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# Complex Fluids

## Viscoelastic Fluids

 Numerical modeling of viscoelastic flows is of great importance for complex engineering applications involving blood, paints, adhesives or foodstuff. When considering viscoelastic flows, the velocity, pressure and stress must satisfy the mass and momentum equation, supplemented with a constitutive equation involving the velocity and stress. Stretching of a Newtoninan Fluid. Stretching of a Viscoelastic Fluid. The viscoelastic fluid can be more stretched before breaking. The simplest model is the so-called Oldroyd-B constitutive relation which can be derived from the kinetic theory of polymer dilute solutions.

### Jet buckling 2D

 The transient flow of a jet injected into a 2D rectangular cavity is reproduced here (from left to right: newtonian fluid, Deborah 1, Deborah 10, Deborah 100). Click on picture to animate (might take some time to load).

### Jet buckling 3D

 The transient flow of a jet injected into a parallelepiped cavity is reproduced here (left: newtonian fluid, right: 1,Deborah 100). Click on picture to animate (might take some time to load).

### Filament Stretching/Fingering Instabilities

 A fluid at rest contained between two parallel coaxial circular disks is considered. At the initial time, the top end-plate is moved vertically (left:newtonian fluid, right: viscoelastic fluid). Click on picture to animate (might take some time to load). When the aspect ratio is small, instabilities appear and can be reproduced. Click on picture to animate (might take some time to load).

## Bouncing Jets

### Newtonian

A newtoninan fluid is poored on a bath of the same fluid flowing with a horizontal velocity (S. Lee PhD 2014). The left computation takes into account the surface tension effect.

### Kaye Effect

When a stream of shampoo is fed onto a pool in ones hand a jet can leap sideways or rebound from the liquid surface in an intriguing phenomenon known as the Kaye effect (S. Lee PhD 2014).

In both cases, the bouncing jets appear after a thin air layer is formed between the jet and the rest of the fluid. This air layer is sustained in the newtonian case by the bath horizontal velocity and in the shampoo case by its ablilty to exihibit shear-thinning.