Abstract
The differential equation for the component local density of a binary fluid was obtained as a result of an isoperimetric problem of the system free energy minimization under condition of particle number stability. The obtained expression can be used in the calculation of liquid's profiles as well as in the investigation of thermodynamic properties in the vicinity of the critical point. An isoperimetric problem solution for the model binary fluid of the system free energy minimization under condition of particle number stability was obtained in different cases: fluid within flat parallel layer under a gravitational field, under a gravitational field and wall potential as well as under a wall potential for another equation of state.
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