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. ${\displaystyle \tau ={\frac {F}{A}}=\eta {\frac {A\cdot u}{h}}}$

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.

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

P_xy 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).

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

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

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

See Also

Wikipedia:Viscosity Wikipedia:Green–Kubo_relations