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The Density and Order Parameter at the Interface

A bubble with radius 20 lu was initialised at the centre of a 64 by 64 site grid and allowed to reach equilibrium. The fluid density and the order parameter are plotted in figures 4-5 and 4-6 respectively for tex2html_wrap_inline12111 , 0.01 and 0.001.

   figure4346
Figure 4-5: The density, along a line through the centre of a bubble, as a function of r The centre of the bubble is at r=32. The density profile across the interface can be seen for three values of the interfacial energy tex2html_wrap_inline12095 .

   figure4355
Figure 4-6: The order parameter, along a line through the centre of a bubble, as a function of r. The centre of the bubble is at r=32. The change in the order parameter across the interface can be seen for three values of the interfacial energy tex2html_wrap_inline12095 .

Figure 4-5 shows a small decrease, of less than 1%, in the fluid density across the interface. The width of this decrease is about 10 lu when tex2html_wrap_inline12111 , 5 lu when tex2html_wrap_inline14929 and 3 lu when tex2html_wrap_inline12417 . There is also a small difference between the fluid density inside and outside the bubble. The difference is about 0.2% when tex2html_wrap_inline12111 and much smaller for the smaller values of tex2html_wrap_inline12095 . The change in tex2html_wrap_inline12083 , the order parameter, across the interface shows a gradual smooth change when tex2html_wrap_inline12111 with an interface width of about 10 lu. The lower values of tex2html_wrap_inline12095 show a much sharper change occurring over a few lattice units. The results displayed in figures 4-5 and 4-6 are consistent with the similar results in [9, 38].



James Buick
Tue Mar 17 17:29:36 GMT 1998