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• 1.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. College of Engineering, University of Kufa, Al Najaf, Iraq.
KTH, School of Engineering Sciences (SCI), Mechanics, Physicochemical Fluid Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
Sedimentation of finite-size particles in quiescent wall-bounded shear-thinning and Newtonian fluidsIn: Journal of International Journal of Multiphase Flow, ISSN 0301-9322Article in journal (Refereed)

We study the sedimentaion of finite-size particles in a quiescent wall-boundedNewtonian and shear-thinning fluids. The problem is studied numerically bymeans of direct numerical simulations with the presence of the particles ac-counted for with an immersed boundary method. The supensions are Non-Brownian rigid spherical particles with particle to fluid density ratio ρ p /ρ f =1.5; three different solid volume fractions Φ = 1%, 5% and 20% are considered.The Archimedes number is kept constant to Ar = 36 for all shear-thinning fluidcases, while it is changed to Ar = 97 for the Newtonian fluid to reproduce thesame terminal velocity of a single particle sedimenting in the shear-thinningfluid. We show that the mean settling velocities decrease with the particle con-centration as a consequence of the hindering effect and that the mean settlingspeed is always larger in the shear thinning fluid than in the Newtonian one.This is due to the decrease of the mean viscosity of the fluid which leads to alower drag force acting on the particles. We show that particles tend to formaggregates in the middle of the channel in a shear-thinning fluid, preferentiallypositioning in the wake of neighboring particles or aside them, resulting in lowerlevels of fluctuation in the gravity direction than in a Newtonian fluid.

• 2.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. College of Engineering, University of Kufa, Al Najaf, Iraq.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
Inertial migration of a deformable particle in pipe flow2019In: Physical Review Fluids, E-ISSN 2469-990X, Vol. 4, no 10, article id 104201Article in journal (Refereed)

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.

• 3.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. College of Engineering, Kufa University, Al Najaf, Iraq.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. Department of Mechanical Engineering, The University of Tokyo, Tokyo, Japan. KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
Interface-resolved simulations of particle suspensions in visco-elastic carrier fluidsIn: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645Article in journal (Refereed)

We study the rheology of a suspension of neutrally buoyant rigid particles subject touniform shear in different kinds of non-Newtonian fluids, chosen in order to disentanglethe effect of elasticity and shear thinning on the macroscopic system behavior. In par-ticular, we adopt the inelastic Carreau, viscoelastic Oldroyd-B and Giesekus models forthe carrier fluid. The rheology of the suspension is analyzed for a wide range of particlevolume fractions, Weissenberg and Reynolds numbers, comparing the results with thoseobtained for a Newtonian carrier fluid. We report here that the effective viscosity per-taining all the non-Newtonian cases is always lower than that of the suspension in theNewtonian carrier fluid and grows monotonically with the solid volume fraction. Theshear-thinning viscoelastic Giesekus fluid behaves similarly to the Oldroyd-B fluid at lowWeissenberg numbers and to the Carreau fluid at high Weissenberg numbers, indicatingthat elastic effects dominate at low Weissenberg and shear thinning is predominant athigh Weissenberg number. These variations in the effective viscosity are mainly due tochanges in the particle induced shear stress component. These data show that, at highshear rates, a viscoelastic carrier fluid can be modelled as a simple shear-thinning fluidfor which theoretical closures exists, while new models are needed at low Weissenbergnumbers to account for elastic effects such as decreased particle stress. Finally, when theinertia is increased, the suspension effective viscosity grows with the particle Reynoldsnumber at the same rate as in a Newtonian fluid for the Oldroyd-B case, while in ashear-thinning fluid the growth is less than in the Newtonian fluid. Also in the presenceof inertia, therefore, the shear-thinning behaviour dominates the suspension dynamics atrelatively high values of the imposed shear rate and elasticity effects saturate.

• 4.
KTH, School of Engineering Sciences (SCI), Mechanics.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Mechanics.
Numerical study of filament suspensions at finite inertiaIn: Article in journal (Other academic)
• 5.
KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics.
KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics.
Numerical study of filament suspensions at finite inertia2020In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 882, article id A5Article in journal (Refereed)

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 behaviour 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.

• 6.
KTH, School of Engineering Sciences in Chemistry, Biotechnology and Health (CBH), Protein Science, Nano Biotechnology.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences in Chemistry, Biotechnology and Health (CBH), Protein Science, Nano Biotechnology. KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences in Chemistry, Biotechnology and Health (CBH), Protein Science, Nano Biotechnology.
Particle focusing dynamics in extended elasto inertial flow2018Conference paper (Refereed)

Elasto Inertial microfluidics has been exploited recently for a number of industrial and biological applications. Recently, we experimentally showed that it is possible to achieve single stream focusing of particles even at higher flow rates in the elasto inertial regime, relevant to flow cytometry applications, and , based on this concept, built a silica fibre based micro flow cytometer.1 However, the physics behind the focusing of particles is still poorly understood, specially for combinations of higher Reynolds (Re) and Weissenberg numbers(Wi).

In the present study, for the first time, we seek to understand both experimentally and with numerical simulations, particle focusing across elasticity regimes. We vary the concentration of PEO (200 ppm to upto 10000 ppm) in PBS solution at sufficiently high flow rates of 100!l/min or above. We introduce a parameter, focusing bandwidth (F) to evaluate the extent of single stream focusing of 15 !m particles in a 75 !m diameter circular channel. Fig.1 shows the flow setup(fig.1a) along with images demonstrating the focused (fig.1b) and unfocused cases(fig.1c), as well as how F is calculated(fig.1d). We evaluate particle focusing by identifying the flow conditions for each concentration that leads to the minimum value of F. Fig.2 shows the variation of the focusing bandwidth(fig.2a) when changing PEO concentration, and the variation in Re along with Wi (fig.2b) and Elasticity number(El). The results show that for identical mass flow conditions across the different regimes the focusing bandwidth slowly shifts to a narrow single stream with increasing elasticity. We validated our experimental results as well as gained new insights into particle focusing with 3D numerical simulations based on a FENE P model. We studied the decoupled effects of Reynolds number and Weissenberg number on particle focusing, as well as the particle trajectories and migration dynamics as the particles reach equilibrium. Interestingly, enough we find a combination of high Re(Re=400) and sufficiently high Wi(Wi=3) for which the particles achieve a single stream focusing (fig.3a). The entire dynamics of particle migration in a circular cross section is also shown (in fig.3b) by changing Wi for a constant Re(Re=200). It can be seen that the particle goes through a longer amount of oscillations to reach its final equilibrium position as Wi is increased. Fig.4a shows the equilibrium position of the particle moving closer to the center with an increase in Wi at the same Re(Re=200). However, in the Non Newtonian cases, the particle has a slight oscillatory behaviour as it reaches its equilibrium position as compared to the Newtonian one. We introduced the particle at two different positions(at Re=200, We=0 and 1) and observed the same equilibrium positions in both cases (Fig.4b).

• 7.
KTH, School of Engineering Sciences in Chemistry, Biotechnology and Health (CBH), Protein Science, Nano Biotechnology.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences in Chemistry, Biotechnology and Health (CBH), Protein Science, Nano Biotechnology. KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences in Chemistry, Biotechnology and Health (CBH), Protein Science, Nano Biotechnology.
Analog particle position tuning in Elasto-inertial microfluidic flowsManuscript (preprint) (Other academic)

We observe for the first time an analog trend in particle focusing in a high throughput weakly viscoelastic regime, where it is possible to tune particles into multiple intermediate focusing positions that lie between the "Segre-Silberberg annulus" and the center of a circular microcapillary. The "Segre-Silberberg annulus" (0.6 times the pipe radius), that describes particle equilibrium in a predominantly inertial flow, shrinks consistently closer to the center for increasing elasticity in extremely dilute PEO concentrations (ranging from 0.001 wt% to 0.05wt%). The experimental observations are supported by direct numerical simulations, where an Immersed Boundary Method is used to account for the presence of particles and a FENE-P model is used to simulate the presence of polymers in a Non-Newtonian fluid. The numerical simulations study the dynamics and stability of finite size particles and are further used to analyze particle behavior at Reynolds number higher than what is allowed by the present experimental setup. In particular, we are able to report the entire migration trajectories of the particles as they reach their final equilibrium positions and extend our predictions to other geometries such as the square cross-section. We believe complex effects originate due to a combination of inertia and elasticity in a weakly viscoelastic regime, where neither inertia nor elasticity are able to mask each other's effect completely, thus leading to a number of intermediate focusing positions. The present study provides a new understanding into the mechanism of particle focusing in elasto-inertial flows and opens up new possibilities for exercising analog control in tuning the particle focusing positions.

• 8.
KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. Univ Naples Federico II, Dept Chem Mat & Ind Prod Engn, Piazzale V Tecchio 80, I-80125 Naples, Italy.. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
On the effect of coalescence on the rheology of emulsions2019In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 880, p. 969-991Article in journal (Refereed)

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 fractions and viscosity ratios 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 approximately 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 versus 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 with 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, except for the smallest viscosity ratio considered, 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 that neglecting droplet merging can lead to erroneous predictions.

• 9.
KTH, School of Engineering Sciences (SCI), Mechanics.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Mechanics, Physicochemical Fluid Mechanics. KTH, School of Engineering Sciences (SCI), Mechanics, Fluid Mechanics of Industrial Processes. KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
Computational modeling of multiphase viscoelastic and elastoviscoplastic flows2018In: International Journal for Numerical Methods in Fluids, ISSN 0271-2091, E-ISSN 1097-0363, Vol. 88, no 12, p. 521-543Article in journal (Refereed)
• 10.
KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
Coherent structures in the turbulent channel flow of an elastoviscoplastic fluid2020In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 888, article id A5Article in journal (Refereed)

In this numerical and theoretical work, we study the turbulent channel flow of Newtonian and elastoviscoplastic fluids. The coherent structures in these flows are identified by means of higher order dynamic mode decomposition (HODMD), applied to a set of data non-equidistant in time, to reveal the role of the near-wall streaks and their breakdown, and the interplay between turbulent dynamics and non-Newtonian effects. HODMD identifies six different high-amplitude modes, which either describe the yielded flow or the yielded-unyielded flow interaction. The structure of the low- and high-frequency modes suggests that the interaction between high- and low-speed streamwise velocity structures is one of the mechanisms triggering the streak breakdown, dominant in Newtonian turbulence where we observe shorter near-wall streaks and a more chaotic dynamics. As the influence of elasticity and plasticity increases, the flow becomes more correlated in the streamwise direction, with long streaks disrupted for short times by localised perturbations, reflected in reduced drag. Finally, we present streamwise-periodic dynamic mode decomposition modes as a viable tool to describe the highly complex turbulent flows, and identify simple well-organised groups of travelling waves.

• 11.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Mechanics.
Turbulent  flow of finite-size spherical particles with viscous hyper-elastic walls2018In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645Article in journal (Other academic)
• 12.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
Turbulent flow of finite-size spherical particles in channels with viscous hyper-elastic walls2019In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 873, p. 410-440, article id PII S0022112019004130Article in journal (Refereed)

We study single-phase and particle-laden turbulent channel flows bounded by two incompressible hyper-elastic walls with different deformability at bulk Reynolds number $5600$ . The solid volume fraction of finite-size neutrally buoyant rigid spherical particles considered is $10\,\%$ . The elastic walls are assumed to be of a neo-Hookean material. A fully Eulerian formulation is employed to model the elastic walls together with a direct-forcing immersed boundary method for the coupling between the fluid and the particles. The data show a significant drag increase and the enhancement of the turbulence activity with growing wall elasticity for both the single-phase and particle-laden flows when compared with the single-phase flow over rigid walls. Drag reduction and turbulence attenuation is obtained, on the other hand, with highly elastic walls when comparing the particle-laden flow with the single-phase flow for the same wall properties; the opposite effect, drag increase, is observed upon adding particles to the flow over less elastic walls. This is explained by investigating the near-wall turbulence, where the strong asymmetry in the magnitude of the wall-normal velocity fluctuations (favouring positive $v<^>{\prime }$ ), is found to push the particles towards the channel centre. The particle layer close to the wall contributes to turbulence production by increasing the wall-normal velocity fluctuations, so that in the absence of this layer, smaller wall deformations and in turn turbulence attenuation is observed. For a moderate wall elasticity, we increase the particle volume fraction up to $20\,\%$ and find that particle migration away from the wall is the cause of turbulence attenuation with respect to the flow over rigid walls. However, for this higher volume fractions, the particle induced stress compensates for the decreasing Reynolds shear stress, resulting in a higher overall drag for the case with elastic walls. The effect of the wall elasticity on the overall drag reduces significantly with increasing particle volume fraction.

• 13.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
Flexible Fiber Reveals the Two-Point Statistical Properties of Turbulence2018In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 121, no 4, article id 044501Article in journal (Refereed)

We study the dynamics of a flexible fiber freely moving in a three-dimensional fully developed turbulent field and present a phenomenological theory to describe the interaction between the fiber elasticity and the turbulent flow. This theory leads to the identification of two distinct regimes of flapping, which we validate against direct numerical simulations fully resolving the fiber dynamics. The main result of our analysis is the identification of a flapping regime where the fiber, despite its elasticity, is slaved to the turbulent fluctuations. In this regime the fiber can be used to measure two-point statistical observables of turbulence, including scaling exponents of velocity structure functions, the sign of the energy cascade and the energy flux of turbulence, as well as the characteristic times of the eddies within the inertial range of scales. Our results are expected to have a deep impact on the experimental turbulence research as a new way, accurate and efficient, to measure two-point, and more generally multipoint, statistics of turbulence.

• 14.
KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
Suspensions of deformable particles in a Couette flow2018In: Journal of Non-Newtonian Fluid Mechanics, ISSN 0377-0257, E-ISSN 1873-2631, Vol. 262, p. 3-11Article in journal (Refereed)

We consider suspensions of deformable particles in a Newtonian fluid by means of fully Eulerian numerical simulations with a one-continuum formulation. We study the rheology of the visco-elastic suspension in plane Couette flow in the limit of vanishing inertia and examine the dependency of the effective viscosity mu on the solid volume-fraction Phi, the capillary number Ca, and the solid to fluid viscosity ratio K. The suspension viscosity decreases with deformation and applied shear (shear-thinning) while still increasing with volume fraction. We show that mu collapses to an universal function, mu(Phi(e)), with an effective volume fraction Phi(e), lower than the nominal one owing to the particle deformation. This universal function is well described by the Eilers fit, which well approximate the rheology of suspension of rigid spheres at all O. We provide a closure for the effective volume fraction Phi(e) as function of volume fraction Phi and capillary number Ca and demonstrate it also applies to data in literature for suspensions of capsules and red-blood cells. In addition, we show that the normal stress differences exhibit a non-linear behavior, with a similar trend as in polymer and filament suspensions. The total stress budgets reveals that the particle-induced stress contribution increases with the volume fraction Phi and decreases with deformability.

• 15.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
Numerical simulations of emulsions in shear flows2019In: Acta Mechanica, ISSN 0001-5970, E-ISSN 1619-6937, Vol. 230, no 2, p. 667-682Article in journal (Refereed)

We present a modification of a recently developed volume of fluid method for multiphase problems (Ii et al. in J Comput Phys 231(5):2328-2358, 2012), so that it can be used in conjunction with a fractional-step method and fast Poisson solver, and validate it with standard benchmark problems. We then consider emulsions of two-fluid systems and study their rheology in a plane Couette flow in the limit of vanishing inertia. We examine the dependency of the effective viscosity on the volume fraction phi (from 10 to 30%) and the Capillary number Ca (from 0.1 to 0.4) for the case of density and viscosity ratio 1. We show that the effective viscosity decreases with the deformation and the applied shear (shear-thinning) while exhibiting a non-monotonic behavior with respect to the volume fraction. We report the appearance of a maximum in the effective viscosity curve and compare the results with those of suspensions of rigid and deformable particles and capsules. We show that the flow in the solvent is mostly a shear flow, while it is mostly rotational in the suspended phase; moreover, this behavior tends to reverse as the volume fraction increases. Finally, we evaluate the contributions to the total shear stress of the viscous stresses in the two fluids and of the interfacial force between them.

• 16.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. Stanford Univ, Ctr Turbulence Res, Stanford, CA 94305 USA.. Stanford Univ, Ctr Turbulence Res, Stanford, CA 94305 USA.. KTH, School of Engineering Sciences (SCI), Mechanics. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. Norwegian Univ Sci & Technol NTNU, Dept Energy & Proc Engn, NO-7491 Trondheim, Norway..
Droplets in homogeneous shear turbulence2019In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 876, p. 962-984Article in journal (Refereed)

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 15 200. 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 droplet 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 break-up in homogeneous isotropic turbulence, provides an excellent estimate notwithstanding the action of significant coalescence and the presence of a mean shear.

• 17.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. Ohio Univ, Dept Mech Engn, Athens, OH 45701 USA.. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
Turbulent channel flow of an elastoviscoplastic fluid2018In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 853, p. 488-514Article in journal (Refereed)

We present numerical simulations of laminar and turbulent channel flow of an elastoviscoplastic fluid. The non-Newtonian flow is simulated by solving the full incompressible Navier-Stokes equations coupled with the evolution equation for the elastoviscoplastic stress tensor. The laminar simulations are carried out for a wide range of Reynolds numbers, Bingham numbers and ratios of the fluid and total viscosity, while the turbulent flow simulations are performed at a fixed bulk Reynolds number equal to 2800 and weak elasticity. We show that in the laminar flow regime the friction factor increases monotonically with the Bingham number (yield stress) and decreases with the viscosity ratio, while in the turbulent regime the friction factor is almost independent of the viscosity ratio and decreases with the Bingham number, until the flow eventually returns to a fully laminar condition for large enough yield stresses. Three main regimes are found in the turbulent case, depending on the Bingham number: for low values, the friction Reynolds number and the turbulent flow statistics only slightly differ from those of a Newtonian fluid; for intermediate values of the Bingham number, the fluctuations increase and the inertial equilibrium range is lost. Finally, for higher values the flow completely laminarizes. These different behaviours are associated with a progressive increases of the volume where the fluid is not yielded, growing from the centreline towards the walls as the Bingham number increases. The unyielded region interacts with the near-wall structures, forming preferentially above the high-speed streaks. In particular, the near-wall streaks and the associated quasi-streamwise vortices are strongly enhanced in an highly elastoviscoplastic fluid and the flow becomes more correlated in the streamwise direction.

• 18.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
The effect of elastic walls on suspension flow2018In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114Article in journal (Other academic)
• 19.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
DICCA, University of Genova, Via Montallegro 1, Genova, 16145, Italy ; INFN, Genova Section, Via Dodecaneso 33, Genova, 16146, Italy. KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. DICCA, University of Genova, Via Montallegro 1, Genova, 16145, Italy ; INFN, Genova Section, Via Dodecaneso 33, Genova, 16146, Italy.
Flowing fibers as a proxy of turbulence statistics2020In: Meccanica (Milano. Print), ISSN 0025-6455, E-ISSN 1572-9648, Vol. 55, p. 357-370Article in journal (Refereed)

The flapping states of a flexible fiber fully coupled to a three-dimensional turbulent flow are investigated via state-of-the-art numerical methods. Two distinct flapping regimes are predicted by the phenomenological theory recently proposed by Rosti et al. (Phys. Rev. Lett. 121:044501, 2018) the under-damped regime, where the elasticity strongly affects the fiber dynamics, and the over-damped regime, where the elastic effects are strongly inhibited. In both cases we can identify a critical value of the bending rigidity of the fiber by a resonance condition, which further provides a distinction between different flapping behaviors, especially in the under-damped case. We validate the theory by means of direct numerical simulations and find that, both for the over-damped regime and for the under-damped one, fibers are effectively slaved to the turbulent fluctuations and can therefore be used as a proxy to measure various two-point statistics of turbulence. Finally, we show that this holds true also in the case of a passive fiber, without any feedback force on the fluid.

• 20.
KTH, School of Engineering Sciences (SCI), Mechanics.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Mechanics.
Flowing fibers as a proxy of turbulence statisticsIn: Meccanica (Milano. Print), ISSN 0025-6455, E-ISSN 1572-9648Article in journal (Refereed)
• 21.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
City Univ London, Sch Math Comp Sci & Engn, London EC1V 0HB, England.. City Univ London, Sch Math Comp Sci & Engn, London EC1V 0HB, England..
Numerical Simulation of a Passive Control of the Flow Around an Aerofoil Using a Flexible, Self Adaptive Flaplet2018In: Flow Turbulence and Combustion, ISSN 1386-6184, E-ISSN 1573-1987, Vol. 100, no 4, p. 1111-1143Article in journal (Refereed)

Self-activated feathers are used by almost all birds to adapt their wing characteristics to delay stall or to moderate its adverse effects (e.g., during landing or sudden increase in angle of attack due to gusts). Some of the feathers are believed to pop up as a consequence of flow separation and to interact with the flow and produce beneficial modifications of the unsteady vorticity field. The use of self adaptive flaplets in aircrafts, inspired by birds feathers, requires the understanding of the physical mechanisms leading to the mentioned aerodynamic benefits and the determination of the characteristics of optimal flaps including their size, positioning and ideal fabrication material. In this framework, this numerical study is divided in two parts. Firstly, in a simplified scenario, we determine the main characteristics that render a flap mounted on an aerofoil at high angle of attack able to deliver increased lift and improved aerodynamic efficiency, by varying its length, position and its natural frequency. Later on, a detailed direct numerical simulation analysis is used to understand the origin of the aerodynamic benefits introduced by the flaplet movement induced by the interaction with the flow field. The parametric study that has been carried out, reveals that an optimal flap can deliver a mean lift increase of about 20% on a NACA0020 aerofoil at an incidence of 20 (o) degrees. The results obtained from the direct numerical simulation of the flow field around the aerofoil equipped with the optimal flap at a chord Reynolds number of 2 x 10(4) shows that the flaplet movement is mainly induced by a cyclic passage of a large recirculation bubble on the aerofoil suction side. In turns, when the flap is pushed downward, the induced plane jet displaces the trailing edge vortices further downstream, away from the wing, moderating the downforce generated by those vortices and regularising the shedding cycle that appears to be much more organised when the optimal flaplet configuration is selected.

• 22.
KTH, School of Engineering Sciences (SCI), Mechanics. City University London, United Kingdom.
Passive control of the flow around unsteady aerofoils using a self-activated deployable flap2018In: Journal of turbulence, ISSN 1468-5248, E-ISSN 1468-5248, Vol. 19, no 3, p. 204-228Article in journal (Refereed)

Self-activated feathers are used by many birds to adapt their wing characteristics to the sudden change of flight incidence angle. In particular, dorsal feathers are believed to pop-up as a consequence of unsteady flow separation and to interact with the flow to palliate the sudden stall breakdown typical of dynamic stall. Inspired by the adaptive character of birds feathers, some authors have envisaged the potential benefits of using of flexible flaps mounted on aerodynamic surfaces to counteract the negative aerodynamic effects associated with dynamic stall. This contribution explores more in depth the physical mechanisms that play a role in the modification of the unsteady flow field generated by a NACA0020 aerofoil equipped with an elastically mounted flap undergoing a specific ramp-up manoeuvre. We discuss the design of flaps that limit the severity of the dynamic stall breakdown by increasing the value of the lift overshoot also smoothing its abrupt decay in time. A detailed analysis on the modification of the turbulent and unsteady vorticity field due to the flap flow interaction during the ramp-up motion is also provided to explain the more benign aerodynamic response obtained when the flap is in use.

• 23.
KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm Univ, SE-10691 Stockholm, Sweden.
The breakdown of Darcy's law in a soft porous material2020In: Soft Matter, ISSN 1744-683X, E-ISSN 1744-6848, Vol. 16, no 4, p. 939-944Article in journal (Refereed)

We perform direct numerical simulations of the flow through a model of 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 (Delta P) 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 material with a linear constitutive relation but can undergo large deformation. Our theory further predicts that the flow permeability is an universal function of Delta P/G, which is confirmed by the present simulations.

• 24.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
Turbulent duct flow with polymers2019In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 859, p. 1057-1083Article in journal (Refereed)

We have performed direct numerical simulation of the turbulent flow of a polymer solution in a square duct, with the FENE-P model used to simulate the presence of polymers. First, a simulation at a fixed moderate Reynolds number is performed and its results compared with those of a Newtonian fluid to understand the mechanism of drag reduction and how the secondary motion, typical of the turbulent flow in non-axisymmetric ducts, is affected by polymer additives. Our study shows that the Prandtl's secondary flow is modified by the polymers: the circulation of the streamwise main vortices increases and the location of the maximum vorticity moves towards the centre of the duct. In-plane fluctuations are reduced while the streamwise ones are enhanced in the centre of the duct and dumped in the corners due to a substantial modification of the quasi-streamwise vortices and the associated near-wall low- and high-speed streaks; these grow in size and depart from the walls, their streamwise coherence increasing. Finally, we investigated the effect of the parameters defining the viscoelastic behaviour of the flow and found that the Weissenberg number strongly influences the flow, with the cross-stream vortical structures growing in size and the in-plane velocity fluctuations reducing for increasing flow elasticity.We have performed direct numerical simulation of the turbulent flow of a polymer solution in a square duct, with the FENE-P model used to simulate the presence of polymers. First, a simulation at a fixed moderate Reynolds number is performed and its results compared with those of a Newtonian fluid to understand the mechanism of drag reduction and how the secondary motion, typical of the turbulent flow in non-axisymmetric ducts, is affected by polymer additives. Our study shows that the Prandtl's secondary flow is modified by the polymers: the circulation of the streamwise main vortices increases and the location of the maximum vorticity moves towards the centre of the duct. In-plane fluctuations are reduced while the streamwise ones are enhanced in the centre of the duct and dumped in the corners due to a substantial modification of the quasi-streamwise vortices and the associated near-wall low- and high-speed streaks; these grow in size and depart from the walls, their streamwise coherence increasing. Finally, we investigated the effect of the parameters defining the viscoelastic behaviour of the flow and found that the Weissenberg number strongly influences the flow, with the cross-stream vortical structures growing in size and the in-plane velocity fluctuations reducing for increasing flow elasticity.

• 25.
Osaka Univ, Grad Sch Engn Sci, 1-3 Machikaneyama, Toyonaka, Osaka 5608531, Japan..
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. Kobe Univ, Grad Sch Engn, Nada Ku, 1-1 Rokkodai, Kobe, Hyogo 6578501, Japan.. Osaka Univ, Grad Sch Engn Sci, 1-3 Machikaneyama, Toyonaka, Osaka 5608531, Japan.. KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
Haemorheology in dilute, semi-dilute and dense suspensions of red blood cells2019In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 872, p. 818-848Article in journal (Refereed)

We present a numerical analysis of the rheology of a suspension of red blood cells (RBCs) in a wall-bounded shear flow. The flow is assumed as almost inertialess. The suspension of RBCs, modelled as biconcave capsules whose membrane follows the Skalak constitutive law, is simulated for a wide range of viscosity ratios between the cytoplasm and plasma, D 0 : 1-10, for volume fractions up to D 0 : 41 and for different capillary numbers (Ca). Our numerical results show that an RBC at low Ca tends to orient to the shear plane and exhibits so-called rolling motion, a stable mode with higher intrinsic viscosity than the so-called tumbling motion. As Ca increases, the mode shifts from the rolling to the swinging motion. Hydrodynamic interactions (higher volume fraction) also allow RBCs to exhibit tumbling or swinging motions resulting in a drop of the intrinsic viscosity for dilute and semi-dilute suspensions. Because of this mode change, conventional ways of modelling the relative viscosity as a polynomial function of cannot be simply applied in suspensions of RBCs at low volume fractions. The relative viscosity for high volume fractions, however, can be well described as a function of an effective volume fraction, defined by the volume of spheres of radius equal to the semi-middle axis of a deformed RBC. We find that the relative viscosity successfully collapses on a single nonlinear curve independently of except for the case with Ca > 0 : 4, where the fit works only in the case of low/ moderate volume fraction, and fails in the case of a fully dense suspension.

• 26.
Univ Napoli Federico II, Dipartimento Ingn Chim Mat & Prod Ind, Ple Tecchio 80, I-80125 Naples, Italy..
KTH, School of Engineering Sciences (SCI), Engineering Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Engineering Mechanics. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Engineering Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
Numerical simulations of oscillatory shear flow of particle suspensions at finite inertia2019In: Rheologica Acta, ISSN 0035-4511, E-ISSN 1435-1528, Vol. 58, no 11-12, p. 741-753Article in journal (Refereed)

We perform immersed-boundary-method numerical simulations of oscillatory shear flow of suspensions of mono-disperse non-colloidal rigid spherical particles in a Newtonian liquid from the dilute to the concentrated regime. Both small and large amplitude oscillatory shear flow (SAOS and LAOS, respectively) are studied and the effects of particle concentration, fluid inertia, particle-to-fluid density ratio, and deformation amplitude on the measured apparent viscoelastic moduli of the suspensions are quantified. In the SAOS regime, a non-zero storage modulus G '-values significantly change with inertia, but depend on the volume fraction of the solid phase only for suspensions of particles denser than the fluid. On the other hand, the loss modulus G '' increases with both inertia and particle concentration. In the LAOS regime, the moduli are only weakly dependent on the deformation amplitude for a dilute suspension, whereas non-monotonic variations are observed at high concentrations.

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