The extensional dynamics of an elasto-viscoplastic (EVP) fluid is studied by means of numerical simulations closely modelling an experimental configuration.  Specifically, we track the interface between the EVP material and the Newtonian medium using an algebraic volume of fluid method (MTHINC-VOF) and employ a fully Eulerian immersed boundary method (IBM) to model the motion of the piston responsible of the extension of the material.

We investigate the role of different values of the yield stress, surface tension at the interface between the EVP material and the surrounding fluid, polymer viscosity ratio, and extension rates on the necking thickness of the material, extensional viscosity, and yielding of the material. 

 The results of the simulations reveal that when the yield stress of the EVP material is much larger than the viscous stresses, the material undergoes an elastic deformation, regardless of the selected values of extension rate, interfacial forces, and viscosity ratio. Moreover, increasing the ratio of the polymeric viscosity to the total viscosity of the system accelerates the EVP rupture due to the high stress concentration in the central part of the material sample. Specific and novel to our study, we show that interfacial forces cannot be ignored when the surface tension coefficient is such that a Capillary number based on the extensional rate is order 1. For large values of the surface tension coefficient, the EVP material fails sooner, with a clear deviation from the exponential reduction in the neck thickness.

We present a fully Eulerian hybrid immersed-boundary/phase-field model to simulate wetting and contact line motion over any arbitrary geometry. The solid wall is described with a volume-penalisation ghost-cell immersed boundary whereas the interface between the two fluids by a diffuse-interface method. The contact line motion on the complex wall is prescribed via slip velocity in the momentum equation and static/dynamic contact angle condition for the order parameter of the Cahn-Hilliard model. This combination requires accurate computations of the normal and tangential gradients of the scalar order parameter and of the components of the velocity. However, the present algorithm requires the computation of averaging weights and other geometrical variables as a preprocessing step. Several validation tests are reported in the manuscript, together with 2D simulations of a droplet spreading over a sinusoidal wall with different contact angles and slip length and a spherical droplet spreading over a sphere, showing that the proposed algorithm is capable to deal with the three-phase contact line motion over any complex wall. The Eulerian feature of the algorithm facilitates the implementation and provides a straight-forward and potentially highly scalable parallelisation. The employed parallelisation of the underlying Navier-Stokes solver can be efficiently used for the multiphase part as well. The procedure proposed here can be directly employed to impose any types of boundary conditions (Neumann, Dirichlet and mixed) for any field variable evolving over a complex geometry, modelled with an immersed-boundary approach (for instance, modelling deformable biological membranes, red blood cells, solidification, evaporation and boiling, to name a few). 

A numerical scheme to simulate three-phase fluid flows with phase change is proposed. By combining the Cahn-Hilliard model for water-air interface, Allen-Cahn equation for ice and fluid and Navier-Stokes equation for momentum, we solve the evolution of the water-air interface and water-ice interface simultaneously, including the volume expansion associated with solidification and due to the density difference between water and ice. Unlike existing schemes assuming a divergence-free flow field, the proposed continuous formulation allows for density changes while ensuring mass conservation. A Poisson equation for the pressure field is derived from mass conservation with constant coefficients, which can efficiently be solved without any pre-conditioning. The results demonstrate that the volume expansion during the ice formation and the subsequent motion of the water-air interface are successfully captured. A parametric study is carried out to examine the dependence of the icing on different physical and numerical parameters. Computations with flow disturbance of different amplitudes demonstrate the robustness of the computational scheme and the uniqueness of the solution over the parameters considered.

We study the role of surface topology, surface chemistry, and wall superheat temperature on the onset of boiling, bubble nucleation and growth, and the possible formation of an insulating vapour film by means of a novel setup for large-scale MD simulations. To minimise the effects of the system size on the bubble growth and the formation of the vapour film, we perform simulations in a box larger than those previously considered. The effect of the system pressure on bubble nucleation and growth is isolated by imposing a constant force on a moving piston and mechanically controlling the pressure. The simulations reveal that the presence of a nanostructure determines the nucleation site and facilitates the energy transfer from the hot substrate to the water. The surface chemistry, on the other hand, governs the shape of the formed bubble. A hydrophilic surface accelerates the bubble nucleation, however, decelerates the bubble expansion, thus postponing the formation of the film of vapour. Hence, a hydrophilic surface provides better energy transfer from the hot wall to the water. By analysing the system energy, we show that irrespective of wall topology and chemistry, there is a wall temperature for which the amount of transferred energy from the wall is maximum.

We study the rheology of suspensions of capsules with a rigid nucleus at negligible and finite flow inertia by means of numerical simulations. The capsule membrane is modeled as a thin Neo-Hookean hyperelastic material and the nucleus as a rigid particle with radius equal to half the radius of the undeformed spherical capsules. The fluid and solid motion are coupled with an immersed boundary method, validated for both the deformable membrane and the rigid nucleus. We examine the effect of the Reynolds number, capillary number, and volume fraction on the macroscopic properties of the suspensions, comparing with the case of capsules without nuclei. To explain the rheological measurables, we examine the mean capsule deformation, the mean orientation with respect to the flow direction, and the stress budget. The results indicate that the relative viscosity decreases with the capillary number, i.e., increasing deformability, and increases with inertia. The presence of a nucleus always reduces the membrane deformation. Capsules align more in the flow direction at higher capillary numbers and at higher volume fractions, where we also see a significant portion of them oriented with their longer deformed axis in the spanwise direction. When increasing inertia, the alignment with the flow decreases while more capsules orient in the spanwise direction. The first normal stress difference increases with the capillary number and it is always less for the nucleated capsules. Finally, the relative viscosity and the first normal stress difference increase with the capsule volume fraction, an effect more pronounced for the first normal stress difference.