Typical domains of physically admissible flow configurations, as predicted by DeProF model simulations. For any fixed, externally imposed, flow conditions, (Ca, r), the two-phase flow visits a canonical ensemble of physically admissible flow configurations depicted by the cloud of small, red balls. Here, Ca = 1.19 × 10⁻⁶, κ = 1.45 and flow rate ratio values, r, span 2 orders of magnitude. A unique triplet of values (S_w, β, ω), the large, black ball, is obtained by averaging over the ensemble and defines the mass center of the red cloud. Note that the shape and position of the red cloud change with flow conditions.