What is pressure at microscopic level in a liquid? how can I imagine it? [duplicate]

Question

what i mean to say is that, in a liquid (ideal) pressure gets transmitted undiminished, what it means is that a molecule applies equal amount of force to all the molecules in its vicinity how? how do non ideal liquids not satisfy this condition.

Answer 1

Pressure is a macroscopic concept which embodies the information about the contact force between two pieces of the same or different material. From a fundamental point it can be obtained as time average of a microscopic observable. In order to develop a correct intuition about pressure at microscopic level, the key point is the time average. It is not the direct instantaneous force between molecules which justifies one of the main properties of pressure in a static fluid: its isotropy.

A possible microscopic observable is the so called microscopic stress tensor. For a system of particles in a volume $V$ interacting through pair-wise forces ${\bf f}_{ij}$ it is $$ {\bf \sigma} = \frac{1}{V}\sum_i \left[ -m_i {\bf \dot u}_i\otimes{\bf \dot u}_i + \frac{1}{2}\sum_{j\neq i} {\bf r}_{ij}\otimes{\bf f}_{ij}\right] $$ where ${\bf u}_i$ is the velocity of the $i$-th particle referred to the average velocity and ${\bf r}_{ij}= {\bf r}_{i}-{\bf r}_{j}$.

At equilibrium, the average of each diagonal component ${\bf \sigma}_{\alpha \alpha}$ is equal to the others and it is also equal to thermodynamic pressure.