Abstract The main goal of this article is to study the oscillatory motion of a spherical gas bubble immersed in a Newtonian liquid subjected to a harmonic pressure excitation. We use the classical Rayleigh-Plesset equation to study the radial motion of the bubble undergoing a forcing acoustic pressure field. The second order nonlinear ordinary differential equation that governs the bubble motion is solved through a robust fifth order Runge-Kutta scheme with adaptive time-step. Several interesting patterns are identified. First we develop an asymptotic solution for low amplitudes of excitation pressure to validate our numerical code. Then we develop a bifurcation diagram in order to show how the parameters of the flow modify the vibrational patterns of the bubble. We also train a neural network to identify the vibrational pattern through its FFT data. The combination of neural networks with a bifurcation diagram could be useful for the identification of the flow physical parameters in practical applications. For each pattern we also provide an analysis of the motion of the bubble on the phase-space and interpret physically the system behavior with its FFT. In addition, we analyze nonlinear patterns using standard tools of dynamical systems such as Poincaré sections and calculate the Lyapunov exponents of the system. Based on that, we have identified topological transitions in phase plane using for instance the analysis of Poincaré sections and the solution in the frequency spectrum. We have seen that the mechanisms that dominate the dynamics of the oscillating bubble is the competition of the acoustic field excitation with surface tension forces and momentum diffusion by the action of the surrounding fluid viscosity.

The main objective of the present work is to analyze the influence of some important operational reaction parameters (agitation speed, polybutadiene - PB - content and initiator concentration) on the final properties of High Impact Polystyrene (HIPS) produced in bulk. Variable effects are analyzed both qualitatively and quantitatively with the help of a fractional factorial design. Physical, chemical and mechanical properties were evaluated through measurement of the weight-average molecular weight (Mw), polydispersity (PD), volume-average diameter of PB particles (D(4,3)) and impact strength (Izod). It was found that PD and D(4,3) depend strongly on the initiator concentration, rubber concentration and agitation speed; Mw depends on initiator and rubber concentrations; and Izod depends on the rubber concentration, PD and D(4,3) in the analyzed experimental range. As a consequence, it was shown that control of final polymer properties can be easily performed through proper manipulation of the analyzed operational variables.

In this paper, three-dimensional boundary integral computer simulations of emulsions in shear flows are described. Results for ordered BCC emulsions with dispersed-phase volume fractions below the critical concentration are presented. Complex rheological features including: shear-thinning viscosities, normal stress differences, and a nonlinear frequency response are also explored. For deformable drops, pairwise collision produces net cross-flow displacements that govern self-diffusion of drops. We compute trajectories of two interacting drops in shearing and present interesting numerical simulations of three dimensional gravity-induced motion of two drops. The results also demonstrate the feasibility of simulating high-volume-fraction emulsions and foam.