Fully three-dimensional, time-dependent, direct simulations of the non-ideal Navier-Stokes equations for a two-component fluid shed light into the mechanism which inhibits droplet breakup in step emulsifiers below a critical threshold of the width-to-height (w/h) ratio of the microfluidic nozzle. Below w/h similar to 2.6, the simulations provide evidence of a smooth topological transition of the fluid from the confined rectangular channel geometry to an isotropic (spherical) expansion of the fluid downstream the nozzle step.

We outline the main ideas behind the numerical modelling of soft flowing crystals, paying special attention to their application to microfluidic devices for the design of novel mesoscale porous materials.

alpha-quartz is one of the most important SiO2 polymorphs because it is the basis of very common minerals, especially for seabed materials with geoscientific importance. The elastic characterization of these materials is particularly relevant when the properties governing phonon and sound propagation are involved. These studies are especially interesting for oil exploration purposes.

Computer simulations of bi-continuous two-phase fluids with interspersed dumbbells show that, unlike rigid colloids, soft dumbbells do not lead to arrested coarsening. However, they significantly alter the curvature dynamics of the fluid-fluid interface, whose probability density distributions are shown to exhibit (i) a universal spontaneous transition (observed even in the absence of colloids) from an initial broad-shape distribution towards a highly localized one and (ii) super-diffusive dynamics with long-range effects.

We present a mesoscale representation of near-contact interactions between colliding droplets which permits one to reach up to the scale of full microfluidic devices, where such droplets are produced. The method is demonstrated for the case of colliding droplets and the formation of soft flowing crystals in flow-focusing microfluidic devices. This model may open up the possibility of multiscale simulation of microfluidic devices for the production of new droplet and bubble-based mesoscale porous materials.

We present a mesoscale kinetic model for multicomponent flows, augmented with a short range forcing term, aimed at describing the combined effect of surface tension and near-contact interactions operating at the fluid interface level. Such a mesoscale approach is shown to (i) accurately capture the complex dynamics of bouncing colliding droplets for different values of the main governing parameters, (ii) predict quantitatively the effective viscosity of dense emulsions in micro-channels and (iii) simulate the formation of the so-called soft flowing crystals in microfluidic focusers.

The dynamic interaction of complex fluid interfaces is highly sensitive to near-contact interactions occurring at the scale of ten of nanometers. Such interactions are difficult to analyze because they couple self-consistently to the dynamic morphology of the evolving interface, as well as to the hydrodynamics of the interstitial fluid film.

Given methane hydrates' importance in marine sediments, as well as the widespread use of seabed acoustic-signaling methods in oil and gas exploration, the elastic characterization of these materials is particularly relevant. A greater understanding of the properties governing phonon, sound, and acoustic propagation would help to better classify methane-hydrate deposits, aiding in their discovery.

The dynamic behaviour of rigid blocks subjected to support excitation is represented by discontinuous differential equations with state jumps. In the numerical simulation of these systems, the jump times corresponding to the numerical trajectory do not coincide with the ones of the given problem. When multiple state jumps occur, this approximation may affect the accuracy of the solution and even cause an order reduction in the method. Focus here is on the error behaviour in the numerical dynamic.

In this paper we propose and study a hybrid discrete-continuous mathematical model of collective motion under alignment and chemotaxis effect. Starting from paper [23], in which the Cucker-Smale model [22] was coupled with other cell mechanisms, to describe the cell migration and self-organization in the zebrafish lateral line primordium, we introduce a simplified model in which the coupling between an alignment and chemotaxis mechanism acts on a system of interacting particles.