Microfluidics and complex fluids

Experiments of the flow of dilute aqueous solutions of polyethylene oxide through curved pipes with circular cross-section are carried out over the Reynolds number range of 500 to 1×104. Concentration of the polymer solution is varied from 0.5ppm to 100ppm. The ratio of the curvature radius to the pipe radius, R/a, of curved pipes is set at 16.3, 28.8 and 46.0. These fluid are found to cause frictional drag reduction under the turbulent flow condition in a curved pipe as well as in a straight pipe. Experimental values of a frictional loss are correlated with the Weissenberg number, the Reynolds number and the radius ratio R/a. The empirical formulas for the frictional loss estimation are proposed separately for both the laminar and the turbulent flow regime. It is also shown that the transition to turbulent flow depends on the Weissenberg number as well as the Reynolds number.

Flow of a liquid-crystalline polymer solution around an obstacle

Although experimental evidence for shear-banding flows in concentrated polymer solutions has accumulated over the last 20 years, the origin of such shear-banding flows is still under heated debate. Experiments that probe the microscopic dynamics of shear-banding polymer solutions are still scarce. Here, using a custom-built high-resolution rheo-confocal shear cell, we experimentally study the dynamics of DNA-bridged colloidal dumbbells in the shear-banding flow of concentrated double-stranded DNA (dsDNA) solutions under large amplitude oscillatory shear. We synthesize dumbbells consisting of two spherical colloids linked by λ-DNA and track their 2D-projected configurations in sheared dsDNA solutions. We first confirm that the velocity profile of the concentrated dsDNA solutions is inhomogeneous at high Weissenberg numbers and exhibits strong shear banding with two distinct shear bands. We then measure the orientational distribution of the DNA-bridged dumbbells and investigate their translational and rotational dynamics within the two shear bands. The preferred alignment of the dumbbells along the flow direction in the high-shear-rate band suggests the dominant role of elastic stresses in that band. In contrast, a bimodal distribution of dumbbell orientations is observed in the low-shear-rate band, indicating more balanced contributions from both normal and elastic stresses. Furthermore, exclusively in the high-shear-rate band, we also find spatially localized correlated enhanced translational and rotational motions and a strong coupling between enhanced translation and chain extension. These unique conformational and dynamic features suggest shear-induced breakage of the local entanglement network in the high-shear band, which we postulate leads to puddles of low viscosity within an otherwise high-viscosity fluid. Together, our quantitative analyses of the spatially distinct dynamics of dsDNA-bridged dumbbells in coexisting shear bands provide important insights into the microscopic origin of shear-banding flows in concentrated polymer solutions.

The present lecture summarizes some of the most recent joint research results from the cooperation between the Federal University of Rio de Janeiro, Brasil, and the University of Miami, USA, on the transient analysis of both fluid flow and heat transfer within microchannels. This collaborative link is a natural extension of a long term cooperation between the two groups, in the context of fundamental work on transient forced convection, aimed at the development of hybrid numerical-analytical techniques and the experimental validation of proposed models and methodologies [19]. The motivation of this new phase of the cooperation was thus to extend the previously developed hybrid tools to handle both transient flow and transient convection problems in microchannels within the slip flow regime. The analysis of internal flows in the slip-flow regime recently gained an important role in association with the fluid mechanics of various microelectromechanical systems (MEMS) applications, as well as in the thermal control of microelectronics, as reviewed in different sources [10-16]. For steady-state incompressible fully developed flow situations and laminar regime within simple geometries such as circular microtubes and parallel-plate microchannels, explicit expressions for the velocity field in terms of the Knudsen number are readily obtainable, and have been widely employed in the heat transfer analysis of microsystems, such as in [17-23]. Only quite recently, attention has been directed to the analysis of transient flow in microchannels [24-33]. Unsteady one-dimensional models have been extended from classical works, and analytical solutions have been sought for fully developed flows in simple geometries. These recent works are also concerned with situations in which a simple and well-defined functional form for the pressure gradient time variation is prescribed or for the time dependence of the wall imposed velocity, in the case of a Couette flow application. Research findings are yet to be further pursued in the analytical and robust solution of more generalized models, which will accommodate more general conditions and parameter specifications, and thus offer a wider validation range for the automatic general purpose numerical codes. Mikhailov and Ozisik [34] presented a unified solution for transient one-dimensional laminar flow models, with the usual no-slip boundary condition, based on the classical integral transform method. Their solution was then specialized to two situations: step change and periodically varying pressure gradient. The knowledge in regular size channels is therefore fairly well consolidated for models that use simple functional forms for the pressure gradient variation such as for the two cases cited above. One of the objectives of this paper is to illustrate the solution of a onedimensional mathematical model for transient laminar incompressible flow in microchannels such as circular tubes and parallel-plate channels, that accounts for a source term time variation in any functional form, including electrokinetic effects for liquid flows, by making use of the Generalized Integral Transform Technique (GITT) [35-40], and thus yielding analytical expressions for the time and space dependence of the velocity fields in the fully developed region. We then demonstrate this hybrid numerical-analytical solution for transient internal slip flow, obtained employing mixed symbolic-numerical computations with the Mathematica platform [41]. The goal here is to improve and complement existing analytical solution implementations to study laminar fully developed flows in micro-ducts subjected to arbitrary source term disturbances in space and time. On the other hand, the heat transfer literature of the last decade has demonstrated a vivid and growing interest in thermal analysis of flows in micro-channels, both through experimental and analytical approaches, in connection with cooling techniques of micro-electronics and with the development of micro-electromechanical sensors and actuators (MEMS), as also pointed out in recent reviews [12-16]. Since the available analytical information on heat transfer in ducts could not be directly extended to flows within microchannels with wall slip, a number of contributions have been recently directed towards the analysis of internal forced convection in the micro-scale. In the paper by Barron et al.

Chapter 2 - Critical factors affecting cells behavior in microfluidic chips

Viscous liquid flow in micro-channels is typically laminar because of the low Reynolds number constraint. However, by introducing elasticity into the fluids, the flow behavior could change drastically to become turbulent; this elasticity can be realized by dissolving small quantities of polymer molecules into an aqueous solvent. Our recent investigation has directly visualized the extension and relaxation of these polymer molecules in an aqueous solution. This elastic-driven phenomenon is known as ‘elastic turbulence’. Hitherto, existing studies on elastic flow instability are mostly limited to single-stream flows, and a comprehensive statistical analysis of a multi-stream elastic turbulent micro-channel flow is needed to provide additional physical understanding. Here, we investigate the flow field characteristics of elastic turbulence in a 3-stream contraction-expansion micro-channel flow. By applying statistical analyses and flow visualization tools, we show that the flow field bares many similarities to that of inertia-driven turbulence. More interestingly, we observed regions with two different types of power-law dependence in the velocity power spectra at high frequencies. This is a typical characteristic of two-dimensional turbulence and has hitherto not been reported for elastic turbulent micro-channel flows.

This paper describes a simple microfluidic sorting system that can perform size profiling and continuous mass-dependent separation of particles through combined use of gravity (1 g) and hydrodynamic flows capable of rapidly amplifying sedimentation-based separation between particles. Operation of the device relies on two microfluidic transport processes: (i) initial hydrodynamic focusing of particles in a microchannel oriented parallel to gravity and (ii) subsequent sample separation where positional difference between particles with different mass generated by sedimentation is further amplified by hydrodynamic flows whose streamlines gradually widen out due to the geometry of a widening microchannel oriented perpendicular to gravity. The microfluidic sorting device was fabricated in poly(dimethylsiloxane), and hydrodynamic flows in microchannels were driven by gravity without using external pumps. We conducted theoretical and experimental studies on fluid dynamic characteristics of laminar flows in widening microchannels and hydrodynamic amplification of particle separation. Direct trajectory monitoring, collection, and post-analysis of separated particles were performed using polystyrene microbeads with different sizes to demonstrate rapid (<1 min) and high-purity (>99.9%) separation. Finally, we demonstrated biomedical applications of our system by isolating small-sized (diameter <6 microm) perfluorocarbon liquid droplets from polydisperse droplet emulsions, which is crucial in preparing contrast agents for safe, reliable ultrasound medical imaging, tracers for magnetic resonance imaging, or transpulmonary droplets used in ultrasound-based occlusion therapy for cancer treatment. Our method enables straightforward, rapid, real-time size monitoring and continuous separation of particles in simple stand-alone microfabricated devices without the need for bulky and complex external power sources. We believe that this system will provide a useful tool to separate colloids and particles for various analytical and preparative applications and may hold potential for separation of cells or development of diagnostic tools requiring point-of-care sample preparation or testing.

Recently, micro-electro-mechanical-systems (MEMS) technology and micromachining techniques have enabled miniaturization of biomedical devices and systems. Not only do these techniques facilitate the development of miniaturized instrumentation for biomedical analysis, but they also open a new era for integration of microdevices for performing accurate and sensitive diagnostic assays. A so-called “micro-total-analysis-system”, which integrates sample pretreatment, transport, reaction, and detection on a small chip in an automatic format, can be realized by combining functional microfluidic components manufactured by specific MEMS technologies. Among the promising applications using microfluidic technologies, nucleic acid-based detection has shown considerable potential recently. For instance, micro-polymerase chain reaction chips for rapid DNA amplification have attracted considerable interest. In addition, microfluidic devices for rapid sample pretreatment prior to nucleic acid-based detection have also achieved significant progress in the recent years. In this review paper, microfluidic systems for sample preparation, nucleic acid amplification and detection for fast diagnosis will be reviewed. These microfluidic devices and systems have several advantages over their large-scale counterparts, including lower sample/reagent consumption, lower power consumption, compact size, faster analysis, and lower per unit cost. The development of these microfluidic devices and systems may provide a revolutionary platform technology for fast sample pretreatment and accurate, sensitive diagnosis.

This Frontiers review analyzes the rapidly growing microfluidic strategies that have been employed in attempts to create physio relevant 'organ-on-chip' models using primary tissue removed from a body (human or animal). Tissue harvested immediately from an organism, and cultured under artificial conditions is referred to as ex vivo tissue. The use of primary (organotypic) tissue offers unique benefits over traditional cell culture experiments, and microfluidic technology can be used to further exploit these advantages. Defining the utility of particular models, determining necessary constituents for acceptable modeling of in vivo physiology, and describing the role of microfluidic systems in tissue modeling processes is paramount to the future of organotypic models ex vivo. Virtually all tissues within the body are characterized by a large diversity of cellular composition, morphology, and blood supply (e.g., nutrient needs including oxygen). Microfluidic technology can provide a means to help maintain tissue in more physiologically relevant environments, for tissue relevant time-frames (e.g., matching the natural rates of cell turnover), and at in vivo oxygen tensions that can be controlled within modern microfluidic culture systems. Models for ex vivo tissues continue to emerge and grow in efficacy as mimics of in vivo physiology. This review addresses developments in microfluidic devices for the study of tissues ex vivo that can serve as an important bridge to translational value.

The flow of dilute polymer solutions in water, through tubes and granular beds, has been compared with the flow of water and of glycerol solutions and common salt solutions through the same tubes and granular beds. Particular attention was paid to the value of the Reynolds number (Re)prime at which the Hagen-Poiseuille law broke down for tubes and at which Darcy's law broke down for beds. The polymer solutions used were: 0·005, 0·01, 0·025 and 0·05% (w/w) polyacrylamide in water and 0·005% (w/w) `Cellofas' (a sodium carboxymethyl cellulose) in water. Two tubes were used; one was 0·30 m long with an internal diameter of 3·68 mm and the pressure difference was measured across it; the other was 0·70 m long with an internal diameter of 4·08 mm and the pressure difference was measured across the last 0·30 m. Two granular beds were made up, one with glass beads of diameter 2·06 mm, the other with glass beads of diameter 1·15 mm. Most experiments were performed at 25°C, but some were done at 15°C and others at 35°C so that the influence of temperature on the results could be studied. Destabilization occurred in the flow of polyacrylamide solutions through the tubes and the beds; that is (Re)prime (polyacrylamide) < (Re)prime (water). However, stabilization occurred in the flow of Cellofas solutions. Drag reduction occurred in the flow of polyacrylamide solutions through the tubes but not in the flow through the beds; no drag reduction occurred in the flow of the Cellofas solutions. The destabilization can be attributed to the release of energy stored in stretched molecules in the flow, and drag reduction can be attributed to energy absorbed by the molecules thus damping down some turbulent eddies.

Unique Ligand Exchange Dynamics of Metal–Organic Polyhedra for Vitrimer-like Gas Separation Membranes

Effect of inertia on thermoelastic flow instability

Canopy flows occur when a moving fluid encounters a matrix of free-standing obstacles and are found in diverse systems, from forests and marine ecology to urban landscapes and biology (e.g. cilia arrays). In large-scale systems, involving Newtonian fluids (like water or air), canopy flows typically exhibit inertial turbulence due to high Reynolds numbers (Re). However, in small-scale systems like cilia, where Re is low, but the fluid can be viscoelastic (like mucus), the relevant control parameter is the Weissenberg number (Wi), quantifying elastic stresses in the flow. Here, we investigate the flow of a viscoelastic polymer solution over a microscopic canopy within a microfluidic device. As the Weissenberg number increases, the flow undergoes distinct transitions, eventually becoming unstable beyond a critical Wi. At high Wi, we observe the emergence of elastic turbulence (ET), a chaotic flow regime that, despite differing underlying mechanisms, exhibits striking similarities to large-scale canopy inertial turbulence. Similar to canopy inertial turbulence, ET within the canopy can be spatially divided into distinct regions: a porous layer within the canopy, a mixing layer at the canopy tips, a transitional region just above the canopy, and a Poiseuille-like flow further up. The separation of the flow into different regions reveals a new analogy between inertial turbulence and ET, providing a fresh insight into ET flows and expanding their potential for innovative microfluidic designs and real-world applications.

A recently developed microfluidic device, the optimized shape cross-slot extensional rheometer or OSCER [S. J. Haward, M. S. N. Oliveira, M. A. Alves, and G. H. McKinley, “Optimized cross-slot flow geometry for microfluidic extensional rheometry,” Phys. Rev. Lett. 109, 128301 (2012)10.1103/PhysRevLett.109.128301], is used to investigate the stability of viscoelastic polymer solutions in an idealized planar stagnation point flow. Aqueous polymer solutions, consisting of poly(ethylene oxide) and of hyaluronic acid with various molecular weights and concentrations, are formulated in order to provide fluids with a wide range of rheological properties. Semi-dilute solutions of high molecular weight polymers provide highly viscoelastic fluids with long relaxation times, which achieve a high Weissenberg number (Wi) at flow rates for which the Reynolds number (Re) remains low; hence the elasticity number El = Wi/Re is high. Lower concentration solutions of moderate molecular weight polymers provide only weakly viscoelastic fluids in which inertia remains important and El is relatively low. Flow birefringence observations are used to visualize the nature of flow instabilities in the fluids as the volumetric flow rate through the OSCER device is steadily incremented. At low Wi and Re, all of the fluids display a steady, symmetric, and uniform “birefringent strand” of highly oriented polymer molecules aligned along the outflowing symmetry axis of the test geometry, indicating the stability of the flow field under such conditions. In fluids of El > 1, we observe steady elastic flow asymmetries beyond a critical Weissenberg number,Wicrit, that are similar in character to those already reported in standard cross-slot geometries [e.g., P. E. Arratia, C. C. Thomas, J. Diorio, and J. P. Gollub, “Elastic instabilities of polymer solutions in cross-channel flow,” Phys. Rev. Lett. 96, 144502 (2006)10.1103/PhysRevLett.96.144502]. However, in fluids with El < 1 we observe a sequence of time-dependent inertio-elastic instabilities beyond a critical Reynolds number, Re crit, characterized by high frequency spatiotemporal oscillations of the birefringent strand. By plotting the critical limits of stability for the various fluids in the Wi-Re operating space, we are able to construct a stability diagram delineating the distinct steady symmetric, steady asymmetric and inertio-elastic flow regimes in this idealized planar elongational flow device.

A recently developed microfluidic device, the optimized shape cross-slot extensional rheometer or OSCER [S. J. Haward, M. S. N. Oliveira, M. A. Alves, and G. H. McKinley, “Optimized cross-slot flow geometry for microfluidic extensional rheometry,” Phys. Rev. Lett. 109, 128301 (2012)10.1103/PhysRevLett.109.128301], is used to investigate the stability of viscoelastic polymer solutions in an idealized planar stagnation point flow. Aqueous polymer solutions, consisting of poly(ethylene oxide) and of hyaluronic acid with various molecular weights and concentrations, are formulated in order to provide fluids with a wide range of rheological properties. Semi-dilute solutions of high molecular weight polymers provide highly viscoelastic fluids with long relaxation times, which achieve a high Weissenberg number (Wi) at flow rates for which the Reynolds number (Re) remains low; hence the elasticity number El = Wi/Re is high. Lower concentration solutions of moderate molecular weight polymers provide only weakly viscoelastic fluids in which inertia remains important and El is relatively low. Flow birefringence observations are used to visualize the nature of flow instabilities in the fluids as the volumetric flow rate through the OSCER device is steadily incremented. At low Wi and Re, all of the fluids display a steady, symmetric, and uniform “birefringent strand” of highly oriented polymer molecules aligned along the outflowing symmetry axis of the test geometry, indicating the stability of the flow field under such conditions. In fluids of El &amp;gt; 1, we observe steady elastic flow asymmetries beyond a critical Weissenberg number,Wicrit, that are similar in character to those already reported in standard cross-slot geometries [e.g., P. E. Arratia, C. C. Thomas, J. Diorio, and J. P. Gollub, “Elastic instabilities of polymer solutions in cross-channel flow,” Phys. Rev. Lett. 96, 144502 (2006)10.1103/PhysRevLett.96.144502]. However, in fluids with El &amp;lt; 1 we observe a sequence of time-dependent inertio-elastic instabilities beyond a critical Reynolds number, ${\mathop{\rm Re}\nolimits} _{crit} $ Re crit, characterized by high frequency spatiotemporal oscillations of the birefringent strand. By plotting the critical limits of stability for the various fluids in the Wi-Re operating space, we are able to construct a stability diagram delineating the distinct steady symmetric, steady asymmetric and inertio-elastic flow regimes in this idealized planar elongational flow device.