  This paper presents the first results of the two-phase flow simulation
obtained using recently introduced physical, mathematical and numerical model
of the intermittency region between two-phases (Wac{\l}awczyk 2017, 2021). The
statistical interpretation of the intermittency region evolution equations
allows to account for the non-equilibrium effects in the domain separating two
phases. The source of non-equilibrium are spatial variations in the ratio of
work done by volume and interfacial forces governing its width. As the
statistical description of the two-phase flow differs from the deterministic
two-phase flow models known in the literature, in the present work we focus
discussion of the results on these differences. To this goal, the rising two
dimensional gas bubble is studied; differences between equilibrium and
non-equilibrium solutions are investigated. It is argued the statistical
description of the intermittency region has potential to account for physical
phenomena not considered previously in the computer simulations of two-phase
flow.
