid, shear stresses are absent, leaving only normal stresses, which act perpendicularly to fluid elements. Notably, pressure — defined as the negative of the normal stress — remains uniform...
1.1K
01:15Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity
774
Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.
774
01:18Newtonian Fluid: Problem Solving
1.1K
Newtonian fluids exhibit a constant viscosity, meaning their shear stress and shear strain rate are directly proportional. This property ensures a predictable and stable response to applied forces, maintaining a linear relationship between force and flow. Examples include water, air, and light oils, consistently demonstrating this proportional behavior regardless of external conditions.
A velocity gradient forms within the fluid when a Newtonian fluid is placed between two parallel plates, with...
A velocity gradient forms within the fluid when a Newtonian fluid is placed between two parallel plates, with...
1.1K
01:20Elastic Strain Energy for Shearing Stresses
630
As discussed in previous lessons, strain energy in a material is the energy stored when it is elastically deformed, a concept crucial in materials science and mechanical engineering. This energy results from the internal work done against the cohesive forces within the material. When a material undergoes shearing stress and corresponding shearing strain, the strain energy density, which is the energy stored per unit volume, is calculated. Within the elastic limit, where the stress is...
630