No. Velocity factor only depends on the dielectric constant. Capacitance depends on both dielectric constant and geometry. A high impedance line will have lower capacitance per meter than a low impedance transmission line of the same dielectric, but the velocity factor is the same.
Or, most specifically, jointly with relative permeability. There are only some contrived scenarios, and the occasional wave propagation through magnetic materials (and more generally, free waves and optics, of course), where one needs to consider permeability and permittivity together; practical TLs are pervasively made with mu_r = 1 materials, hence it can be ignored in most all cases.
Usually, such applications are something obscure, like wire/cable with a strong filtering quality thanks to the high-frequency lossiness of the ferrite material. In other words, a distributed ferrite bead sort of material. Occasionally, one can employ this to effect, like using magnetic saturation of the loading material to launch shock waves down such a line -- a magnetic pulse compressor. But those are more often crafted from particular material stackups, rather than bulk fillers.
A short section of transmission line that is open circuit or high impedance load is treated as a small capacitor. This comes up when using coax for a shielded connection to high impedance sensors such as photodiodes, piezeo transducers, and strain gauges. The extra capacitance limits the bandwidth and noise of amplifiers, so you want to keep the cables as short as possible.
Just to expand on that, when the transmission line is not terminated, then there are reflections back and forth. The level of the reflections gradually decreases as more energy is lost, and the average voltage in the transmission line charges to that of the source as if the transmission line was a capacitor. The curves are identical.
If the transmission line is made longer, then the reflections take more time traveling back and forth, so it takes more time for them to lose energy, and the average voltage settles more slowly, just as if the capacitance is larger. It is pretty easy to see on an oscilloscope if you care to look.
As I summed up / hinted at in my earlier message, the low-frequency approximation of a transmission line is an inductor for Z < Zo, and capacitor for Z > Zo.
What is "low"? When we don't have to worry about reflections.
It's a surprisingly powerful and deep statement in so few words; but it takes some contemplation to realize that power. One can (and should!) demonstrate it using simulations, and derive it from basic theory.
For moderately higher frequencies, or Z ~ Zo, we can use both, i.e. an LC section, to model it up to the first resonance, say; it quickly gets unwieldy as more and more harmonics need be modeled, and we find a growing discrepancy between lumped-equivalent (rational polynomial valued expression) and wave (TLs have impedance/transfer functions with trig functions in them, relating electrical length to phase angle). The limiting case of course is the Taylor series expansion of same, but convergence to within some margin of accuracy need not be rapid. At some point, we prefer the 1-D wave solution (i.e., RLC + TL lumped equivalent circuits) instead.
Tim
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