# I Non Newtonian / Newtonian Fluid interface

Tags:
1. Mar 14, 2018

### Tom79Tom

Suppose I have a wave tank partially filled with a shear thickening Newtonian fluid (Oobleck), on top of which sits a layer of water (separated by a thin membrane to prevent mixing)

If I propagate a surface wave in the water layer how will it conduct itself at the Newtonian/Non Newtonian Fluid interface and into the Non Newtonian fluid

Will it be an applied force upon the Non Newtonian fluid that causes shear thickening ? Will it cause reflection of the wave at the interface ?

I also notice that Oobleck has a higher density than water- will Snells law also apply and the surface wave will travel slower in the higher density medium

Last edited: Mar 14, 2018
2. Mar 14, 2018

### Staff: Mentor

In my judgment, you need to do actual modeling of this problem to get a definitive answer. Neglecting surface tension, the boundary condition at the interface must be that the traction must be continuous (i.e., normal- and shear stresses).

3. Mar 15, 2018

### Andy Resnick

The thin membrane will cause additional effects; better to consider (for example) oobleck and vegetable oil; the oil is Newtonian and immiscible with oobleck (or a cornstarch solution if you prefer that).

Otherwise, I agree with Chestermiller- the system is too complex (nonlinear, for one) to make 'simple' predictions.

4. Mar 15, 2018

### Tom79Tom

5. Mar 18, 2018 at 2:06 AM

### Stavros Kiri

6. Mar 18, 2018 at 2:41 AM

### Stavros Kiri

For water waves
"In water whose depth is large compared to the wavelength, the wave speed expression contains two terms, one for gravity effects and one for surface tension effects. The wave speed is

where g is the gravitational field strength, γ is the surface tension, ρ is the density of the water, and λ the wavelength. As this equation makes clear (wave speed depends on wavelength), water is a dispersive medium."
(http://practicalphysics.org/speed-water-waves.html) [I made a couple of obvious typo corrections spotted in the original quote above regarding the quantites in the equation ...]
I don't know if that can help. Perhaps it's not enough.
Snell's law (of refraction) involves the angles of incidence and refraction. For surface waves (i.e. in 2 dim), you have to be more careful and specify the exact geometry. (Are we talking about surface waves at the same level, with the interface surface between the two media perpendicular? ...)