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 ]
