text: To correctly solve the -phase momentum equation, a feasible set of closure relations must be considered to include all the possible interactions between the phases, expressed as a momentum transfer per unit volume at the phase interface. Interfacial momentum forces are added as a source term in the momentum equation and can be divided into drag and non-drag forces. The drag force has a dominant role and can be considered as the most important contribution in bubbly flows. It reflects the resistance opposing bubble motion relative to the surrounding fluid.  
  The non drag forces are the lift, turbulent dispersion, wall lubrication and virtual mass forces: 
  * Lift force: force perpendicular to bubble motion. It results from the pressure and stress acting on the bubble surface. Experimental and numerical studies show that the lift force change sign depending on the bubble diameter. For small bubbles, the lift force acts in the direction of decreasing liquid velocity, which is, in the case of batch or co-current mode, toward the pipe wall. Conversely, when large bubbles are considered, the lift force pushes the bubbles toward the center of the column. The change in sign of the lift force occurs at a bubble diameter of approximately 5.8 mm.
  * Turbulent dispersion: it accounts for the fluctuation in the liquid velocity that affects the dispersed phase by scattering it. The turbulent eddies redistribute the bubbles in the lateral direction from the high-concentration to the low-concentration bubble region. The turbulent dispersion force modulates the peaks of small bubbles near the wall pipes and spreads out large bubbles.
  * Wall lubrication: force due to the surface tension. It prevents the bubbles from touching the walls, ensuring zero presence of bubbles near vertical walls (found experimentally).
  * Virtual mass force: it arises from the relative acceleration of an immersed moving object to its surrounding fluid. Its effect is significant when the liquid phase density is much higher than the gas phase.
  All the interfacial forces can be added to the numerical model using suitable correlations derived from experimental studies.