Generalize composition diffusivity used for thermohaline calculations

[evbauer]

When the composition diffusivity enters into thermohaline calculations (e.g. when thermohaline_option = Brown_Garaud_Stellmach_13), currently we assume a H/He-dominated mixture. See

mesa/turb/private/thermohaline.f90

Lines 128 to 153 in d215b38

	if(chemZ.gt.2) then
	! This is if the driving chemical is NOT He.
	! Log Lambda for H-dominant chem mixture (equation 10)
	loglambdacx = loglambdah - log(chemz)
	! Log Lambda for He-dominant chem mixture (equation 10)
	loglambdacy = loglambdah - log(2.d0*chemz)
	! Calculation of C_ij coeffs (equation 12)
	ccx = log(exp(1.2d0*loglambdacx)+1.)/1.2d0
	ccy = log(exp(1.2d0*loglambdacy)+1.)/1.2d0
	! Reduced masses (I had to guess, from Bahcall & Loeb 1990), with H and He
	acx = (1.d0*chemA)/(1.d0+chemA)
	acy = 4*chemA/(4.d0+chemA)
	! My formula (see notes) based on Proffitt and Michaud 1993
	kmu = 2*Bcoeff*pow(T,2.5d0)/(sqrt5*rho*chemZ*chemZ)/ &
	(XH1*sqrt(acx)*ccx + (1-XH1)*sqrt(acy)*ccy)
	else
	! Log Lambda for H-He mixture (equation 10)
	loglambdah = -19.26d0 - log(2d0) - 0.5d0*log(rho) + &
	1.5d0*log(T) - 0.5d0*log(1d0 + 0.5d0*(1+XH1))
	! Calculation of C_ij coeffs (equation 12)
	ccy = log(exp(1.2d0*loglambdah)+1d0)/1.2d0
	! My formula (see notes) based on Proffitt and Michaud 1993
	kmu = (Bcoeff*pow(T,2.5d0)/(rho*ccy))*(3+XH1)/((1+XH1)*(3+5*XH1)*(0.7d0+0.3d0*XH1))
	endif

We already have all of the physics in the code to do the more general case elsewhere for element diffusion, so we should take advantage of that here.

[evbauer]

The current implementation is based on https://ui.adsabs.harvard.edu/abs/1993ASPC...40..246M/abstract

That's derived in the same general picture that we use for the full implementation of the Burgers equations for diffusion, but with some simplifying assumptions about composition and some fits used to estimate the Coulomb logarithm. So we should be able to translate the MESA implementation of https://ui.adsabs.harvard.edu/abs/2016PhRvE..93d3203S/abstract into an updated version of this without making any composition assumptions.