Modelling the fluidity of a fluid (grease) based on temperature I am trying to create a statistical model of a lubrication system. A central grease pump takes grease from a tank and injects it into some cavities (via grease lines) until a pressure set-point is reached.
I noticed that the system takes longer to pump grease through all the lines when the temperature is colder. I assume this is because the grease's fluidity reduces in cold temperature, therefore it travels slower through the lines and is pumped less efficiently.
Back to my statistical model: I am trying to do a regression to correlate temperature records with observations of the time required to lubricate all parts. I am wondering which regression model I should use: 


*

*a linear function time = a + b x temperature doesn't work well. 

*a second-order polynomial fits the data quite well

*a log time = a+ b x log(temperature) fits the data quite well too


Can you give me an insight in the underlying science behind my observations? I assume there are a lot of other factors, such as pressure, velocity of the fluid inside the lines, type of lines, diameter, etc...
But for a start, which law determines the fluidity of a lubricant like grease, based on temperature ? For instance, is it a polynomial, an exponential, 1/x, or something else ?
EDIT
I just stumbled upon this: Wikipedia Temperature dependence of liquid viscosity.
I guess Grease is not exactly a fluid, but all these laws seem to be exponential or log.
 A: Viscosity is the material's resistance to shearing stress. According to the Wikipedia entry, water has a viscosity that is exponential:
$$
\mu\sim A\cdot10^{B/(T-C)}
$$
If we then look at the Navier-Stokes equations (which holds for Newtonian fluids, something grease is not (instead a non-Newtonian fluid)),
$$
\rho\left(\color{blue}{\frac{\partial\mathbf v}{\partial t}}+\mathbf v\cdot\nabla\mathbf v\right)=-\nabla p+\color{blue}{\mu\nabla^2\mathbf v}+\mathbf f,
$$
where $\rho$ is the mass-density, $\mathbf v$ the fluid velocity, $p$ the fluid pressure, and $\mathbf f$ other forces involved (e.g., gravity), the highlighted colors suggest a linear relation between viscosity and time might be a good start. The fact that grease is non-Newtonian would change the relation between $t$ and $\mu$, however, since it appears to be the case that $\mu$ is non-linearly dependent on temperature, a logarithmic relation between $t$ and $\mu$ might be the direction to take.
I would suggest looking at the chi-squared test of both the polynomial fit and the exponential fit. Note that free software like R and Python do have some built-in chi-squared algorithms (though the Python requires SciPy)--I presume also other for-pay software also have this feature, but I am not aware of it.
