Mutual inductance of bifilar winding, vs transmission line parameter

[Swamp Thing]

Is there a relation between the mutual inductance across a pair of bifilar wound coils, and the inductance per meter of the same winding considered as a transmission line? I.e., can one calculate one from the other?

 

[Baluncore]

No.
The twisted pair line has an impedance to differential mode signals.
The inductance of the line about the transformer core is in common mode.

 

[Swamp Thing]

Yet intuitively, it seems that changing something (eg twist per cm or insulation thickness) that reduces the L/m would also push the K closer to 1.

 

[DaveE]

Is there a relation between the mutual inductance across a pair of bifilar wound coils, and the inductance per meter of the same winding considered as a transmission line? I.e., can one calculate one from the other?

This is a very confusingly worded question. Which "inductance per meter" did you mean? Ref @Baluncore's distinction of common mode vs. differential mode. Maybe a sketch would be in order, or a clear identification with standard jargon about which inductances you meant?

If you are comparing mutual inductance between two windings with and without a core, then no. The core has a huge influence, that's why we put it there.

There is a crude approximation for the leakage inductance (see this post for a definition), that it is independent of the core. This assumption is that it is due to flux that doesn't link to the core and that the flux that does link to the core will also link to the other winding. So all of the core parameters would then contained in the magnetizing inductance in that model. But, as I said, it's crude; as in not right but better than nothing.

 

[Baluncore]

Yet intuitively, it seems that changing something (eg twist per cm or insulation thickness) that reduces the L/m would also push the K nearer to 1.

The twisted pair impedance is really determined by wire diameter and insulation type/thickness. More twists simply shorten the wavelength at which the twisted pair will operate without radiative losses.

Impedance changes, due to a proportional increases in L and C, will cancel, since impedance is proportional to; √(L/C).

The K for a bifilar-wound, twisted pair, will be close to 1. More twists will make no substantial difference to K.

Once the wire helix length starts to rise steeply, more twists will slow the signal velocity slightly, since the velocity factor is proportional to; 1/√(L⋅C).

In effect, the situation you are considering, is called a "transmission line transformer".
https://en.wikipedia.org/wiki/Balun#Transmission-line_transformer_type