Interaction of a pair of in-line bubbles ascending in an Oldroyd-B liquid: A numerical study

Bubble rising and interaction in ternary fluid flow: a phase field study

“…In eqn (12) n is the unit normal perpendicular to but pointing away from the arc AB, and t is the unit tangent normal. It is to be noted that t a and t b are collinear with s 12 .…”

“…Previous studies, both numerical and experimental, have been mostly on the behavior of a single bubble rising in a heavier medium, and on the rising velocity, aspect ratio, terminal shape, and the like. [10][11][12] In different ow conditions, denoted by a couple of dimensionless parameters, like the Eötvös number (dened later on), bubbles display distinct nal shapes and rising velocities. Besides, some empirical correlations for the rising velocity have been proposed.…”

Numerical simulation of drop deformation under simple shear flow of Giesekus fluids by SPH

“…These equations are solved with the kinematic equation of the particles' movement over the whole computational domain. In the Lagrangian framework, denoting material derivative by D/Dt, these governing equations are written as follows (Vahabi et al, 2021):…”

“…These equations are solved with the kinematic equation of the particles’ movement over the whole computational domain. In the Lagrangian framework, denoting material derivative by D/D t , these governing equations are written as follows (Vahabi et al , 2021): where ρ, t , trueV→, p , τ , truef→σ and boldXtrue→ are density, time, velocity vector, pressure, stress tensor, surface tension and position vector, respectively.…”

“…The no-slip condition is enforced by using some dummy particles on the top and bottom walls. These dummy particles are located out of the domain in front of each near-boundary inner particle, and they are included in the inner particle’s interpolating summation (Vahabi et al , 2021). The velocity of each dummy particle is determined as follows: …”