Dynamics of prolate spheroids in the vicinity of an air-water interface.

In this article, we present the mobilities of prolate ellipsoidal micrometric particles close to an air-water interface measured by dual wave reflection interference microscopy. Particle's position and orientation with respect to the interface are simultaneously measured as a function of time. From the measured mean square displacement, five particle mobilities (3 translational and 2 rotational) and two translational-rotational cross-correlations are extracted. The fluid dynamics governing equations are solved by the finite element method to numerically evaluate the same mobilities, imposing either slip and no-slip boundary conditions to the flow at the air-water interface. The comparison between experiments and simulations reveals an agreement with no-slip boundary conditions prediction for the translation normal to the interface and the out-of-plane rotation, and with slip ones for parallel translations and in-plane rotation. We rationalize these evidences in the framework of surface incompressibility at the interface.

Experimental and Numerical Investigation of the Die Swell in 3D Printing Processes.

Fused deposition modelling is one of the most widely used additive manufacturing techniques and the diffusion of 3D printers has increased in popularity even further in recent times. Since high precision is required in 3D printing, a good control over the extrusion process is necessary. In this regard, a crucial phenomenon to be accounted for is the die or extrudate swell, i.e., the enlargement of the cross-section of the strand when coming out of the printer nozzle. While this phenomenon has been studied in large scale extruders, it has not yet been investigated in depth for 3D printing processes. In this work, the die swell phenomenon observed in a printed PLA filament is studied by experiments and fluid dynamic simulations. A novel, easy-to-use, accurate and fast procedure for measuring the value of the die swell ratio during the printing process is developed, accounting for typical errors related to a non-constant strand diameter and possible oscillations of the filament with respect to the extrusion direction. As the printing velocity is increased, a linearly increasing swelling ratio is observed at low printing speeds. The trend flattens at moderate speed values. A sudden increase is found at high printing velocities. The swelling ratio measured with the proposed technique is compared with the results of multi-mode viscoelastic simulations at different temperatures. A fair agreement between the experimental measurements and the numerical predictions is found for printing velocities that are typically employed in commercial 3D printers, supporting the reliability of the developed procedure.

Effect of wall slip on the viscoelastic particle ordering in a microfluidic channel.

The formation of a line of equally spaced particles at the centerline of a microchannel, referred as "particle ordering," is desired in several microfluidic applications. Recent experiments and simulations highlighted the capability of viscoelastic fluids to form a row of particles characterized by a preferential spacing. When dealing with non-Newtonian fluids in microfluidics, the adherence condition of the liquid at the channel wall may be violated and the liquid can slip over the surface, possibly affecting the ordering efficiency. In this work, we investigate the effect of wall slip on the ordering of particles suspended in a viscoelastic liquid by numerical simulations. The dynamics of a triplet of particles in an infinite cylindrical channel is first addressed by solving the fluid and particle governing equations. The relative velocities computed for the three-particle system are used to predict the dynamics of a train of particles flowing in a long microchannel. The distributions of the interparticle spacing evaluated at different slip coefficients, linear particle concentrations, and distances from the channel inlet show that wall slip slows down the self-assembly mechanism. For strong slipping surfaces, no significant change of the initial microstructure is observed at low particle concentrations, whereas strings of particles in contact form at higher concentrations. The detrimental effect of wall slip on viscoelastic ordering suggests care when designing microdevices, especially in case of hydrophobic surfaces that may enhance the slipping phenomenon.

An Experimental and Numerical Investigation on Bubble Growth in Polymeric Foams.

The cellular morphology of thermoplastic polymeric foams is a key factor for their performances. Three possible foam morphologies exist, namely, with closed cells, interconnected cellular structure, and open cells. In the gas foaming technology, a physical blowing agent, e.g., CO2 or N2, is used to form bubbles at high pressure in softened/melted polymers. As a consequence of a pressure quench, the bubbles grow in the liquid matrix until they impinge and possibly break the thin liquid films among them. If film breakage happens, the broken film may retract due to the elastic energy accumulated by the polymeric liquid during the bubble growth. This, in turn, determines the final morphology of the foam. In this work, we experimentally study the growth of CO2 bubbles in a poly(e-caprolactone) (PCL) matrix under different pressure conditions. In addition, we perform three-dimensional direct numerical simulations to support the experimental findings and rationalize the effects of the process parameters on the elastic energy accumulated in the liquid at the end of the bubble growth, and thus on the expected morphology of the foam. To do that, we also extend the analytic model available in the literature for the growth of a single bubble in a liquid to the case of a liquid with a multi-mode viscoelastic constitutive equation.

Numerical simulations of viscoelastic particle migration in a microchannel with triangular cross-section.

The migration of a spherical particle immersed in a viscoelastic liquid flowing in a microchannel with a triangular cross-section is investigated by direct numerical simulations under inertialess conditions. The viscoelastic fluid is modeled through two constitutive equations to investigate the effect of the second normal stress difference and the resulting secondary flows on the migration phenomenon. The results are presented in terms of trajectories followed by the particles released at different initial positions over the channel cross-section in a wide range of Weissenberg numbers and confinement ratios. Particles suspended in a fluid with a negligible second normal stress difference migrate toward the channel centerline or the closest wall, depending on their initial position. A much more complex dynamics is found for particles suspended in a fluid with a relevant second normal stress difference due to the appearance of secondary flows that compete with the migration phenomenon. Depending on the Weissenberg number and confinement ratio, additional equilibrium positions (points or closed orbits) may appear. In this case, the channel centerline becomes unstable and the particles are driven to the corners or "entrapped" in recirculation regions within the channel cross-section. The inversion of the centerline stability can be exploited to design efficient size-based separation devices.

Microfluidic formation of crystal-like structures.

Crystal-like structures find application in several fields ranging from biomedical engineering to material science. For instance, droplet crystals are critical for high throughput assays and material synthesis, while particle crystals are important for particles and cell encapsulation, Drop-seq technologies, and single-cell analysis. Formation of crystal-like structures relies entirely on the possibility of manipulating with great accuracy the micrometer-size objects forming the crystal. In this context, microfluidic devices offer versatile tools for the precise manipulation of droplets and particles, thus enabling fabrication of crystal-like structures that form due to hydrodynamic interactions among droplets or particles. In this review, we aim at providing an holistic representation of crystal-like structure formation mediated by hydrodynamic interactions in microfluidic devices. We also discuss the physical origin of these hydrodynamic interactions and their relation to parameters such as device geometry, fluid properties, and flow conditions.

Axisymmetric bare freestanding films of highly viscous liquids: Preparation and real-time investigation of capillary leveling.

HYPOTHESIS: Thin liquid films are important in many scientific fields. In particular, films with both the surface layers exposed to a different fluid phase, known as freestanding films, are relevant in the ambit of foams and emulsions. Hence, there is a great interest in developing novel techniques allowing to form large and stable freestanding liquid films and to follow their dynamics. EXPERIMENTS: We develop a novel opto-mechanical tool allowing to perform and study the preparation and the capillary leveling flow of axisymmetric bare freestanding liquid films. The tool is composed by a customized motorized iris diaphragm and by an innovative joint imaging setup combining digital holography and white light color interferometry that enables real-time measurement of film thickness over a large field of view. The dynamics of films made of a model Newtonian fluid, i.e., high-viscosity silicone oil, is studied. Direct numerical simulations and a hydrodynamic model based on the lubrication theory are used to support the experimental results. FINDINGS: Iris opening induces the formation of large circular freestanding films with a stepped profile. Once iris opening is stopped, the films undergo a capillary leveling flow tending to flatten their profile. The leveling flow follows the theoretical scaling given by Ilton et al. [1]. We prove through numerical simulations that an equi-biaxial extensional flow occurs at the film center. Furthermore, we observe the formation and dynamics of dimples in bare freestanding films for the first time.

Discrete Element Method Analysis of the Spreading Mechanism and Its Influence on Powder Bed Characteristics in Additive Manufacturing.

Laser powder bed fusion additive manufacturing is among the most used industrial processes, allowing for the production of customizable and geometrically complex parts at relatively low cost. Although different aspects of the powder spreading process have been investigated, questions remain on the process repeatability on the actual beam-powder bed interaction. Given the influence of the formed bed on the quality of the final part, understanding the spreading mechanism is crucial for process optimization. In this work, a Discrete Element Method (DEM) model of the spreading process is adopted to investigate the spreading process and underline the physical phenomena occurring. With parameters validated through ad hoc experiments, two spreading velocities, accounting for two different flow regimes, are simulated. The powder distribution in both the accumulation and deposition zone is investigated. Attention is placed on how density, effective layer thickness, and particle size distribution vary throughout the powder bed. The physical mechanism leading to the observed characteristics is discussed, effectively defining the window for the process parameters.

Viscoelastic Particle Train Formation in Microfluidic Flows Using a Xanthan Gum Aqueous Solution.

Viscoelastic polymer solutions have been widely employed as suspending liquids for a myriad of microfluidic applications including particle and cell focusing, sorting, and encapsulation. It has been recently shown that viscoelastic solutions can drive the formation of equally spaced particles called "particle trains" as a result of the viscoelasticity-mediated hydrodynamic interactions between adjacent particles. Despite their potential impact on applications such as droplet encapsulation and flow cytometry, only limited experimental studies on viscoelastic ordering are currently available. In this work, we demonstrate that a viscoelastic shear-thinning aqueous xanthan gum solution drives the self-assembly of particle trains on the centerline of a serpentine microfluidic device with a nearly circular cross section. After focusing, the flowing particles change their mutual distance and organize in aligned structures characterized by a preferential spacing, quantified in terms of distributions of the interparticle distance. We observe the occurrence of multi-particle strings, mainly doublets and triplets, that interrupt the continuity of the particle train. To account for the fluctuations in the number of flowing particles in the experimental window, we introduce the concept of local particle concentration, observing that an increase of the local particle concentration leads to an increase of doublets and triplets. We also demonstrate that using only a single tube to connect the sample to the microfluidic device results in a drastic reduction of doublets/triplets, thus leading to a more uniform particle train. Our findings establish the foundation for optimized applications such as deterministic droplet encapsulation in viscoelastic liquids and optimized flow cytometry.

Nanoparticles Synthesis in Wet-Operating Stirred Media: Investigation on the Grinding Efficiency.

The use of nanomaterials, thanks to their peculiar properties and versatility, is becoming central in an increasing number of scientific and engineering applications. At the same time, the growing concern towards environmental issues drives the seeking of alternative strategies for a safer and more sustainable production of nanoparticles. Here we focus on a low-energy, magnetically-driven wet milling technique for the synthesis of metal nanoparticles starting from a bulky solid. The proposed approach is simple, economical, sustainable, and provides numerous advantages, including the minimization of the nanoparticles air dispersion and a greater control over the final product. This process is investigated by experiments and discrete element method simulations to reproduce the movement of the grinding beads and study the collision dynamics. The effect of several parameters is analyzed, including the stirring bar velocity, its inclination, and the grinding bead size, to quantify the actual frequency, energy, and angle of collisions. Experiments reveal a non-monotonous effect of the stirring velocity on the abrasion efficiency, whereas numerical simulations highlight the prevalent tangential nature of collisions, which is only weakly affected by the stirring velocity. On the other hand, the stirring velocity affects the collision frequency and relative kinetic energy, suggesting the existence of an optimal parameters combination. Although a small variation of the stirring bar length does not significantly affect the collision dynamics, the use of grinding beads of different dimensions offers several tuning opportunities.

Rheology of a Dilute Suspension of Aggregates in Shear-Thinning Fluids.

The prediction of the viscosity of suspensions is of fundamental importance in several fields. Most of the available studies have been focused on particles with simple shapes, for example, spheres or spheroids. In this work, we study the viscosity of a dilute suspension of fractal-shape aggregates suspended in a shear-thinning fluid by direct numerical simulations. The suspending fluid is modeled by the power-law constitutive equation. For each morphology, a map of particle angular velocities is obtained by solving the governing equations for several particle orientations. The map is used to integrate the kinematic equation for the orientation vectors and reconstruct the aggregate orientational dynamics. The intrinsic viscosity is computed by a homogenization procedure along the particle orbits. In agreement with previous results on Newtonian suspensions, the intrinsic viscosity, averaged over different initial orientations and aggregate morphologies characterized by the same fractal parameters, decreases by increasing the fractal dimension, that is, from rod-like to spherical-like aggregates. Shear-thinning further reduces the intrinsic viscosity showing a linear dependence with the flow index in the investigated range. The intrinsic viscosity can be properly scaled with respect to the number of primary particles and the flow index to obtain a single curve as a function of the fractal dimension.

Elasticity in Bubble Rupture.

When a Newtonian bubble ruptures, the film retraction dynamics is controlled by the interplay of surface, inertial, and viscous forces. In case a viscoelastic liquid is considered, the scenario is enriched by the appearance of a new significant contribution, namely, the elastic force. In this paper, we investigate experimentally the retraction of viscoelastic bubbles inflated at different blowing rates, showing that the amount of elastic energy stored by the liquid film enclosing the bubble depends on the inflation history and in turn affects the velocity of film retraction when the bubble is punctured. Several viscoelastic liquids are considered. We also perform direct numerical simulations to support the experimental findings. Finally, we develop a simple heuristic model able to interpret the physical mechanism underlying the process.

"From the Edge to the Center": Viscoelastic Migration of Particles and Cells in a Strongly Shear-Thinning Liquid Flowing in a Microchannel.

Controlling the fate of particles and cells in microfluidic devices is critical in many biomedical applications, such as particle and cell alignment and separation. Recently, viscoelastic polymer solutions have been successfully used to promote transversal migration of particles and cells toward fixed positions in straight microchannels. When inertia is negligible, numerical simulations have shown that strongly shear-thinning polymer solutions (fluids with a shear viscosity that decreases with increasing flow rates) promote transversal migration of particles and cells toward the corners or toward the centerline in a straight microchannel with a square cross section, as a function of particle size, cell deformability, and channel height. However, no experimental evidence of such shifting in the positions for particles or cells suspended in strongly shear-thinning liquids has been presented so far. In this work, we demonstrate that particle positions over the channel cross section can be shifted "from the edge to the center" in a strongly shear-thinning liquid. We investigate the viscoelasticity-induced migration of both rigid particles and living cells (Jurkat cells and NIH 3T3 fibroblasts) in an aqueous 0.8 wt % hyaluronic acid solution. The combined effect of fluid elasticity, shear-thinning, geometric confinement, and cell deformability on the distribution of the particle/cell positions over the channel cross section is presented and discussed. In the same shear-thinning liquid, separation of 10 and 20 µm particles is also achieved in a straight microchannel with an abrupt expansion. Our results envisage further applications in viscoelasticity-based microfluidics, such as deformability-based cell separation and viscoelastic spacing of particles/cells.

Dynamics of a microorganism in a sheared viscoelastic liquid.

In this paper, we investigate the dynamics of a model spherical microorganism, called squirmer, suspended in a viscoelastic fluid undergoing unconfined shear flow. The effect of the interplay of shear flow, fluid viscoelasticity, and self-propulsion on the orientational dynamics is addressed. In the limit of weak viscoelasticity, quantified by the Deborah number, an analytical expression for the squirmer angular velocity is derived by means of the generalized reciprocity theorem. Direct finite element simulations are carried out to study the squirmer dynamics at larger Deborah numbers. Our results show that the orientational dynamics of active microorganisms in a sheared viscoelastic fluid greatly differs from that observed in Newtonian suspensions. Fluid viscoelasticity leads to a drift of the particle orientation vector towards the vorticity axis or the flow-gradient plane depending on the Deborah number, the relative weight between the self-propulsion velocity and the flow characteristic velocity, and the type of swimming. Generally, pullers and pushers show an opposite equilibrium orientation. The results reported in the present paper could be helpful in designing devices where separation of microorganisms, based on their self-propulsion mechanism, is obtained.

Magnetophoresis 'meets' viscoelasticity: deterministic separation of magnetic particles in a modular microfluidic device.

The deflection of magnetic beads in a microfluidic channel through magnetophoresis can be improved if the particles are somehow focused along the same streamline in the device. We design and fabricate a microfluidic device made of two modules, each one performing a unit operation. A suspension of magnetic beads in a viscoelastic medium is fed to the first module, which is a straight rectangular-shaped channel. Here, the magnetic particles are focused by exploiting fluid viscoelasticity. Such a channel is one inlet of the second module, which is a H-shaped channel, where a buffer stream is injected in the second inlet. A permanent magnet is used to displace the magnetic beads from the original to the buffer stream. Experiments with a Newtonian suspending fluid, where no focusing occurs, are carried out for comparison. When viscoelastic focusing and magnetophoresis are combined, magnetic particles can be deterministically separated from the original streamflow to the buffer, thus leading to a high deflection efficiency (up to ~96%) in a wide range of flow rates. The effect of the focusing length on the deflection of particles is also investigated. Finally, the proposed modular device is tested to separate magnetic and non-magnetic beads.

Hindered Brownian diffusion in a square-shaped geometry.

We study the spatial dependence of the mobility of microparticles diffusing close to an edge of a square microtube. Confocal particle tracking is used to measure the local diffusion coefficients of fluorescent latex 1.1µm particles suspended in an aqueous solution in a borosilicate square capillary of 50µm section side. Observations are made for a set of planes obtained by confocal sectioning of the capillary volume. The translational diffusion coefficients parallel to the axis channel and perpendicular to one of the walls are measured as a function of the distance from both the two channel walls concurring in an edge. A complete 3D spatial map of the colloid diffusion coefficients is thus obtained. Near the corner, the diffusion is hindered up to about 40% as compared to its bulk value. The three translational diffusion coefficients pertaining to the motions along the channel axis and within the channel cross-section turn out to be different from each other and differently affected by the confinement, i.e., we are in the presence of an anisotropic diffusion. The hindered diffusion phenomenon is also examined by finite element numerical simulations, and the numerical predictions fairly agree with the measured diffusion coefficients.

Rheometry-on-a-chip: measuring the relaxation time of a viscoelastic liquid through particle migration in microchannel flows.

A novel method to estimate the relaxation time of viscoelastic fluids, down to milliseconds, is here proposed. The adopted technique is based on the particle migration phenomenon occurring when the suspending viscoelastic fluid flows in microfluidic channels. The method is applied to measure the fluid relaxation times of two water-glycerol polymer solutions in an ample range of concentrations. A remarkable improvement in the accuracy of the measure of the relaxation time is found, as compared with experimental data obtained from shear or elongational experiments available in the literature. Good agreement with available theoretical predictions is also found. The proposed method is reliable, handy and does not need a calibration curve, opening an effective way to measure relaxation times of viscoelastic fluids otherwise not easily detectable by conventional techniques.

Particle alignment in a viscoelastic liquid flowing in a square-shaped microchannel.

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.

Viscoelastic flow-focusing in microchannels: scaling properties of the particle radial distributions.

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 (Θ) 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 Θ 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.