Linear shear flow past a hemispherical droplet adhering to a solid surface

This paper investigates the properties of a three dimensional shear flow overpassing a hemispherical droplet resting on a plane wall. The exact solution is computed as a function of the viscosity ratio between the droplet and the surrounding fluid and generalizes the solution for the hemispherical no-slip bump given in an earlier paper by Price (1985). Several expressions including the torque and the force acting on the drop will be considered as well as the importance of the deformations on the surface for small Capillary numbers.Comment: 10 figures, Accepted for publication in Journal of Engineering Mathematic

Interaction Pressure Tensor for a class of Multicomponent Lattice Boltzmann models

We present a theory to obtain the pressure tensor for a class of non-ideal multicomponent lattice Boltzmann models, thus extending the theory presented by Shan (X. Shan, Phys. Rev. E 77, 066702 (2008)) for single component fluids. We obtain the correct form of the pressure tensor directly on the lattice and the resulting equilibrium properties are shown to agree very well with those measured from numerical simulations. Results are compared with those of alternative theories.Comment: 7 Pages, 5 figure

Deformation and break-up of viscoelastic droplets in confined shear flow

The deformation and break-up of Newtonian/viscoelastic droplets are studied in confined shear flow. Our numerical approach is based on a combination of Lattice-Boltzmann models (LBM) and finite difference schemes, the former used to model two immiscible fluids with variable viscous ratio, and the latter used to model the polymer dynamics. The kinetics of the polymers is introduced using constitutive equations for viscoelastic fluids with finitely extensible non-linear elastic dumbbells with Peterlin's closure (FENE-P). We quantify the droplet response by changing the polymer relaxation time $\tau_P$, the maximum extensibility $L$ of the polymers, and the degree of confinement, i.e. the ratio of the droplet diameter to gap spacing. In unconfined shear flow, the effects of droplet viscoelasticity on the critical Capillary number \mbox{Ca}_{\mbox{\tiny{cr}}} for break-up are moderate in all cases studied. However, in confined conditions a different behaviour is observed: the critical Capillary number of a viscoelastic droplet increases or decreases, depending on the maximum elongation of the polymers, the latter affecting the extensional viscosity of the polymeric solution. Force balance is monitored in the numerical simulations to validate the physical picture.Comment: 34 Pages, 13 Figures. This Work applies the Numerical Methodology described in arXiv:1406.2686 to the Problem of Droplet Break-up in confined microchannel

Phase-field model of long-time glass-like relaxation in binary fluid mixtures

We present a new phase-field model for binary fluids exhibiting typical signatures of self-glassiness, such as long-time relaxation, ageing and long-term dynamical arrest. The present model allows the cost of building an interface to become locally zero, while preserving global positivity of the overall surface tension. An important consequence of this property, which we prove analytically, is the emergence of compact configurations of fluid density. Owing to their finite-size support, these "compactons" can be arbitrarily superposed, thereby providing a direct link between the ruggedness of the free-energy landscape and morphological complexity in configurational space. The analytical picture is supported by numerical simulations of the proposed phase-field equation.Comment: 5 Pages, 6 Figure

Viscoelastic Multicomponent Fluids in confined Flow-Focusing Devices

The effects of elasticity on the break-up of liquid threads in microfluidic cross-junctions is investigated using numerical simulations based on the "lattice Boltzmann models" (LBM). Working at small Capillary numbers, we investigate the effects of non-Newtonian phases in the transition from droplet formation at the cross-junction (DCJ) and droplet formation downstream of the cross-junction (DC) (Liu & Zhang, ${\it Phys. Fluids.}$ ${\bf 23}$, 082101 (2011)). Viscoelasticity is found to influence the break-up point of the threads, which moves closer to the cross-junction and stabilizes. This is attributed to an increase of the polymer feedback stress forming in the corner flows, where the side channels of the device meet the main channel.Comment: 4 pages, 2 figures, AIP Conference Proceedings, 201

Natural convection with mixed insulating and conducting boundary conditions: low and high Rayleigh numbers regimes

We investigate the stability and dynamics of natural convection in two dimensions, subject to inhomogeneous boundary conditions. In particular, we consider a Rayleigh-B\`enard (RB) cell, where the horizontal top boundary contains a periodic sequence of alternating thermal insulating and conducting patches, and we study the effects of the heterogeneous pattern on the global heat exchange, both at low and high Rayleigh numbers. At low Rayleigh numbers, we determine numerically the transition from a regime characterized by the presence of small convective cells localized at the inhomogeneous boundary to the onset of bulk convective rolls spanning the entire domain. Such a transition is also controlled analytically in the limit when the boundary pattern length is small compared with the cell vertical size. At higher Rayleigh number, we use numerical simulations based on a lattice Boltzmann method to assess the impact of boundary inhomogeneities on the fully turbulent regime up to $Ra \sim 10^{10}$

Lattice Boltzmann simulations of droplet dynamics in time-dependent flows

We study the deformation and dynamics of droplets in time-dependent flows using 3D numerical simulations of two immiscible fluids based on the lattice Boltzmann model (LBM). Analytical models are available in the literature, which assume the droplet shape to be an ellipsoid at all times (P.L. Maffettone, M. Minale, J. Non-Newton. Fluid Mech 78, 227 (1998); M. Minale, Rheol. Acta 47, 667 (2008)). Beyond the practical importance of using a mesoscale simulation to assess ab-initio the robustness and limitations of such theoretical models, our simulations are also key to discuss - in controlled situations - some relevant phenomenology related to the interplay between the flow time scales and the droplet time scales regarding the transparency transition for high enough shear frequencies for an external oscillating flow. This work may be regarded as a step forward to discuss extensions towards a novel DNS approach, describing the mesoscale physics of small droplets subjected to a generic hydrodynamical strain field, possibly mimicking the effect of a realistic turbulent flow on dilute droplet suspensions

On the impact of controlled wall roughness shape on the flow of a soft-material

We explore the impact of geometrical corrugations on the near-wall flow properties of a soft-material driven in a confined rough microchannel. By means of numerical simulations, we perform a quantitative analysis of the relation between the flow rate $\Phi$ and the wall stress $\sigma_w$ for a number of setups, by changing both the roughness values as well as the roughness shape. Roughness suppresses the flow, with the existence of a characteristic value of $\sigma_w$ at which flow sets in. Just above the onset of flow, we quantitatively analyze the relation between $\Phi$ and $\sigma_w$. While for smooth walls a linear dependency is observed, steeper behaviours are found to set in by increasing wall roughness. The variation of the steepness, in turn, depends on the shape of the wall roughness, wherein gentle steepness changes are promoted by a variable space localization of the roughness