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, $\eta =\frac{V}{k_{B}T}\underset{0}{\overset{\mathrm{\infty }}{\int }}⟨P_{xy}(t_0)P_{xy}(t_0+\tau )⟩\text{d}\tau$

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).

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

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

$\lambda =\frac{1}{3V{k}_B{T}^2}\underset{0}{\overset{\mathrm{\infty }}{\int }}⟨j(t)\cdot j(t+\tau )⟩d\tau$

See Also

Wikipedia:Viscosity Wikipedia:Green–Kubo_relations Template:BookCat