arXiv subjects

Luca Brandt

Publications and source records attributed to Luca Brandt.

At least 55 records · Page 3Linked to original sources

arXiv2020

The impact of porous walls on the rheology of suspensions

We study the effect of isotropic porous walls on a plane Couette flow laden with spherical and rigid particles. We perform a parametric study varying the volume fraction between $0$ and $30\%$, the porosity between $0.3$ and $0.9$ and the non-dimensional permeability between $0$ and $7.9 \times 10^{-3}$ We find that the porous walls induce a progressive decrease in the suspension effective viscosity as the wall permeability increases. This behavior is explained by the weakening of the wall-blocking effect and by the appearance of a slip velocity at the interface of the porous medium, which reduces the shear rate in the channel. Therefore, particle rotation and the consequent velocity fluctuations in the two phases are dampened, leading to reduced particle interactions and particle stresses. Based on our numerical evidence, we provide a closed set of equations for the suspension viscosity, which can be used to estimate the suspension rheology in the presence of porous walls.

physics.flu-dyn↗

arXiv2020

Aerodynamically-driven rupture of a liquid film by turbulent shear flow

The rupture of a liquid film due to co-flowing turbulent shear flows in the gas phase is studied using a volume-of-fluid method. To simulate this multiphase problem, we use a simplified numerical setup where the liquid film is 'sandwiched' between two fully developed boundary layers from a turbulent channel simulation. The film deforms and eventually ruptures within the shear zone created by the co-flows. This efficient setup allows systematic variation of physical parameters to gauge their role in the aerodynamically-driven deformation and rupture of a liquid film under fully developed sheared turbulence. The present work presents a detailed study of the developing pressure field over the deforming film and related aerodynamic effects, as previously suggested by other authors, in particular the role of the inviscid lift and drag forces. A cumulative lift force is introduced to capture the effect of the alternating pressure minima and maxima forming over the film which amplify and eventually rupture the film. A velocity scale derived from the lift-induced drag force reflects the state of the turbulent boundary layer over the film and collapses the temporal development of this cumulative lift force as well as the amplitude of film deformation with some success for the different film thicknesses and Reynolds numbers.

physics.flu-dyn↗

arXiv2020

Low Reynolds number turbulent flows over elastic walls

We study the laminar and turbulent channel flow over a viscous hyper-elastic wall and show that it is possible to sustain an unsteady chaotic turbulent-like flow at any Reynolds number by properly choosing the wall elastic modulus. We propose a physical explanation for this effect by evaluating the shear stress and the turbulent kinetic energy budget in the fluid and elastic layer. We vary the bulk Reynolds number from 2800 to 10 and identify two distinct mechanisms for turbulence production. At moderate and high Reynolds numbers, turbulent fluctuations activate the wall oscillations, which, in turn, amplify the turbulent Reynolds stresses in the fluid. At very low Reynolds number, the only production term is due to the energy input from the elastic wall, which increases with the wall elasticity. This mechanism may be exploited to passively enhance mixing in microfluidic devices.

physics.flu-dyn↗

arXiv2020

Regimes of heat transfer in particle suspensions

We present results of interface-resolved simulations of heat transfer in suspensions of finite-size neutrally-buoyant spherical particles for solid volume fractions up to 35% and bulk Reynolds numbers from 500 to 5600. An Immersed Boundary-Volume of Fluid method is used to solve the energy equation in the fluid and solid phase. We relate the heat transfer to the regimes of particle motion previously identified, i.e. a viscous regime at low volume fractions and low Reynolds number, particle-laden turbulence at high Reynolds and moderate volume fraction and particulate regime at high volume fractions. We show that in the viscous dominated regime, the heat transfer is mainly due to thermal diffusion with enhancement due to the particle-induced fluctuations. In the turbulent-like regime, we observe the largest enhancement of the global heat transfer, dominated by the turbulent heat flux. In the particulate shear-thickening regime, however, the heat transfer enhancement decreases as mixing is quenched by the particle migration towards the channel core. As a result, a compact loosely-packed core region forms and the contribution of thermal diffusion to the total heat transfer becomes significant once again. The global heat transfer becomes, in these flows at volume fractions larger than 25%, lower than in single-phase turbulence.

physics.flu-dyn↗

arXiv2020

Effects of surface nanostructure and wettability on pool boiling: A molecular dynamics study

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 large-scale MD simulations. In the numerical experiments, we control the system pressure by imposing a constant force on a moving piston. The simulations reveal that the presence of a nanostructure triggers the bubble formation, 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 chemistry accelerates the bubble nucleation, however, decelerates the bubble expansion, thus postponing the formation of the film of vapour. Therefore, 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 is maximum.

cond-mat.soft↗

arXiv2020

Weakly adhesive suspension shows rate-dependence in oscillatory but not steady shear flows

We report rheological measurements of a noncolloidal particle suspension in a Newtonian solvent at 40% solid volume fraction. An anomalous, frequency-dependent complex viscosity is found under oscillatory shear (OS) flow, whereas a constant dynamic viscosity is found under the same shear rates in steady shear (SS) flow. We show that this contradiction arises from the underlying microstructural difference between OS and SS, mediated by weak interparticle forces. Discrete element simulations of proxy particle suspensions confirm this hypothesis and reveal an adhesion-induced, shear thinning mechanism with a -1/5 slope, only in OS, in agreement with experiments.

cond-mat.soft↗

arXiv2020

An interface capturing method for liquid-gas flows at low-Mach number

Multiphase, compressible and viscous flows are of crucial importance in a wide range of scientific and engineering problems. Despite the large effort paid in the last decades to develop accurate and efficient numerical techniques to address this kind of problems, current models need to be further improved to address realistic applications. In this context, we propose a numerical approach to the simulation of multiphase, viscous flows where a compressible and an incompressible phase interact in the low-Mach number regime. In this frame, acoustics is neglected but large density variations of the compressible phase can be accounted for as well as heat transfer, convection and diffusion processes. The problem is addressed in a fully Eulerian framework exploiting a low-Mach number asymptotic expansion of the Navier-Stokes equations. A Volume of Fluid approach (VOF) is used to capture the liquid-gas interface, built on top of a massive parallel solver, second order accurate both in time and space. The second-order-pressure term is treated implicitly and the resulting pressure equation is solved with the eigenexpansion method employing a robust and novel formulation. We provide a detailed and complete description of the theoretical approach together with information about the numerical technique and implementation details. Results of benchmarking tests are provided for five different test cases.

physics.flu-dyn↗

arXiv2020

Implementation note on a minimal hybrid lubrication/granular dynamics model for dense suspensions

We describe and summarize a class of minimal numerical models emerged from recent development of simulation methods for dense particle suspensions in overdamped linear flows. The main ingredients include (i) a frame-invariant, short-range lubrication model for spherical particles, and (ii) a soft-core, stick/slide frictional contact model activated when particles overlap. We implement a version of the model using a modified velocity-Verlet algorithm that explicitly solves the $N$-body dynamical system in $\mathcal{O}(cN)$ operations, where $c$ is a kernel constant depending on the cutoff of particle interactions. The implementation is validated against literature results on jamming transition and shear thickening suspensions from 40% to 64% volume fractions. Potential strategies to extend the present methodology to non-spherical particles are also suggested for very concentrated suspensions.

cond-mat.soft↗

arXiv2020

Numerical simulations of a sphere settling in simple shear flows of yield stress fluids

We perform $3$D numerical simulations to investigate the sedimentation of a single sphere in the absence and presence of a simple cross shear flow in a yield stress fluid with weak inertia. In our simulations, the settling flow is considered to be the primary flow, whereas the linear cross shear flow is a secondary flow with amplitude $10\%$ of the primary flow. To study the effects of elasticity and plasticity of the carrying fluid on the sphere drag as well as the flow dynamics, the fluid is modeled using the elastovisco-plastic (EVP) constitutive laws proposed by \cite{saramito2009new}. The extra non-Newtonian stress tensor is fully coupled with the flow equation and the solid particle is represented by an immersed boundary (IB) method. Our results show that the fore-aft asymmetry in the velocity is less pronounced and the negative wake disappears when a linear cross shear flow is applied. We find that the drag on a sphere settling in a sheared yield stress fluid is reduced significantly as compared to an otherwise quiescent fluid. More importantly, the sphere drag in the presence of a secondary cross shear flow cannot be derived from the pure sedimentation drag law owing to the non-linear coupling between the simple shear flow and the uniform flow. Finally, we show that the drag on the sphere settling in a sheared yield-stress fluid is reduced at higher material elasticity mainly due to the form and viscous drag reduction.

physics.flu-dyn↗

arXiv2020

Numerical Simulations of Vorticity Banding of Emulsions in Shear Flows

Multiphase shear flows often show banded structures that affect the global behavior of complex fluids e.g. in microdevices. Here we investigate numerically the banding of emulsions, i.e. the formation of regions of high and low volume fraction, alternated in the vorticity direction and aligned with the flow (shear bands). These bands are associated with a decrease of the effective viscosity of the system. To understand the mechanism of banding experimentally observed we have performed interface resolved simulations of the two-fluid system. The experiments were perfomed starting with a random distribution of droplets which, under the applied shear, evolves in time resulting in a phase separation. To numerically reproduce this process, the banded structures are initialized in a narrow channel confined by two walls moving in opposite direction. We find that the initial banded distribution is stable when droplets are free to merge and unstable when coalescence is prevented. In this case, additionally, the effective viscosity of the system increases, resembling the rheological behavior of suspensions of deformable particles. Droplets coalescence, on the other hand, allows emulsions to reduce the total surface of the system and hence the energy dissipation associated to the deformation, which in turn reduces the effective viscosity.

physics.flu-dyn↗

arXiv2020

A volume-of-fluid method for interface-resolved simulations of phase-changing two-fluid flows

We present a numerical method for interface-resolved simulations of evaporating two-fluid flows based on the volume-of-fluid (VoF) method. The method has been implemented in an efficient FFT-based two-fluid Navier-Stokes solver, using an algebraic VoF method for the interface representation, and extended with the transport equations of thermal energy and vaporized liquid mass for the single-component evaporating liquid in an inert gas. The conservation of vaporizing liquid and computation of the interfacial mass flux are performed with the aid of a reconstructed signed-distance field, which enables the use of well-established methods for phase change solvers based on level-set methods. The interface velocity is computed with a novel approach that ensures accurate mass conservation, by constructing a divergence-free extension of the liquid velocity field onto the entire domain. The resulting approach does not depend on the type of interface reconstruction (i.e.\ can be employed in both algebraic and geometrical VoF methods). We extensively verified and validated the overall method against several benchmark cases, and demonstrated its excellent mass conservation and good overall performance for simulating evaporating two-fluid flows in two and three dimensions.

physics.comp-ph↗

arXiv2019

The breakdown of Darcy's law in a soft porous material

We perform direct numerical simulations of the flow through a model of a deformable porous medium. Our model is a two-dimensional hexagonal lattice, with defects, of soft elastic cylindrical pillars, with elastic shear modulus $G$, immersed in a liquid. We use a two-phase approach: the liquid phase is a viscous fluid and the solid phase is modeled as an incompressible viscoelastic material, whose complete nonlinear structural response is considered. We observe that the Darcy flux ($q$) is a nonlinear function -- steeper than linear -- of the pressure-difference ($ΔP$) across the medium. Furthermore, the flux is larger for a softer medium (smaller $G$). We construct a theory of this super-linear behavior by modelling the channels between the solid cylinders as elastic channels whose walls are made of a material with a linear constitutive relation but can undergo large deformation. Our theory further predicts that the flow permeability is a universal function of $ΔP/G$, which is confirmed by the present simulations.

physics.flu-dyn↗

arXiv2019

Numerical study of filament suspensions at finite inertia

We present a numerical study on the rheology of semi-dilute and concentrated filament suspensions of different bending stiffness and Reynolds number, with the immersed boundary method used to couple the fluid and solid. The filaments are considered as one-dimensional inextensible slender bodies with fixed aspect ratio, obeying the Euler-Bernoulli beam equation. To understand the global suspension behavior we relate it to the filament microstructure, deformation and elastic energy and examine the stress budget to quantify the effect of the elastic contribution. At fixed volume fraction, the viscosity of the suspension reduces when decreasing the bending rigidity and grows when increasing the Reynolds number. The change in the relative viscosity is stronger at finite inertia, although still in the laminar flow regime as considered here. Moreover, we find the first normal stress difference to be positive as in polymeric fluids, and to increase with the Reynolds number; its value has a peak for an intermediate value of the filament bending stiffness. The peak value is found to be proportional to the Reynolds number, moving towards more rigid suspensions at larger inertia. Moreover, the viscosity increases when increasing the filament volume fraction, and the rate of increase of the filament stress with the bending rigidity is stronger at higher Reynolds numbers and reduces with the volume fraction. We show that this behaviour is associated with the formation of a more ordered structure in the flow, where filaments tend to be more aligned and move as a compact aggregate, thus reducing the filament-filament interactions despite their volume fraction increases.

physics.flu-dyn↗

arXiv2019

Inertial migration of a deformable particle in pipe flow

We perform fully Eulerian numerical simulations of an initially spherical hyperelastic particle suspended in a Newtonian pressure-driven flow in a cylindrical straight pipe. We study the full particle migration and deformation for different Reynolds numbers and for various levels of particle elasticity, to disentangle the interplay of inertia and elasticity on the particle focusing. We observe that the particle deforms and undergoes a lateral displacement while traveling downstream through the pipe, finally focusing at the pipe centerline. We note that the migration dynamics and the final equilibrium position are almost independent of the Reynolds number, while they strongly depend on the particle elasticity; in particular, the migration is faster as the elasticity increases (i.e. the particle is more deformable), with the particle reaching the final equilibrium position at the centerline in shorter times. Our simulations show that the results are not affected by the particle initial conditions, position and velocity. Finally, we explain the particle migration by computing the total force acting on the particle and its different components, viscous and elastic.

physics.flu-dyn↗

arXiv2019

The effect of a wall on the interaction of two spheres in shear flow: Batchelor-Green theory revisited

The seminal Batchelor-Green's (BG) theory on the hydrodynamic interaction of two spherical particles of radii a suspended in a viscous shear flow neglects the effect of the boundaries. In the present paper we study how a plane wall modifies this interaction. Using an integral equation for the surface traction we derive the expression for the particles' relative velocity as a sum of the BG's velocity and the term due to the presence of a wall at finite distance, z_0. Our calculation is not the perturbation theory of the BG solution, so the contribution due to the wall is not necessarily small. The distance at which the wall significantly alters the particles interaction scales as z_0^{3/5}. The phase portrait of the particles' relative motion is different from the BG theory, where there are two singly-connected regions of open and closed trajectories both of infinite volume. For finite z_0, there is a new domain of closed (dancing) and open (swapping) trajectories. The width of this region behaves as 1/z_0. Along the swapping trajectories, that have been previously observed numerically, the incoming particle is turning back after the encounter with the reference particle, rather than passing it by, as in the BG theory. The region of dancing trajectories has infinite volume. We found a one-parameter family of equilibrium states, overlooked previously, whereas the pair of spheres flows as a whole without changing its configuration. These states are marginally stable and their perturbation yields a two-parameter family of the dancing trajectories, where the particle is orbiting around a fixed point in a frame co-moving with the reference particle. We suggest that the phase portrait obtained at z_0>>a is topologically stable and can be extended down to rather small z_0 of several particle diameters. We confirm this by direct numerical simulations of the Navier-Stokes equations with z_0=5a.

physics.flu-dyn↗

arXiv2019

On the effect of coalescence on the rheology of emulsions

We present a numerical study of the rheology of a two-fluid emulsion in dilute and semidilute conditions. The analysis is performed for different capillary numbers, volume fraction and viscosity ratio under the assumption of negligible inertia and zero buoyancy force. The effective viscosity of the system increases for low values of the volume fraction and decreases for higher values, with a maximum for about 20 % concentration of the disperse phase. When the dispersed fluid has lower viscosity, the normalised effective viscosity becomes smaller than 1 for high enough volume fractions. To single out the effect of droplet coalescence on the rheology of the emulsion we introduce an Eulerian force which prevents merging, effectively modelling the presence of surfactants in the system. When the coalescence is inhibited the effective viscosity is always greater than 1 and the curvature of the function representing the emulsion effective viscosity vs. the volume fraction becomes positive, resembling the behaviour of suspensions of deformable particles. The reduction of the effective viscosity in the presence of coalescence is associated to the reduction of the total surface of the disperse phase when the droplets merge, which leads to a reduction of the interface tension contribution to the total shear stress. The probability density function of the flow topology parameter shows that the flow is mostly a shear flow in the matrix phase, with regions of extensional flow when the coalescence is prohibited. The flow in the disperse phase, instead, always shows rotational components. The first normal stress difference is positive whereas the second normal difference is negative, with their ratio being constant with the volume fraction. Our results clearly show that the coalescence efficiency strongly affects the system rheology and neglecting droplet merging can lead to erroneous predictions.

physics.flu-dyn↗

arXiv2019

Droplets in homogeneous shear turbulence

We simulate the flow of two immiscible and incompressible fluids separated by an interface in a homogeneous turbulent shear flow at a shear Reynolds number equal to 15200. The viscosity and density of the two fluids are equal, and various surface tensions and initial droplet diameters are considered in the present study. We show that the two-phase flow reaches a statistically stationary turbulent state sustained by a non-zero mean turbulent production rate due to the presence of the mean shear. Compared to single-phase flow, we find that the resulting steady state conditions exhibit reduced Taylor microscale Reynolds numbers owing to the presence of the dispersed phase, which acts as a sink of turbulent kinetic energy for the carrier fluid. At steady state, the mean power of surface tension is zero and the turbulent production rate is in balance with the turbulent dissipation rate, with their values being larger than in the reference single-phase case. The interface modifies the energy spectrum by introducing energy at small-scales, with the difference from the single-phase case reducing as the Weber number increases. This is caused by both the number of droplets in the domain and the total surface area increasing monotonically with the Weber number. This reflects also in the droplets size distribution which changes with the Weber number, with the peak of the distribution moving to smaller sizes as the Weber number increases. We show that the Hinze estimate for the maximum droplet size, obtained considering breakup in homogeneous isotropic turbulence, provides an excellent estimate notwithstanding the action of significant coalescence and the presence of a mean shear.

physics.flu-dyn↗

arXiv2019

The effect of elastic walls on suspension flow

We study suspensions of rigid particles in a plane Couette flow with deformable elastic walls. We find that, in the limit of vanishing inertia, the elastic walls induce shear thinning of the suspension flow such that the effective viscosity decreases as the wall deformability increases. This shear-thinning behavior originates from the interactions between rigid particles, soft wall and carrier fluid; an asymmetric wall deformation induces a net lift force acting on the particles which therefore migrate towards the bulk of the channel. Based on our observations, we provide a closure for the suspension viscosity which can be used to model the rheology of suspensions with arbitrary volume fraction in elastic channels.

cond-mat.soft↗