The Density Profile Of Inhomogeneous Fluid System Under Gravity

The matter exists in three states in nature: solid, liquid, and gas, and the gas and liquid are called fluid. For the solid and gas our study methods are ralative mature, however, the study of liquid is not. In 1964,Hohenberg and Kohn^[1] derived two significant theorems for the ground state of the quantum many-body system and established the density functional theory, which is called DFT. One year later this was generalized to non-zero temperature by Mermin^[2] who indicated that the free energy of many-body system is a functional of the density. After a further decade it was realized that the density functional variational methods were readily applicable to classical fluids, so the DFT became an important research method for the structure and thermodynamic properties of inhomogeneous fluid. According to the density functional theory, other physical quantities can be obtained as long as we know the denstiy profile and the free energy. For the general many-body system some common methods that construct the free energy functional include the local density approximation^[3,4], weighted density approximation^[5,6], functional expansion approximation etc. Rosenfeld^[7] obtained the free energy functional for the simple hard sphere fluid system by using the weighted density approximation, through which we can obtain some related thermodynamic properties of confined hard sphere fluid, and we call it Rosenfeld density functional theory. Besides, Tarazona^[8] specified a free energy functional of the system on the basis of weighted density approximation too, which is called Tarazona density functional theory. We mainly utilize the two basic theories to study the inhomogeneous fluids under gravity.In this thesis we apply the Rosenfeld DFT and Tarazona DFT, respectively, combining with the dimensional crossover technique to study the hard disk and hard rod fluid confined between two parallel hard walls. For the hard disk fluid system we calculated the density profile by using both the scaled particle theory^[9] (SPT) and Santos^[10] functional, then we made a comparison between the two results. We found the result of Rosenfeld density functional theory is consistent with the result of SPT, whereas the result of Tarazona functional is not quite satisfactory after dimensional crossover, which may be caused by the simple weight function. Thus looking for a better weight function is the key to improvement. The thesis is organized as follows: we introduce the general density functional theory firstly, and then the Rosenfeld DFT and Tarazona DFT are given for the concrete hard sphere model system. Secondly we apply the two theories to the hard disk and hard rod fluid systems through the dimensional crossover technique and make some related calculations. At last we present the results and some discussions.