# Molecular Simulation/Transport properties

## Viscosity

The viscosity of a liquid is defined by the drag force experienced by a moving plate separated from a stationary plate by a layer of the liquid. $\tau ={\frac {F}{A}}=\eta {\frac {A\cdot u}{h}}$

u is the speed of the moving plate. h is distance by which the two plates are separated. A is the surface area of the moving plate.

$\eta$  can be calculated from a molecular dynamics simulation using the Green–Kubo relation, $\eta ={\frac {V}{k_{B}T}}\int _{0}^{\infty }\langle P_{xy}(t_{0})P_{xy}(t_{0}+\tau )\rangle {\textrm {d}}\tau$

Pxy is the xy component of the pressure tensor. The xz or yx off-diagonal components can be used instead.

## Thermal Conductivity

The thermal conductivity of a liquid is defined by the rate of heat transfer between an upper and lower plate at different temperatures (T1 and T2).

$J(J/m^{2}/s)=\lambda \Delta T$

The Green-Kubo relation for thermal conductivity relates lambda to the autocorrelation function of the heat current,

$\lambda ={\frac {1}{3Vk_{B}T^{2}}}\int _{0}^{\infty }\langle j(t)\cdot j(t+\tau )\rangle d\tau$