HYDRODYNAMIC THEORY

Hydrodynamic Theory

In this chapter the basic theoretical framework of this thesis is introduced, in particular

the microscopic expressions for the continuity equations. We then proceed to derive the

pressure tensor and heat °ux vector for °uids under the in°uence of three-body forces.

Our derivation is validated against nonequilibrium molecular dynamics simulations of

a con¯ned °uid acted upon by a two-body Barker-Fisher-Watts force coupled with the

Axilrod-Teller three-body force in Chapter 5.

Macroscopic hydrodynamics

A central problem in the study of hydrodynamics is the computation of transport

coe±cients. Therefore, we are interested in the macroscopic process of mass, energy

and momentum transfer. Because of conservation of these quantities, they can only

change by a process of redistribution. If the process occurs on a molecular time scale,

it would be unobservable at a macroscopic level. But if it is slow, it is observable

and plays a macroscopic role. The macroscopic equations of motion for the densities

of conserved quantities are called the Navier-Stokes equations [1]. We will now give a

brief description of how these equations are derived. It is important to understand this

derivation because based on these equations the microscopic expressions for the mass,

Macroscopic hydrodynamics

A central problem in the study of hydrodynamics is the computation of transport

coe±cients. Therefore, we are interested in the macroscopic process of mass, energy

and momentum transfer. Because of conservation of these quantities, they can only

change by a process of redistribution. If the process occurs on a molecular time scale,

it would be unobservable at a macroscopic level. But if it is slow, it is observable

and plays a macroscopic role. The macroscopic equations of motion for the densities

of conserved quantities are called the Navier-Stokes equations [1]. We will now give a

brief description of how these equations are derived. It is important to understand this

derivation because based on these equations the microscopic expressions for the mass,

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