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.
>
>
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