Originally Posted by Gokhan
Originally Posted by Gokhan
Originally Posted by Shannow
OK...but like most things, the assumption that it passes through zero, and behaves predictably at near zero pressures (40 versus multiple thousands) can't be made...
I used the equation from the book reference I had posted and they cited two references on that.
Are there correction terms to the simple exponential form? Perhaps there are. Nevertheless, this simple exponential form is common.
Regarding the dependence of the pressure-viscosity coefficient α on the pressure
P, here is an excerpt from the paper I linked in my previous post:
The local pressure-viscosity coefficient, α = ∂ℓn(μ)/∂p, has been assumed by many authors to generally decrease with pressure or remain constant over the high-pressure region of contact so that the parameters of the Eyring rheological model may be obtained from traction curves. However, viscosity measurements to 3 GPa have been available in the literature for at least fifty years [2] which refute these assumptions. The limiting low shear viscosity has been measurable to 1.2 GPa for at least seventy years. Figure 1 compares pressure-viscosity behavior obtained from viscometers against that derived from traction using a sinh law model [3., 4.]. Clearly there is a misconception among some tribologists concerning the nature of piezoviscosity at high pressure.
So, it could be roughly constant but it could also vary greatly over a large pressure range.
Here are the results from the traction-rig rheometer Shannow posted, which provides an indirect measurement of the viscosity, vs. direct measurements using high-pressure viscometers ZeeOSix was inquiring about, the latter of which obviously capable of measuring the true viscosity values.
Traction-rig rheometers can be rather inaccurate because the pressure-viscosity coefficient α can vary greatly with the pressure
P, which makes a good theoretical fit to obtain the viscosity very difficult.
So, the short answer to the question asked earlier is that the pressure-viscosity coefficient α
does vary a lot with the pressure
P in general and the simple exponential equation μ = μ₀ exp(α
P) is only a first-order approximation.