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Several technologies and biotechnologies employing small-sized particles in microfluidics and nanofluidics rely on the ability of hampering thermal motion for progress. We experimentally demonstrate that nanoparticles suspended in a dilute polymer solution in Poiseuille flow can be trapped in the central region of a microtube, with a trapping efficiency that depends on the squared flow rate. The trap force is caused by the viscoelasticity of the suspending fluid, and can be modulated by selecting liquids with specific rheology. We also propose a simple theoretical argument that supports the experimental evidence, and links the trapping force to a dimensionless parameter comparing viscoelastic normal forces and Brownian forces. The theoretical argument distills into a simple equation, which could be used to downscale flow cytometers, or to design microfluidic devices for counting, coding, or separating nanoparticles.

The motion of an ellipsoidal particle in a viscoelastic liquid subjected to an unconfined shear flow is addressed by numerical simulations. A complex dynamics is found with different transients and long-time regimes depending on the Deborah number De (De is the product of the viscoelastic liquid intrinsic time times the applied shear rate). Spiraling orbits toward a log-rolling motion around the vorticity are observed for low Deborah numbers, whereas the particle aligns with its major axis near to the flow direction at high Deborah numbers. The transition from vorticity to flow alignment is characterized by a periodic regime with small amplitude oscillations around orientations progressively shifting from vorticity to flow direction by increasing De. A range of Deborah numbers is detected such that the periodic solution coexists with the flow alignment regime (bistability). A further range of De is found where flow alignment is attained differently for particles starting far from or next to the shear plane: in the latter case, very long transients are found; hence an effective bistability (metabistability) is predicted to occur in a large time lapse before reaching the fully aligned state. Finally, the computed Deborah number values for flow alignment favorably compare with available experimental data. © 2014 American Physical Society.

We demonstrate the possibility to achieve 3D particle focusing in a straight microchannel with a square cross-section by exploiting purely viscoelastic effects. Experiments are carried out by considering an elastic, constant-viscosity aqueous solution of PVP (polyvinylpyrrolidone) as the suspending liquid. Several flow rates and two channel dimensions (with a fixed particle size to channel dimension ratio) are investigated. A novel technique combining particle tracking measurements and numerical simulations is used to reconstruct the position of the flowing particles over the channel cross-section. The results show that, for all the investigated experimental conditions, particles migrate towards the channel centerline. Flow-focusing is enhanced by higher flow rates. The measured particle fractions can be rescaled according to a single dimensionless parameter, as already reported in the literature for the case of cylindrical channels. The so-obtained master curve can be used as a guide to predict the required focusing length. The effect of the entrance on the focusing channel length is also addressed. Finally, analogies and discrepancies with similar previous works are discussed.

Particles suspended in non-Newtonian liquids flowing in channels may migrate transversally to the main flow direction as a result of normal stress gradients. Viscoelasticity-induced migration has proven to be an efficient mechanism to promote 3D flow-focusing in cylindrical microchannels, avoiding the need for complex and expensive apparati. In this work, we demonstrate the existence of a single dimensionless number (Theta) that governs the migration dynamics of particles in viscoelastic liquids flowing in micropipes at low Deborah numbers (Deborah number is the ratio of fluid and flow characteristic times). The definition of Theta in terms of the relevant fluid, flow and geometrical quantities is obtained by generalizing the particle migration velocity expression given in previous asymptotic analytical theories through numerical simulations. An extensive experimental investigation quantitatively confirms the novel predictions: the experimental particle distributions along the channel axial direction collapse on a single curve when rescaled in terms of the proposed dimensionless number. The results reported in this work give a simple and general way to define the flow-focusing conditions promoted by viscoelastic effects

Deterministic lateral displacement devices have been proved to be an efficient way to perform continuous particle separation in microfluidic applications (Huang et al. Science 304:987–990, 2004). On the basis of their size, particles traveling through an array of obstacles follow different paths and can be separated in outflow. One limitation of such a technique is that each device works for a specific critical size to achieve particle separation, and a new device with different geometrical properties needs to be fabricated, as the dimensions of the particles to be separated change. In this work, we demonstrate the possibility to tune the critical particle size in a deterministic lateral displacement device by using non-Newtonian fluids as suspending liquid. The analysis is carried out by extending the theory developed for a Newtonian constitutive law (Inglis et al. Lab Chip 6:655–658, 2006) to account for fluid shear-thinning. 3-D finite element simulations are performed to compute the dynamics of a spherical particle flowing through the deterministic ratchet. The results show that fluid shear-thinning, by altering the flow field between the obstacles, contributes to decrease the critical particle diameter as compared to the Newtonian case. Numerical simulations demonstrate that tunability of the critical separation size can be achieved by using the flow rate as control parameter. A design formula, relating the separation diameter to the fluid rheology and the relevant geometrical parameters of the device, is derived. Such a formula, originally developed for a power-law model, is proved to work for non-Newtonian liquids with a general viscosity trend.

The dynamic response of a viscoelastic suspension of spheres under small and large amplitude oscillatory shear is investigated by three-dimensional direct numerical simulations. A sliding triperiodic domain is implemented whereby the computational domain is regarded as the bulk of an infinite suspension. A fictitious domain method is used to manage the particle motion. After the stress field is computed, the bulk properties are recovered by an averaging procedure. The numerical method is validated by comparing the computed linear viscoelastic response of Newtonian and non-Newtonian suspensions with previous theories and simulations. The numerical predictions are in very good quantitative agreement with experimental data for the Newtonian case, whereas deviations are found with respect to some sets of experiments for semidilute and concentrated viscoelastic suspensions. To investigate on such discrepancies, the effect of aggregates in the bulk of the suspension is examined. The simulations show that the presence of structures significantly alters the loss modulus. Such an effect is more pronounced as the volume fraction increases. In this light, the above mentioned disagreement between simulations and data (and among experimental data themselves) can be rationalized, as its origin can be attributed to inhomogeneous particle configurations. For increasing strain amplitudes, both loss and storage moduli depart from the linear viscoelastic values. Although the deviations are qualitatively similar to the large amplitude response of the unfilled suspending matrix, our results for dilute and semidilute suspensions show that the decrease of the moduli is more and more pronounced as the volume fraction is higher. Furthermore, a higher concentration of solid particles reduces the value of strain amplitude such that the nonlinear behavior is observed. Simulations at higher frequencies also correctly capture the overshoot in the loss modulus for intermediate strain amplitudes. Finally, the effect of fluid elasticity on the particle motion is analyzed. The particles are found to move away from their starting positions and the average distance, computed at the beginning of each cycle with respect to the initial configuration, linearly increases with the number of cycles. The change in the microstructure is attributed to the long-range hydrodynamic interactions mediated by fluid viscoelasticity.

We perform 3D numerical simulations, heuristic modeling and microfluidic experiments to demonstrate, for the first time, the presence of a bistability scenario for transversal migration of particles suspended in a viscoelastic liquid flowing in a pipe. Our results show that particle migration, either at the centerline or at the wall, can be controlled by the rheological properties of the suspending liquid and by the relative dimensions of the particle and tube. Proper selection of these parameters can promote strict aligning of particles on a line, i.e., 3-D focusing. Simple design rules are given to rationally control particle focusing under flow in micropipes.

The intrinsically coupled effects of the curvature of the flow-field and of the viscoelastic nature of suspending medium on the cross-stream lateral migration of a single non-Brownian sphere in wide-gap Couette flow are studied. Quantitative videomicroscopy experiments using a counterrotating device are compared to the results of 3D finite element simulations. To evaluate the effects of differences in rheological properties of the suspending media, fluids have been selected which highlight specific constitutive features, including a reference Newtonian fluid, a single relaxation time wormlike micellar surfactant solution, a broad spectrum shear-thinning elastic polymer solution and a constant viscosity, highly elastic Boger fluid. As expected for conditions corresponding to Stokes flow, migration is absent in the Newtonian fluid. In the wormlike micellar solution and the shear-thinning polymer solution, spheres are observed to migrate in the direction of decreasing shear rate gradient, i.e. the outer cylinder, except when the sphere is initially released close to the inner cylinder, in which case the migration is towards it. The migration is enhanced by faster relative angular velocities of the cylinders. Shear-thinning reduces the migration velocity, showing an opposite behavior as compared to previous results in planar shear flow. In the Boger fluid, within experimental error no migration could be observed, likely due to the large solvent contribution to the overall viscosity. For small Deborah numbers the migration results are well described by an heuristic argument based on a local stress balance.

Solid–liquid disperse systems are complex fluids, extensively used for a variety of applications. The flow behavior of such materials is strongly dependent on the matrix rheological properties: when the suspending fluid shows viscoelastic behavior, isolated suspended particles in confined flow fields tend to migrate across the streamlines. In this work, we carry out a detailed experimental investigation of such migration phenomenon for a rigid, spherical particle in planar shear flow, and compare the experimental findings with 3D numerical simulations based on finite elements. A highly elastic non-Newtonian fluid is chosen as the suspending medium. The migration is studied by varying the confinement, the external shear rate and the fluid normal stresses. The particle is always found to move towards the closest wall, regardless of its initial position. For a fixed set of geometrical and flow parameters, the trajectories from different initial positions can be shifted in time to overlap on a single curve. Migration dynamics is governed by an exponential law as the particle is in the region around the midgap. Stronger confinements, higher shear rates and higher levels of normal stresses all enhance the migration speed. We found qualitative agreement between predictions from numerical simulations and experimental results.

When particles are dispersed in viscoelastic rather than Newtonian media, the hydrodynamics will be changed entailing differences in suspension rheology. The disturbance velocity profiles and stress distributions around the particle will depend on the viscoelastic material functions. Even in inertialess flows, changes in particle rotation and migration will occur. The problem of the rotation of a single spherical particle in simple shear flow in viscoelastic fluids was recently studied to understand the effects of changes in the rheological properties with both numerical simulations [D’Avino et al., J. Rheol. 52 (2008) 1331–1346] and experiments [Snijkers et al., J. Rheol. 53 (2009) 459–480]. In the simulations, different constitutive models were used to demonstrate the effects of different rheological behavior. In the experiments, fluids with different constitutive properties were chosen. In both studies a slowing down of the rotation speed of the particles was found, when compared to the Newtonian case, as elasticity increases. Surprisingly, the extent of the slowing down of the rotation rate did not depend strongly on the details of the fluid rheology, but primarily on the Weissenberg number defined as the ratio between the first normal stress difference and the shear stress. In the present work, a quantitative comparison between the experimental measurements and novel simulation results is made by considering more realistic constitutive equations as compared to the model fluids used in previous numerical simulations [D’Avino et al., J. Rheol. 52 (2008) 1331–1346]. A multimode Giesekus model with Newtonian solvent as constitutive equation is fitted to the experimentally obtained linear and nonlinear fluid properties and used to simulate the rotation of a torque-free sphere in a range of Weissenberg numbers similar to those in the experiments. A good agreement between the experimental and numerical results is obtained. The local torque and pressure distributions on the particle surface calculated by simulations are shown.

Suspensions of solid particles in liquids are often made to flow in devices with characteristic dimensions comparable to that of the suspended particles, the so-called confined situation, as in the case of several microfluidic applications. Combination of confinement with viscoelasticity of the suspending liquid can lead to peculiar effects. In this paper we present the first 3D simulation of the dynamics of a particle suspended in a viscoelastic liquid under imposed confined shear flow. The full system of equations is solved through the finite element method. A DEVSS/SUPG formulation with a log-representation of the conformation tensor is implemented, assuring stable and convergent results up to high flow rates. Particle motion is handled through an ALE formulation. To optimize the computational effort and to reduce the remeshing and pro jection steps required when the mesh becomes too distorted, a rigid motion of the grid in the flow direction is performed, so that, in fact, the particle moves along the cross-streamline direction only. Confinement and viscoelasticity are found to induce particle migration, i.e., transverse motion across the main flow direction, towards the closest wall. Under continuous shearing, three different dynamical regimes are recognized, related to the particle-wall distance. A simple heuristic argument is given to link the crossflow migration to normal stresses in the suspending liquid. The analysis is then extended to a time-dependent shear flow imposed by periodically inverting the direction of wall motion. A slower migration is found for higher forcing frequency. A peculiar effect arises if the inversion period is chosen close to the fluid relaxation time: the migration velocity oscillates around zero, and the overall migration is suppressed. Such novel prediction of a dynamic instability scenario, with the particle escaping the center plane of the channel, and many features of the computed results, are in nice agreement with recent experiments reported in the literature (B.M. Lormand and R.J. Phillips, J. Rheol. 48 (2004) 551-570).

Dilute suspensions of spheres in a viscoelastic liquid under oscillatory shear flow are studied via numerical simulations. In linear viscoelastic regime, the 3D finite element simulation results agree with the analytical results from Palierne (1990). The analysis is extended to Large Amplitude Oscillations (LAOS). The rotation rate of the sphere as well as the bulk rheology are investigated. The moduli increase when particles are added into the fluid, in agreement with experimental findings. In the nonlinear range both moduli are found to be decreasing functions of the forcing amplitude. The non-linear response of the material is also illustrated by performing a Fourier analysis of the bulk shear stress signal which shows the appearance of higher harmonic contributions.

In this contribution we investigate the impact of the forcing waveform on the productivity of a continuous bioreactor governed by an unstructured, nonlinear kinetic model. The (periodic) forcing is applied on the substrate concentration in the feed. To this end, some alternative waveforms commonly encountered in practice are evaluated and their performance is compared. An analytical/numerical approach is used. The preliminary analytical step is based on the π-criterion that gives useful information for small amplitudes. The extension to larger amplitudes, when significant improvements are expected, is then performed through a continuation-optimization procedure. It is found that the choice of the specific waveform has an impact on the performance of the process and there is no unique best forcing for any process condition, but its choice depends on the operating parameters and the forcing amplitude and frequency values. Further, the influence of the waveform functions on the wash-out conditions are extensively examined. The analysis shows that all the waveforms examined in this work may lead to significant enlargement of the nontrivial regime with respect to a steady state operation. In particular, square-wave forcing leads in practice to the extinction of the wash-out conditions for any feed substrate concentration and for a well defined choice of the forcing parameters. © 2010 American Institute of Chemical Engineers Biotechnol. Prog., 2010

In this work, we implemented and compared two different methods to impose the rigid-body motion constraint on a solid particle moving inside a fluid. We consider a fictitious domain method to easily manage the particle motion. As the solid as well as the fluid inertia are neglected, the particle can be discretized through its boundary only. The rigid-body motion is imposed via Lagrange multipliers on the boundary. In the first method, such constraints are imposed in discrete points on the boundary (collocation), whereas in the second the constraint is imposed in a weak way on elements dividing the particle surface. Two test problems, that is, a spherical and an ellipsoidal particle in a sheared Newtonian fluid, are chosen to compare the methods. In both cases, the analysis is carried out in 2D as well as in 3D. The results show that for the collocation method an optimal number of collocation points exist leading to the smallest error. However, small variations in the optimal value can generate large deviations. In the weak implementation, the error is only mildly affected by the number of elements used to discretize the particle boundary and by the Lagrange multiplier's interpolation space. A further analysis is carried out to study the effect of an approximated integration of weak constraints. A comparison between the two methods showed that the same accuracy can be achieved by using less constraints if the weak discretization is used. Finally, the rigid-body motion imposed via weak constraints leads to better conditioned linear systems. Copyright © 2009 John Wiley & Sons, Ltd.

In inertialess suspensions of rigid particles, the rotational motion of each particle is governed by the so-called freely rotating condition, whereby the total torque acting on the particle must be zero. In this work, we study the effect of viscoelasticity of the suspending liquid on the rotation period of a sphere by means of three-dimensional finite element simulations, for conditions corresponding to a macroscopic shear flow. The simulation results capture the slowing down of the rotation, relative to the Newtonian case, which was recently observed in experiments. It is shown that such a phenomenon depends on the specific constitutive equation adopted for the viscoelastic liquid. Analysis of transients shows a clear correlation between rotation rate and the development of first normal stress difference.

The stress tensor for a dilute suspension of buoyancy-free, inertialess, non-Brownian, rigid spheres immersed in a viscoelastic liquid is determined via a perturbative expansion. The perturbation parameter is the Deborah number De, giving the ratio between the characteristic time of the liquid and the characteristic time of the imposed flow. The stress is also calculated from numerical simulations of continuity and momentum equations for the single sphere problem. Excellent agreement is found between the two predictions. Good agreement is found also with respect to experimental data found in the literature.