Non-Newtonian Fluids, Between Solids and Fluids
Valerio Marra January 22, 2013
One of my favorite sitcoms is “The Big Bang Theory”, thanks to its focus on physics. From time to time they run funny experiments that can be easily arranged at home, causing me to wonder if I know the physics that are at work. One of my favorite episodes is when they fill the cone of a speaker with a suspension of starch in water. Instead of spattering around, the suspension starts to dance because it behaves more like a solid than a fluid under the percussive action of the speaker’s cone. Non-Newtonian fluids are another fascinating counter-intuitive effect to study.
Materials Between Solids and Fluids
Solids deform under an applied stress and reach a position of equilibrium in which their deformation ceases. When the stress is removed, they will go back to their original shape. On the contrary, fluids deform continuously and don’t retain any particular shape. In scientific terms, we say that solids are characterized by elasticity while fluids are characterized by viscosity.
In between these two extremes lie non-Newtonian fluids, exhibiting both elasticity and viscosity. A suspension of starch in water belongs to this broad class of fluids and can be further classified as shear thickening: its viscosity increases with increasing shear rate. Another example of shear thickening fluid is sand soaked in water. The material dancing on a speaker’s cone on the TV show must therefore have been a non-Newtonian fluid.
Have you ever painted?
If the answer is yes, I’m pretty sure you noticed that the shear created by the brush made the paint thin and capable of wetting out the wall surface evenly. Once applied, the paint regained its original higher viscosity, leaving your wall without drips and runs. This is what is called a shear thinning fluid, the exact opposite of shear thickening. Can you recall other fluids exhibiting a non-Newtonian behavior?
Simulating Non-Newtonian Fluids
When looking to simulate non-Newtonian fluids, one example that comes to mind is the injection molding of a polymer. A ready-to-run model is available to download from the Model Gallery. I suggest starting from this model if you’re interested in simulating non-Newtonian flows. Below are a few images highlighting the shear thinning behavior of this polystyrene solution flowing into a mold.
In this model the polystyrene solution is flowing into the mold from the top to
the bottom. Results show how for a shear thinning fluid, the dynamic viscosity is
lower when the shear rate is higher. Top: velocity magnitude. Bottom left: shear rate.
Bottom right: dynamic viscosity.
Dynamic viscosity as a function of shear rate. Values are measured in p1.
Top left: shear rate as a function of inlet pressure. Top right: dynamics viscosity as a
function of inlet pressure. Values are measured in p1. Bottom: comparison between the
non-Newtonian polystyrene solution and an equivalent Newtonian fluid. As expected, the
volumetric flow rate is higher for the polystyrene solution since at higher shear rates its
viscosity is lower.