Why the Allen-Cahn equation can not be used to characterize the time evolution of a conserved order parameter?

Why not to use Allen-Cahn equation plus a Lagrange multiplier term (to the free energy to apply the conservation) to characterize the time evolution of a conserved order parameter?

There is an answer at Page 38, last paragraph of the book "Phase-field methods in materials science and engineering"

How to visualize 3D results of phase field simulation?

Following is a matlab script I used to visualize 3D result of phase field simulation. If someone has better choice, please let me know.

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figure

data = timekk;

data = smooth3(data,'box',5);

isoval = 0.0;

h = patch(isosurface(data,isoval),...

'FaceColor','blue',...

'EdgeColor','none',...

'AmbientStrength',.2,...

'SpecularStrength',.7,...

'DiffuseStrength',.4);

isonormals(data,h)

patch(isocaps(data,isoval),...

'FaceColor','interp',...

'EdgeColor','none')

colormap winter

colorbar

daspect([1,1,1])

axis tight

view(3)

camlight right

camlight left

set(gcf,'Renderer','zbuffer');

lighting phong

saveas(gcf,f3d,'jpg')

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