Surfactant stabilized bubbles flowing in a Newtonian fluid

Abstract

Bubbles suspended in a fluid cause the suspension to have different rheological properties than the base fluid. In general, the viscosity of the suspension increases as the volume fraction of the bubbles is increased. A current application, and motivation for this study, is in wellbore cements used for hydrocarbon extraction and carbon sequestration. In these settings, the gas bubbles are dispersed into the cement to reduce the density as well as improve the properties for specific conditions or wellbore issues. In this paper, we use Stokesian dynamics to numerically simulate the behavior of a large number of bubbles suspended in a Newtonian fluid. Going beyond prior work on simulating particles in suspension, we account for the nature of bubbles by allowing for slip on the bubble surface, the deflection on the bubble surface, and a bubble–bubble pairwise interaction that represents the surfactant physics; we do not account for bubble compressibility. We incorporate these interactions and simulate bubble suspensions of monodisperse size at several volume fractions. We find that the bubbles remain better dispersed compared with hard spherical particles that show a greater tendency to structure or cluster.

The Influence of Bubbles on Foamed Cement Viscosity Using an Extended Stokesian Dynamics Approach

“…Foamed cement samples that have been produced in the laboratory and collected as part of a collaborative field effort show spherical, stable, discrete bubbles [14,15]. Though the interaction considers spherical bubbles, the surface is allowed to deflect in the region of bubble pair interaction [16]. Another assumption is that the bubbles are neutrally buoyant.…”

“…The FLD method further increases the efficiency by using fast approximate methods for the far-field interaction [19,20]. We employ an extended FLD method with specific pairwise near-field interactions for bubbles [16].…”

“…A depiction of the three forces is shown in Figure 1. The total hydrodynamic force for the bubbles is then defined by [16]:…”

“…The direct force was chosen so that it enabled the bubble pairs to approach very close to each other to allow a small surface deflection but did not allow complete bubble overlap. The hydrodynamic interaction for a pair of bubbles, with the same size diameter, has been derived by [21] for the case of two bubbles approaching each other and is given by [16,21]:…”

“…is the energy scale and σ is the length scale. The influence of the values of and σ on system dynamics are described in detail in [16], so we do not present them again here. A value of 0.008 was used for and a value of 0.9 was used for σ. σ r 10 is the repulsive part and σ r 7 is the attractive portion.…”