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We generalise the description of the dynamics of the order book of financialmarkets in terms of a Brownian particle embedded in a fluid of incoming,exiting and annihilating particles by presenting a model of the velocity oneach side (buy and sell) independently. The improved model builds on thetime-averaged number of particles in the inner layer and its change per unittime, where the inner layer is revealed by the correlations between pricevelocity and change in the number of particles (limit orders). This allows usto introduce the Knudsen number of the financial Brownian particle motion andits asymmetric version (on the buy and sell sides). Not being consideredpreviously, the asymmetric Knudsen numbers are crucial in finance in order todetect asymmetric price changes. The Knudsen numbers allows us to characterisethe conditions for the market dynamics to be correctly described by acontinuous stochastic process. Not questioned until now for large liquidmarkets such as the USD/JPY and EUR/USD exchange rates, we show that there areregimes when the Knudsen numbers are so high that discrete particle effectsdominate, such as during market stresses and crashes. We document the presenceof imbalances of particles depletion rates on the buy and sell sides that areassociated with high Knudsen numbers and violent directional price changes.This indicator can detect the direction of the price motion at the early stagewhile the usual volatility risk measure is blind to the price direction.

Financial Knudsen number: breakdown of continuous price dynamics and  asymmetric buy and sell structures confirmed by high precision order book  information