Pressure-driven Flow Research Articles

A novel lower bound for the friction factor-Reynolds number product in laminar flows of Newtonian fluids through singly connected ducts

We revisit the analytical solution for steady, fully developed, pressure-driven flows of Newtonian fluids through n-sided cusped ducts and find that the friction factor–Reynolds number product is a non-monotonic function of n and converges to fRe=64/π2(≅6.486) in the limit as n→∞. To the best of our knowledge, this is the lowest fRe ever reported for laminar flows of Newtonian fluids through singly connected ducts. We discuss the implications of these results in the context of small-scale fluid flow and heat transfer systems and point directions for future studies in the field.

Numerical studies of manipulation and separation of microparticles in ODEP-based microfluidic chips.

A novel optical-induced dielectrophoresis (ODEP) method employing a pressure-driven flow for the continuous separation of microparticles is presented in this study. By applying alternate current electric field on conductive indium tin oxide substrate and projecting the light geometry into the photoconductive layer, an inhomogeneous electric field is locally induced. The particles experience the dielectrophoretic force when passing through the lighting area, where the strongest electrical field gradient exists. By optimizing the structure of the lighting pattern, a stronger nonuniform electric field gradient is generated which predicts the separation of 1 and 3µm polystyrene particles. Moreover, the effects of key parameters, including the light pattern geometry, applied voltage, and flow rate, were investigated in this study, leading to the successful sorting of 700nm and 1µm particles. To further examine the separation sensitivity and practicability of the proposed ODEP microfluidic method, the isolation of two different types of circulating tumor cells from T-cells and red blood cells are demonstrated, providing a novel method for the manipulation and separation of microparticles and nanoparticles.

Analytical models for pressure-driven Stokes flow through superhydrophobic and liquid-infused tubes and annular pipes – ERRATUM

Analytical models for pressure-driven Stokes flow through superhydrophobic and liquid-infused tubes and annular pipes – ERRATUM

Purely elastic turbulence in pressure-driven channel flows

Solutions of long, flexible polymer molecules are complex fluids that simultaneously exhibit fluid-like and solid-like behavior. When subjected to an external flow, dilute polymer solutions exhibit elastic turbulence-a unique, chaotic flow state absent in Newtonian fluids, like water. Unlike its Newtonian counterpart, elastic turbulence is caused by polymer molecules stretching and aligning in the flow, and can occur at vanishing inertia. While experimental realizations of elastic turbulence are well-documented, there is currently no understanding of its mechanism. Here, we present large-scale direct numerical simulations of elastic turbulence in pressure-driven flows through straight channels. We demonstrate that the transition to elastic turbulence is sub-critical, giving rise to spot-like flow structures that, further away from the transition, eventually spread throughout the domain. We provide evidence that elastic turbulence is organized around unstable coherent states that are localized close to the channel midplane.

On-chip label-free sorting and enrichment of microplastic particles by using deterministic lateral displacement

A novel deterministic lateral displacement (DLD) method employing a pressure-driven flow for the continuous size-based separation of microplastic particles is presented in this paper. To induce the DLD effect, arrays of triangular posts were designed to enhance the sorting resolution and reduce the particles clogging. For the particles with a diameter larger than the critical diameter (Dc) in the DLD device, they move in bump mode with collision to microposts. While, the particles flow in zigzag mode if their sizes are below the Dc value. The DLD microfluidic chip enables simplified fabrication process and shows property of label-free and high throughput. Numerical studies were conducted to discuss the Dc values in the microchannel with horizontally symmetrical and asymmetrical posts, where Dc was found smaller in the asymmetric horizontal flow, enabling higher separation sensitivity and resolution. Experiments were conducted to demonstrate the separation of 10 μm and 15 μm polystyrene microplastic particles, and different types of polystyrene and polyethylene microplastic particles by adjusting the flow rates. In order to achieve successful separation, the flow rates between the sheath flow and the sample solution were well matched. In this way, the proposed DLD microfluidic chip with horizontally asymmetrical triangular posts shows property of label-free, high throughput, capability to analyze microplastic particle selectively and sensitively, possibility of sorting nanoplastic particles.

Hydrodynamics of pitching hydrofoil in a plane Poiseuille flow

Several advanced medical and engineering tasks, such as microsurgery, drug delivery through arteries, pipe inspection, and sewage cleaning, can be more efficiently handled using micro- and nano-robots. Pressure-driven flows are commonly encountered in these practical scenarios. In our current research, we delve into the hydrodynamics of pitching hydrofoils within narrow channels, which may find their potential applications in designing bio-inspired robots capable of navigating through pressure-driven flows in confined channels. In this paper, we have conducted a numerical investigation into the flow characteristics of a National Advisory Committee for Aeronautics (NACA) 0012 hydrofoil pitching around its leading edge within a plane Poiseuille flow using a graphical processing unit accelerated sharp interface immersed boundary method solver. Our study considers variations of the wall clearance from 20% to 50% of the channel width. We have explored the hydrodynamic features such as instantaneous and time-averaged values of lift, drag, input power, and torque for different wall clearance ratios and oscillation frequencies in the range of Reynolds number 100–200 based on the mean velocity and channel width. We have tried to explain the force, torque, and power variations by examining the flow features in the near wake. While the hydrodynamic coefficients showed significant variations with changes in wall clearance and the Strouhal number (St), we did not observe significant variations with alterations in the Reynolds number (Re).

A review of interaction mechanisms and microscopic simulation methods for CO2-water-rock system

This work systematically reviews the complex mechanisms of CO2-water-rock interactions, microscopic simulations of reactive transport (dissolution, precipitation and precipitate migration) in porous media, and microscopic simulations of CO2-water-rock system. The work points out the key issues in current research and provides suggestions for future research. After injection of CO2 into underground reservoirs, not only conventional pressure-driven flow and mass transfer processes occur, but also special physicochemical phenomena like dissolution, precipitation, and precipitate migration. The coupling of these processes causes complex changes in permeability and porosity parameters of the porous media. Pore-scale microscopic flow simulations can provide detailed information within the three-dimensional pore and throat space and explicitly observe changes in the fluid-solid interfaces of porous media during reactions. At present, the research has limitations in the decoupling of complex mechanisms, characterization of differential multi-mineral reactions, precipitation generation mechanisms and characterization (crystal nucleation and mineral detachment), simulation methods for precipitation-fluid interaction, and coupling mechanisms of multiple physicochemical processes. In future studies, it is essential to innovate experimental methods to decouple “dissolution–precipitation–precipitate migration” processes, improve the accuracy of experimental testing of minerals geochemical reaction-related parameters, build reliable characterization of various precipitation types, establish precipitation-fluid interaction simulation methods, coordinate the boundary conditions of different physicochemical processes, and, finally, achieve coupled flow simulation of “dissolution−precipitation−precipitate migration” within CO2-water-rock systems.

Heating-induced release of trapped bubbles from dead-end pore throats filled with nonvolatile liquid

The release of trapped bubbles from dead-end pore throats filled with nonvolatile liquid has widespread applications in gas–liquid reactors, radiators, foam flooding, ceramic sintering, and droplet microcarriers. As conventional pressure-driven flow cannot induce the transport of bubbles in dead-end pores, this paper explores the possibility of using heating to control the release of bubbles from dead-end pore throats. Visualization experiments of the microfluidics within a dead-end pore throat structure are conducted to address the release process of bubbles during heating. An increase in temperature causes dissolved gas in the solution to be transferred to the bubble, which enhances the bubble pressure and enables the bubble to pass through the pore throat. We analyze the effects of the initial bubble radius and initial temperature on the critical temperature Tcr at which the bubble passes through the pore throat. A larger initial radius does not necessarily make it more difficult for the bubble to pass through the throat, but there is a critical radius above which any increase in radius produces a lower value of Tcr. A theoretical model considering diffusion mass transfer, capillary forces, and corner film flows is developed, and this model is found to be in good agreement with the experimental results. Finally, we obtain three dimensionless numbers that can be used to predict Tcr. Our work provides guidance for the effective regulation of diffusive growth and the heating-induced release of bubbles from dead-end pore throats.

Inertial Migration in a Pressure-Driven Channel Flow: Beyond the Segre-Silberberg Pinch.

We examine theoretically the inertial migration of a neutrally buoyant rigid sphere in pressure-driven channel flow, accounting for its finite size relative to the channel width (the confinement ratio). For sufficiently large channel Reynolds numbers (Re_{c}), a small but finite confinement ratio qualitatively alters the inertial lift velocity profiles obtained using a point-particle formulation. Finite size effects lead to new equilibria, in addition to the well-known Segre-Silberberg pinch locations. Consequently, a sphere can migrate to either the near-wall Segre-Silberberg equilibria, or the new stable equilibria located closer to the channel centerline, depending on Re_{c} and its initial position. Our findings are in accord with recent experiments and simulations, and have implications for passive sorting of particles based on size, shape, and other physical characteristics, in microfluidic applications.

Flow-induced periodic chiral structures in an achiral nematic liquid crystal

Supramolecular chirality typically originates from either chiral molecular building blocks or external chiral stimuli. Generating chirality in achiral systems in the absence of a chiral input, however, is non-trivial and necessitates spontaneous mirror symmetry breaking. Achiral nematic lyotropic chromonic liquid crystals have been reported to break mirror symmetry under strong surface or geometric constraints. Here we describe a previously unrecognised mechanism for creating chiral structures by subjecting the material to a pressure-driven flow in a microfluidic cell. The chirality arises from a periodic double-twist configuration of the liquid crystal and manifests as a striking stripe pattern. We show that the mirror symmetry breaking is triggered at regions of flow-induced biaxial-splay configurations of the director field, which are unstable to small perturbations and evolve into lower energy structures. The simplicity of this unique pathway to mirror symmetry breaking can shed light on the requirements for forming macroscopic chiral structures.

Analytical Solutions to the Unsteady Poiseuille Flow of a Second Grade Fluid with Slip Boundary Conditions.

This paper deals with an initial-boundary value problem modeling the unidirectional pressure-driven flow of a second grade fluid in a plane channel with impermeable solid walls. On the channel walls, Navier-type slip boundary conditions are stated. Our aim is to investigate the well-posedness of this problem and obtain its analytical solution under weak regularity requirements on a function describing the velocity distribution at initial time. In order to overcome difficulties related to finding classical solutions, we propose the concept of a generalized solution that is defined as the limit of a uniformly convergent sequence of classical solutions with vanishing perturbations in the initial data. We prove the unique solvability of the problem under consideration in the class of generalized solutions. The main ingredients of our proof are a generalized Abel criterion for uniform convergence of function series and the use of an orthonormal basis consisting of eigenfunctions of the related Sturm-Liouville problem. As a result, explicit expressions for the flow velocity and the pressure in the channel are established. The constructed analytical solutions favor a better understanding of the qualitative features of time-dependent flows of polymer fluids and can be applied to the verification of relevant numerical, asymptotic, and approximate analytical methods.

Analytical models for pressure-driven Stokes flow through superhydrophobic and liquid-infused tubes and annular pipes

Analytical expressions for the velocity field and the effective slip length of pressure-driven Stokes flow through slippery pipes and annuli with rotationally symmetrical longitudinal slits are derived. Specifically, the developed models incorporate a finite local slip length and constant shear stress along the slits, and thus go beyond the assumption of perfect slip employed commonly for superhydrophobic surfaces. Thereby, they provide the possibility to assess the influence of both the viscosity of the air or other fluid that is modelled to fill the slits as well as the influence of the micro-geometry of these slits. First, expressions for tubes and annular pipes with superhydrophobic or slippery walls are provided. Second, these solutions are combined to a tube-within-a circular-pipe scenario, where one fluid domain provides a slip to the other. This scenario is interesting as an application to achieve stable fluid–fluid interfaces. With respect to modelling, it illustrates the specification of the local slip length depending on a linked flow field. The comparison of the analytically calculated solutions with numerical simulations shows excellent agreement. The results of this paper thus represent an important instrument for the design and optimization of slippage along surfaces in circular geometries.

Arsenic removal from aqueous solution using PWN-type zeolite membrane: A theoretical investigation

Arsenic contamination in drinking water is a global health concern due to its extreme toxicity. This study explores the efficacy of PWN-type zeolite membranes in selectively removing dissolved arsenic ions. Molecular dynamics simulations analyze the permeation of aqueous arsenic solutions through the zeolite membrane under pressure-driven flow (5 to 600 MPa over 5 ns). The goal is to assess PWN-type zeolites as nanofiltration membranes for arsenic removal. The zeolite's nanoporous structure immobilizes arsenic ions while permitting water transport. Remarkably, the membrane exhibits high ion rejection, even at pressures up to 600 MPa. These findings underscore the potential of PWN-type zeolite membranes for separating As (III) ions from water supplies. With ultra-high porosity and selectivity, these nanoengineered membranes enable effective mechanical filtration processes for arsenic removal. In summary, this theoretical investigation highlights the significant promise of PWN-type zeolites as high-performance membranes for arsenic decontamination, crucial for safeguarding human health.

Electrokinetic energy conversion efficiency in a nanochannel with slip-dependent zeta potential

Abstract Electrokinetic energy conversion in hydrophobic nanochannels has been studied by many scholars because of its high estimated conversion efficiency. However, these studies mainly focued on the the case of slip-independent zeta potential, ignoring the effect of slip length on zeta potential. In the paper, we study the energy conversion of pressure-driven flow in plane nanochannel with slip-dependent (S.D.) zeta potential. Through the derived analytical expression and schematic analysis of electrokinetic energy conversion efficiency, it can be observed that, within specific parameter ranges, when taking into account the S.D. zeta potential, the conversion efficiency is improved. The maximum conversion efficiency obtained is approximately 23%, which is an improvement of 5.9% compared to the slip-independent (S.I.) zeta potential. This study may have a positive impact on achieving more efficient energy collection and play a important role in the energy field.

Convection-Diffusion-Adsorption Model for the Description of the Analyte-Binding Reactions on a Membrane

The performance of many biomedical assays strongly depends on the transport of analyte molecules to the surface where the binding reactions occur. In some experimental systems, liquid flow can drastically improve the detection limit and decrease the analysis time. This is true for many membrane-based analyses, such as dot-blotting and immunofiltration, in which the sample flows through a porous membrane and adsorbs onto the polymer surface in the pores. Here, we use the convection-diffusion-adsorption equation to calculate the amount of the adsorbed analyte as a function of time. The analyte-binding efficiency is compared for the two sample loading procedures—pressure-driven flow and incubation. Computation shows that when the liquid flow rate reaches a certain threshold, the pressure-driven flow setup ensures higher analyte adsorption than incubation. The convection can drastically decrease the time necessary to capture a small detectable amount of the analyte. However, the infinite increase of the flow rate seems useless because it cannot overcome the kinetic limitation of the adsorption. The model proposed here is in good agreement with the experimental data and can be valuable for the development of membrane-based biosensors.

Resistive pulse analysis of chiral amino acids utilizing metal-amino acid crystallization differences.

Here, we report a proof-of-concept resistive pulse method for analyzing chiral amino acids utilizing metal-amino acid crystallization differences. This method involves introducing an amino acid sample solution into a micropipette through a pressure-driven flow. The sample then mixes with a metal ion solution inside the pipette, forming metal-amino acid crystals. The crystal size depends on the enantiomeric excess (x) of chiral amino acid samples. Large x values lead to large crystals. The crystal size difference is then reflected in the resistive pulse size as they block the ionic transport in a micropipette to different extents. We used Cd-cystine crystallization as a model system and found approximately five times the mean current pulse size difference for racemic (x = 0) and L-only (x = +1) cystine samples. A similar result was observed for aspartate. Our discovery opens up new opportunities for micro/nanoscopic chiral amino acid analysis, which can potentially be used in single-cell analysis.

Cross-streamline migration and near-wall depletion of elastic fibers in micro-channel flows.

The complex dynamics of elastic fibers in viscous fluids are central to many biological and industrial systems. Fluid-structure interactions underlying these dynamics govern the shape and transport of flexible fibers, and understanding these interactions can help tune flow properties in applications such as microfluidic separation, printing and clogging. In this work, we use slender-body theory to study micromechanical dynamics that arise from the coupling between the elastic backbone of a fiber and the local straining flow that contributes to filament flipping and cross-streamline migration. The resulting transverse drift is unbiased in either direction in simple shear flow. However, a non-uniform shear rate results in bias towards regions of high shear, which we connect to the shape transitions during flips. We discover a depletion layer that forms near the boundaries of pressure-driven channel flow due to the competition between such a cross-streamline drift and steric exclusion from the walls. Finally, we develop scaling laws for the curvature of filaments during flip events, demonstrating the origin of the drift bias in non-uniform flows, and confirm this behavior from our simulations. Put together, these results shed light on the role of a local and dominant coupling between elasticity and viscous resistance in dictating long-term dynamics and transport of elastic fibers in confined flows.

Prediction of mean flow and over-tip shock distribution in pressure-driven tip leakage flows

The flow across the blade tip clearance in turbomachinery is simplified as pressure-driven tip leakage flow (TLF) by isolating it from the mainstream. Based on schlieren visualization and numerical simulations, several common features of TLF are achieved. Consequently, a diffusion model is proposed to evaluate the mean flow and shock motions within the clearance. It takes into consideration the effects of relative wall motion by superposing a fully developed Couette flow. In addition, the over-tip shock waves are treated as repeated sawtooth wave to model the propagation. This approach enables quick and accurate evaluations of the meanflow and shock motions under configurations of stationery and moving casing wall. Given the flow variables at boundaries of the shock region, the meanflow and the evolution of the over-tip shock waves can be achieved instantly with an error less than 2%. Another advantage of this model is it can be non-intrusive. Hence, the challenges, arising from spatial constraints in direct measuring of TLF within the clearance, are surmounted. This is beneficial for locating the tip flow loss and the shock-induced heat load. Two flow mechanisms are unveiled from the predictions: (1) The strongest shock–boundary interaction accompanied by strong momentum exchange occurs above the separation bubble. (2) The oscillation of over-tip shock waves is self-sustained by a feedback loop formed by the pressure-side vortex shedding, shock generation, and shock–boundary interactions.

A Theoretical Study of a Micro-Channel Pressure-Driven Flow of Electrically Conducting Liquids in the Presence of a Transversal Magnetic Field

A Theoretical Study of a Micro-Channel Pressure-Driven Flow of Electrically Conducting Liquids in the Presence of a Transversal Magnetic Field

Microphysiological pancreas-on-chip platform with integrated sensors to model endocrine function and metabolism.

Pancreatic in vitro research is of major importance to advance mechanistic understanding and development of treatment options for diseases such as diabetes mellitus. We present a thermoplastic-based microphysiological system aiming to model the complex microphysiological structure and function of the endocrine pancreas with concurrent real-time read-out capabilities. The specifically tailored platform enables self-guided trapping of single islets at defined locations: β-cells are assembled to pseudo-islets and injected into the tissue chamber using hydrostatic pressure-driven flow. The pseudo-islets can further be embedded in an ECM-like hydrogel mimicking the native microenvironment of pancreatic islets in vivo. Non-invasive real-time monitoring of the oxygen levels on-chip is realized by the integration of luminescence-based optical sensors to the platform. To monitor insulin secretion kinetics in response to glucose stimulation in a time-resolved manner, an automated cycling of different glucose conditions is implemented. The model's response to glucose stimulation can be monitored via offline analysis of insulin secretion and via specific changes in oxygen consumption due to higher metabolic activity of pseudo-islets at high glucose levels. To demonstrate applicability for drug testing, the effects of antidiabetic medications are assessed and changes in dynamic insulin secretion are observed in line with the respective mechanism of action. Finally, by integrating human pancreatic islet microtissues, we highlight the flexibility of the platform and demonstrate the preservation of long-term functionality of human endocrine pancreatic tissue.