Thanks, I will take a look at these papers. Adam
On 06/18/2013 11:23 AM, Jonathan Guyer wrote: > On Jun 15, 2013, at 12:11 PM, Adam Stone <[email protected]> wrote: > >> At the end of the phase.simple example, the expected velocity is calculated >> from the undercooling and the parameter beta in order to choose a time step >> within the CFL limit. Beta (linear kinetic coefficient) is given a constant >> value in the example, but other than calculating the expected velocity, this >> only is used once, in the expression for the kinetic term, >> Mphi = Tm * >> b >> eta >> / (6. * Lv * delta) >> >> Rearranging gives >> beta = Mphi * (6. * Lv * delta) / Tm >> and if >> velocity = beta * abs(Tm - T()) >> then it should follow that >> velocity = Mphi * (6. * Lv * delta) * abs(Tm - T()) >> / Tm >> >> >> This would mean the velocity depends on the kinetic coefficient (Mphi), the >> latent heat (Lv), the interface width (delta), and the undercooling; but not >> the surface energy (sigma) or the parameters it affects, the gradient energy >> coefficient (kappa) or the barrier height (W). >> >> I am wondering if this is really correct, that these parameters are not >> expected to affect the interface growth rate? I find that when I do change >> the surface energy in my test case (with Mphi specified by an expression >> varying with T, and beta defined by the expression above), it does seem to >> affect it. > That treatment is taken from section 4 of > > Warren and Boettinger. PREDICTION OF DENDRITIC GROWTH AND MICROSEGREGATION > PATTERNS IN A BINARY ALLOY USING THE PHASE-FIELD METHOD. Acta Metall Mater > (1995) vol. 43 (2) pp. 689-703 > > and, in turn, from section II.B.3 of > > WHEELER et al. PHASE-FIELD MODEL FOR ISOTHERMAL PHASE-TRANSITIONS IN > BINARY-ALLOYS. Phys Rev A (1992) vol. 45 (10) pp. 7424-7439 > > You certainly can write the interfacial velocity in a form that depends on > surface energy, but it is also dependent on gradient energy and/or barrier > height and all of those terms are coupled. > > > > NOTE: One significant error in our FiPy implementation is that Mphi should be > proportional to Tm**2, not to Tm. > > > _______________________________________________ > fipy mailing list > [email protected] > http://www.ctcms.nist.gov/fipy > [ NIST internal ONLY: https://email.nist.gov/mailman/listinfo/fipy ] _______________________________________________ fipy mailing list [email protected] http://www.ctcms.nist.gov/fipy [ NIST internal ONLY: https://email.nist.gov/mailman/listinfo/fipy ]
