  We generalise the description of the dynamics of the order book of financial
markets in terms of a Brownian particle embedded in a fluid of incoming,
exiting and annihilating particles by presenting a model of the velocity on
each side (buy and sell) independently. The improved model builds on the
time-averaged number of particles in the inner layer and its change per unit
time, where the inner layer is revealed by the correlations between price
velocity and change in the number of particles (limit orders). This allows us
to introduce the Knudsen number of the financial Brownian particle motion and
its asymmetric version (on the buy and sell sides). Not being considered
previously, the asymmetric Knudsen numbers are crucial in finance in order to
detect asymmetric price changes. The Knudsen numbers allows us to characterise
the conditions for the market dynamics to be correctly described by a
continuous stochastic process. Not questioned until now for large liquid
markets such as the USD/JPY and EUR/USD exchange rates, we show that there are
regimes when the Knudsen numbers are so high that discrete particle effects
dominate, such as during market stresses and crashes. We document the presence
of imbalances of particles depletion rates on the buy and sell sides that are
associated with high Knudsen numbers and violent directional price changes.
This indicator can detect the direction of the price motion at the early stage
while the usual volatility risk measure is blind to the price direction.
