The motion of a deforming capsule through a corner

A three-dimensional deformable capsule convected through a square duct with a corner is studied via numerical simulations. We develop an accelerated boundary integral implementation adapted to general geometries and boundary conditions. A global spectral method is adopted to resolve the dynamics of the capsule membrane developing elastic tension according to the neo-Hookean constitutive law and bending moments in an inertialess flow. The simulations show that the trajectory of the capsule closely follows the underlying streamlines independently of the capillary number. The membrane deformability, on the other hand, significantly influences the relative area variations, the advection velocity and the principal tensions observed during the capsule motion. The evolution of the capsule velocity displays a loss of the time-reversal symmetry of Stokes flow due to the elasticity of the membrane. The velocity decreases while the capsule is approaching the corner as the background flow does, reaches a minimum at the corner and displays an overshoot past the corner due to the streamwise elongation induced by the flow acceleration in the downstream branch. This velocity overshoot increases with confinement while the maxima of the major principal tension increase linearly with the inverse of the duct width. Finally, the deformation and tension of the capsule are shown to decrease in a curved corner

Modeling of water droplets response in a time- and space-dependent light-induced electric field

openIt has been observed that droplets under electric fields change shape and this phenomenon plays an important role in tailoring the droplet size. This aspect is one of primary importance, allowing the droplet to become a resonator cavity for the light therein coupled. Light amplification as well as fluorescence enhancement induced by efficient light confinement in a droplet have attracted great attention in medical and biological applications, where luminescent molecules are often attached to the biounit under investigation for sorting, targeting and dynamical responses investigations. Bio activity, as well as efficiencies in medical treatments, require online monitoring and are eager to find systems in which it is possible to isolate the bio unit to be investigated and measure its response. Microfluidics has been addressed as a perfect tool for handling small quantities of bio units at a time but requires the implementation of a suitable physical tool to probe and analyze the physical response. The crucial factor is the synergic combination of the functionalities of integrated optics with microfluidics: this is achieved integrating on the same lithium niobate (LN) substrate a microfluidic stage and an optical one, i. e., an array of waveguides in Mach-Zehnder interferometer (MZI) configuration. Such a device is able to illuminate and detect the transmitted light of droplets, measuring their speed, refractive index and size. This thesis is focusing on a new theoretical modeling oriented to the phenomenology of the response of microfluidic water droplets to a time-varying, spatially non-uniform electric field, identifying the key parameters that control the droplet deformation. The photoinduced electric field acts in the microchannel of the platform by exploiting the photo-inducing properties of lithium niobate, a widely employed material in the photonic and integrated optics industry thanks to its excellent properties. In addition to the electrohydrodynamic problem, this thesis proposes a novel approach to describe an observed novel interaction between the electric field and the water droplets. The research is relying on a wide-ranging scientific project that has already developed several new methods of real-time detection and monitoring of micro and sub-micrometric objects dispersed in fluid media.It has been observed that droplets under electric fields change shape and this phenomenon plays an important role in tailoring the droplet size. This aspect is one of primary importance, allowing the droplet to become a resonator cavity for the light therein coupled. Light amplification as well as fluorescence enhancement induced by efficient light confinement in a droplet have attracted great attention in medical and biological applications, where luminescent molecules are often attached to the biounit under investigation for sorting, targeting and dynamical responses investigations. Bio activity, as well as efficiencies in medical treatments, require online monitoring and are eager to find systems in which it is possible to isolate the bio unit to be investigated and measure its response. Microfluidics has been addressed as a perfect tool for handling small quantities of bio units at a time but requires the implementation of a suitable physical tool to probe and analyze the physical response. The crucial factor is the synergic combination of the functionalities of integrated optics with microfluidics: this is achieved integrating on the same lithium niobate (LN) substrate a microfluidic stage and an optical one, i. e., an array of waveguides in Mach-Zehnder interferometer (MZI) configuration. Such a device is able to illuminate and detect the transmitted light of droplets, measuring their speed, refractive index and size. This thesis is focusing on a new theoretical modeling oriented to the phenomenology of the response of microfluidic water droplets to a time-varying, spatially non-uniform electric field, identifying the key parameters that control the droplet deformation. The photoinduced electric field acts in the microchannel of the platform by exploiting the photo-inducing properties of lithium niobate, a widely employed material in the photonic and integrated optics industry thanks to its excellent properties. In addition to the electrohydrodynamic problem, this thesis proposes a novel approach to describe an observed novel interaction between the electric field and the water droplets. The research is relying on a wide-ranging scientific project that has already developed several new methods of real-time detection and monitoring of micro and sub-micrometric objects dispersed in fluid media

Deformability-induced effects of red blood cells in flow

To ensure a proper health state in the human body, a steady transport of blood is necessary. As the main cellular constituent in the blood suspension, red blood cells (RBCs) are governing the physical properties of the entire blood flow. Remarkably, these RBCs can adapt their shape to the prevailing surrounding flow conditions, ultimately allowing them to pass through narrow capillaries smaller than their equilibrium diameter. However, several diseases such as diabetes mellitus or malaria are linked to an alteration of the deformability. In this work, we investigate the shapes of RBCs in microcapillary flow in vitro, culminating in a shape phase diagram of two distinct, hydrodynamically induced shapes, the croissant and the slipper. Due to the simplicity of the RBC structure, the obtained phase diagram leads to further insights into the complex interaction between deformable objects in general, such as vesicles, and the surrounding fluid. Furthermore, the phase diagram is highly correlated to the deformability of the RBCs and represents thus a cornerstone of a potential diagnostic tool to detect pathological blood parameters. To further promote this idea, we train a convolutional neural network (CNN) to classify the distinct RBC shapes. The benchmark of the CNN is validated by manual classification of the cellular shapes and yields very good performance. In the second part, we investigate an effect that is associated with the deformability of RBCs, the lingering phenomenon. Lingering events may occur at bifurcation apices and are characterized by a straddling of RBCs at an apex, which have been shown in silico to cause a piling up of subsequent RBCs. Here, we provide insight into the dynamics of such lingering events in vivo, which we consequently relate to the partitioning of RBCs at bifurcating vessels in the microvasculature. Specifically, the lingering of RBCs causes an increased intercellular distance to RBCs further downstream, and thus, a reduced hematocrit.Um die biologischen Funktionen im menschlichen Körper aufrechtzuerhalten ist eine stetige Versorgung mit Blut notwendig. Rote Blutzellen bilden den Hauptanteil aller zellulären Komponenten im Blut und beeinflussen somit maßgeblich dessen Fließeigenschaften. Eine bemerkenswerte Eigenschaft dieser roten Blutzellen ist ihre Deformierbarkeit, die es ihnen ermöglicht, ihre Form den vorherrschenden Strömungsbedingungen anzupassen und sogar durch Kapillaren zu strömen, deren Durchmesser kleiner ist als der Gleichgewichtsdurchmesser einer roten Blutzelle. Zahlreiche Erkrankungen wie beispielsweise Diabetes mellitus oder Malaria sind jedoch mit einer Veränderung dieser Deformierbarkeit verbunden. In der vorliegenden Arbeit untersuchen wir die hydrodynamisch induzierten Formen der roten Blutzellen in mikrokapillarer Strömung in vitro systematisch für verschiedene Fließgeschwindigkeiten. Aus diesen Daten erzeugen wir ein Phasendiagramm zweier charakteristischer auftretender Formen: dem Croissant und dem Slipper. Aufgrund der Einfachheit der Struktur der roten Blutzellen führt das erhaltene Phasendiagramm zu weiteren Erkenntnissen über die komplexe Interaktion zwischen deformierbaren Objekten im Allgemeinen, wie z.B. Vesikeln, und des sie umgebenden Fluids. Darüber hinaus ist das Phasendiagramm korreliert mit der Deformierbarkeit der Erythrozyten und stellt somit einen Eckpfeiler eines potentiellen Diagnosewerkzeugs zur Erkennung pathologischer Blutparameter dar. Um diese Idee weiter voranzutreiben, trainieren wir ein künstliches neuronales Netz, um die auftretenden Formen der Erythrozyten zu klassifizieren. Die Ausgabe dieses künstlichen neuronalen Netzes wird durch manuelle Klassifizierung der Zellformen validiert und weist eine sehr hohe Übereinstimmung mit dieser manuellen Klassifikation auf. Im zweiten Teil der Arbeit untersuchen wir einen Effekt, der sich direkt aus der Deformierbarkeit der roten Blutzellen ergibt, das Lingering-Phänomen. Diese Lingering-Ereignisse können an Bifurkationsscheiteln zweier benachbarter Kapillaren auftreten und sind durch ein längeres Verweilen von Erythrozyten an einem Scheitelpunkt gekennzeichnet. In Simulationen hat sich gezeigt, dass diese Dynamik eine Anhäufung von nachfolgenden roten Blutzellen verursacht. Wir analysieren die Dynamik solcher Verweilereignisse in vivo, die wir folglich mit der Aufteilung von Erythrozyten an sich gabelnden Gefäßen in der Mikrovaskulatur in Verbindung bringen. Insbesondere verursacht das Verweilen von Erythrozyten einen erhöhten interzellulären Abstand zu weiter stromabwärts liegenden Erythrozyten und damit einen reduzierten Hämatokrit

Parallel algorithms for direct blood flow simulations

Fluid mechanics of blood can be well approximated by a mixture model of a Newtonian fluid and deformable particles representing the red blood cells. Experimental and theoretical evidence suggests that the deformation and rheology of red blood cells is similar to that of phospholipid vesicles. Vesicles and red blood cells are both area preserving closed membranes that resist bending. Beyond red blood cells, vesicles can be used to investigate the behavior of cell membranes, intracellular organelles, and viral particles. Given the importance of vesicle flows, in this thesis we focus in efficient numerical methods for such problems: we present computationally scalable algorithms for the simulation of dilute suspension of deformable vesicles in two and three dimensions. Our method is based on the boundary integral formulation of Stokes flow. We present new schemes for simulating the three-dimensional hydrodynamic interactions of large number of vesicles with viscosity contrast. The algorithms incorporate a stable time-stepping scheme, high-order spatiotemporal discretizations, spectral preconditioners, and a reparametrization scheme capable of resolving extreme mesh distortions in dynamic simulations. The associated linear systems are solved in optimal time using spectral preconditioners. The highlights of our numerical scheme are that (i) the physics of vesicles is faithfully represented by using nonlinear solid mechanics to capture the deformations of each cell, (ii) the long-range, N-body, hydrodynamic interactions between vesicles are accurately resolved using the fast multipole method (FMM), and (iii) our time stepping scheme is unconditionally stable for the flow of single and multiple vesicles with viscosity contrast and its computational cost-per-simulation-unit-time is comparable to or less than that of an explicit scheme. We report scaling of our algorithms to simulations with millions of vesicles on thousands of computational cores.PhDCommittee Chair: Biros, George; Committee Member: Alben, Silas; Committee Member: Fernandez-Nieves, Alberto; Committee Member: Hu, David; Committee Member: Vuduc, Richar

EXPERIMENTAL STUDIES OF PARTICLE ASSEMBLY INTO STREAMWISE BANDS

Over the last twenty years, methods that use external forces to manipulate and arrange, or assemble, colloidal particles have become a research topic of interest with applications in microfluidics and nanotechnology. This research studies a novel method that uses a combination of Poiseuille flow driven by a pressure gradient, and electroosmotic (EO) flow driven by a voltage gradient, or electric field, to manipulate radius a < 0.5 mm polystyrene particles suspended at very low concentrations (<0.5 vol%) flowing through a microchannel. When the particles lead the flow due to electrophoresis, they are attracted to, and accumulate near, the wall. Above a minimum electric field, these concentrated particles ultimately assemble into “bands”: streamwise structures a few microns in diameter and a few cm long with a consistent transverse spacing. These structures are unique because they form in a flowing (vs. quiescent) suspension, which could lead to a method for continuous particle assembly. This thesis is an experimental study based on evanescent-wave visualizations to characterize how, and under what flow and conditions, these bands form. Bands form over a range of particle radii and zeta-potentials, near-wall shear rates, where the parabolic velocity profile for Poiseuille flow near the wall can be approximated by a constant shear rate, and electric fields. The bands are characterized in terms of the time for band formation, which appears to be scaled by the near-wall shear rate, and the average transverse period of bands over a ~200 mm square field of view. Estimates based on tracking individual tracer particles imply that near-wall particle concentrations increase 100- to 200-fold (compared with the bulk concentration) as the particles are attracted to the wall. Estimates of the wall-normal “lift” force that attracts particles from the bulk to the channel wall suggest that this force is comparable to the force predicted by models recently proposed by other researchers. Measurements of the streamwise near-wall particle velocities are significantly different from what would be expected, namely the superposition of the flow and particle electrophoretic velocities. If the flow velocity is, as expected, the superposition of Poiseuille and EO flow, these results suggest that wall effects greatly suppress particle electrophoresis.Ph.D

Computational design of stable particles in inertial microfluidic flows: A step towards passive manipulation

Precise and passive manipulation of particles in microscale flow channels is of interest to promising challenges in chemical, biomedical and bioengineering applications such as particle separation, ordering, cell-detection and analysis. Ease of operation, low sample-volumes, portability, cost-effectiveness, and scalability, are some of the compelling benefits in these technologies as opposed to active-manipulation systems requiring additional machinery for flow and/or particle control, which are invariably disadvantageous in one or more of the above aspects. The motion of particles and their equilibrium (if any) in such flows directly depends on their shape and parameters such as channel geometry and fluid/particle inertia. As such, a significant portion of these applications can be described by steady-state physics models, and the current work details methodologies that leverage this advantage to address two primary aspects under inertial flows: development and experimental validation of a quasi-dynamic computational framework to characterize \textit{focusing} positions for spherical particles (the forward problem) and extending this framework to design particle geometries for certain desirable long-term characteristics in flow such as non-tumbling/bobbing modes for self-alignment in flow (the inverse problem). The former is relevant in scenarios outlined above where particle geometries are known and it is desired to understand trends in focusing patterns of particles for configurations defined by parametric sweeps over arbitrary channel geometries (based on cross-section, curvature, etc.), flow speeds, and channel confinements, where the configuration space quickly becomes prohibitively expensive for experiments. The latter however has only gained momentum over the past few decades, with work being mostly analytical/empirical in nature and restrictive due to simplifications such as zero-inertia, unbounded domains, linear shear etc. The frameworks developed herein are extensible to incorporate additional flow physics such as non-Newtonian fluids, and envisioned to provide thumbrules for the microfluidics community for further work in this burgeoning field concerning next-generation microfluidic cell analysis devices

Statistical Fluid Dynamics

Modeling micrometric and nanometric suspensions remains a major issue. They help to model the mechanical, thermal, and electrical properties, among others, of the suspensions, and then of the resulting product, in a controlled way, when considered in material formation. In some cases, they can help to improve the energy transport performance. The optimal use of these products is based on an accurate prediction of the flow-induced properties of the suspensions and, consequently, of the resulting products and parts. The final properties of the resulting micro-structured fluid or solid are radically different from the simple mixing rule. In this book, we found numerous works addressing the description of these specific fluid behaviors