Antonio L. Sánchez

Particle-image velocimetry was employed to investigate the structure of the cold boundary layer surrounding a fire whirl generated in an experimental setup consisting of a pool fire enclosed by distant, inclined vertical vanes that deflect the entraining air. Results obtained for two different vane inclinations were compared with theoretical predictions previously derived using high-Reynolds-number asymptotics. The experiments confirmed the presence of a near-wall region characterized by pronounced inward radial flow, with its magnitude increasing with decreasing radial distance. Under the specific conditions examined, boundary-layer separation and reattachment were observed, giving rise to a long bubble of slow, recirculating flow along the wall. This feature has potential implications for future numerical modeling of fire-whirl structure and dynamics. Novelty and significance An accurate understanding of the flow surrounding fire whirls is necessary to support numerical investigations of their structure and dynamics. Particle-Image Velocimetry (PIV) is applied, for the first time, to obtain an experimental characterization of the cold boundary layer that develops around fire whirls. These novel measurements provide new insights into the structure and morphology of the boundary layer that are not captured by existing theories.

Computational fluid dynamics (CFD) has been widely used to study cerebrospinal fluid (CSF) flow in Chiari Malformation Type I (CM-I). However, most approaches rely on limited patient-specific detail, and it remains unclear whether such minimal input is sufficient to yield physiologically realistic flow predictions. In this study, we construct a series of MRI-based models of the craniocervical CSF space in a CM-I patient, complemented with representations of microanatomical features derived from ex vivo measurements and patient MRI data, to assess how CFD predictions are influenced by the choice of boundary conditions in the numerical integrations and the inclusion or omission of nerve roots and denticulate ligaments in the anatomical model. Our results reveal that while increasing patient-specific detail in boundary conditions improves agreement with velocity fields measured via phase-contrast MRI, key flow features—most notably anterior–posterior compartmentalization and bidirectional patterns during flow reversal—only emerge when denticulate ligaments are included in the model. In contrast, inclusion of nerve roots has a more localized effect on the velocity field and a modest impact on pressure drops. Our findings not only clarify how more detailed boundary conditions and improved anatomical fidelity affect velocity and pressure predictions, but also provide a mechanistic explanation for flow patterns commonly observed in CM-I that have remained unexplained, highlighting the critical role of denticulate ligaments.

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We examine flow and transport through an orifice in a flat wall separating semi-infinite atmospheres of two dissimilar gases. The analysis assumes steady conditions and order-unity values of the Schmidt number Sc and Péclet number Pe, such that advection and diffusion contribute comparably to mass and momentum transport. Mixing between the two gases induces order-unity variations in viscosity and density, resulting in coupled concentration and velocity fields. The solution yields the mass transfer rates of both gases, expressed in terms of an appropriately defined Sherwood number, as well as the overpressure required to sustain the flow, all as functions of Sc and Pe. An explicit analytical solution is obtained in the limit of small Pe, while numerical integration is used to describe flows with Pe = O(1). The mixing of hydrogen and air is used as an illustrative example that serves to highlight the influence of large gas-molecular-weight differences on the flow structure and associated mixing rate, with additional selected results given for the case of hydrogen and water vapor.

We examine flow and transport through an orifice in a flat wall separating semi-infinite atmospheres of two dissimilar gases. The analysis assumes steady conditions and order-unity values of the Schmidt number Sc and Péclet number Pe, such that advection and diffusion contribute comparably to mass and momentum transport. Mixing between the two gases induces order-unity variations in viscosity and density, resulting in coupled concentration and velocity fields. The solution yields the mass transfer rates of both gases, expressed in terms of an appropriately defined Sherwood number, as well as the overpressure required to sustain the flow, all as functions of Sc and Pe. An explicit analytical solution is obtained in the limit of small Pe, while numerical integration is used to describe flows with Pe = O(1). The mixing of hydrogen and air is used as an illustrative example that serves to highlight the influence of large gas-molecular-weight differences on the flow structure and associated mixing rate, with additional selected results given for the case of hydrogen and water vapor.

A simple method is presented for calculating the structure of entropy layers generated by bow shocks over blunt-nosed wedges in hypersonic flow. The model employs a streamfunction-based framework to track entropy jumps introduced at the bow shock. It is shown that entropy conservation along streamlines, combined with the condition of uniform total enthalpy, determines the transverse profiles of velocity and thermodynamic properties in the downstream parallel-flow region at distances much larger than the wedge radius. A key finding is that the variation of entropy with streamfunction, computed numerically for ideal gas at freestream Mach numbers ranging from 3 to 10 and wedge half-angles ranging from 0 to 10 degrees, identifies a specific nondimensional streamfunction scaled by freestream parameters that collapses the entropy data onto a single quasi-universal curve. The proposed model provides a robust and efficient means of reconstructing the density and velocity fields within the entropy layer for prescribed freestream Mach number and wedge angle, eliminating the need for direct CFD simulation and enabling rapid generation of base states for stability analysis and preliminary design.

In this paper, we provide a practical assessment of high-level functional verification by systematically injecting nine different design-level faults into a 4-bit Arithmetic Logic Unit (ALU) and comparing the effectiveness of directed and random test vectors for fault detection. Injected faults include bus source errors, module substitution errors, Control-Logic faults, and Signed-bit faults. Directed vectors were manually created to exercise specific design scenarios, whereas random vectors were generated automatically. Using a Verilog testbench, we measured mutation kill rates per fault. A 16-vector directed set achieved 60.4% overall detection, outperforming 100 random vectors at 30.4% (average over 5 independent runs). Results show that vector quality, not sheer quantity, drives early fault detection, especially for control and data-path faults that random stimulus often misses. All code and methodology are provided in an open-source testbench for reproducible mutation-based hardware verification.

Numerical simulations are conducted to study fundamental aspects of combustion stabilization in hydrogen-fueled gas turbines. The study focuses on laminar lifted flames at moderate Reynolds numbers in axisymmetric configurations, where a swirling hydrogen jet diluted with nitrogen is injected into stagnant, preheated, pre-compressed air. The conservation equations are formulated in the low-Mach-number approximation, employing a mixture-averaged model for molecular transport. Fuel oxidation is modeled using both detailed chemical kinetics and a previously derived explicit one-step reduced mechanism, which assumes steady-state behavior for chemical intermediates—a valid approximation under the high-pressure conditions typical of gas-turbine combustion chambers, and the accuracy of that approximation is ascertained. The investigation explores the interplay between vortex breakdown and flame dynamics, including liftoff and blowoff, as functions of the swirl and Damköhler numbers. The results elucidate the required flow criteria for lifted-flame stabilization and demonstrate the predictive capability and computational cost reduction of the one-step chemistry in connection with hydrogen combustion at high pressures. A regime diagram in a plane of swirl number and Damköhler number is derived, and conditions for the occurrence of steadily pulsating flames are established, along with indications of amplitudes and frequencies of those oscillations. While clearly not directly applicable to practical turbulent-flow conditions, the results can be useful in future analyses and design concepts for combustion chambers of hydrogen-fueled gas turbines. Novelty and significance statement This work presents, for the first time, results of computations of nitrogen-diluted hydrogen flame behavior for swirling fuel jets issuing into air that has been heated to temperatures expected at the entrance to gas-turbine combustion chambers. It is novel in that it compares predictions made using both detailed combustion chemistry and one-step systematically derived reduced chemistry. A significant finding is that the results obtained with the reduced chemistry are in general agreement with those of the detailed chemistry, thereby affording substantial reductions in computational cost. Another novel and significant result is the determination of injection and swirl gas-turbine conditions required for stable lifted flames to occur, rather than attached flames or blowoff. The existence and characteristics of pulsating oscillations also are established for the first time. These results will be useful in the design and analysis of hydrogen-fueled gas-turbine combustion chambers.

Previous studies involving extremely fuel-lean hydrogen–air mixtures enclosed between two parallel plates have revealed that combustion can occur in the form of isolated nearly circular flames propagating steadily. The structure and propagation velocity of these reactive fronts is investigated here via asymptotic methods and numerical analysis, exploiting the disparity of scales present in the problem. The modeling approach, accounting for the non-unity value of the fuel Lewis number and the presence of stabilizing heat losses to the confining walls, considers a one-step irreversible reaction with an Arrhenius rate having a large activation energy. The drift velocity is assumed to be small compared to the planar flame speed, leading to a low-Péclet-number approximation consistent with the nearly circular flame shape. Under this approximation, the flow exhibits an asymptotic structure comprising a near-field region dominated by molecular transport, containing the thin flame front, and a far-field region where reactant convection becomes significant. Through matched asymptotic expansions, a continuous family of steady-state solutions is obtained, with the propagation speed depending non-monotonically on the flame radius. The solution includes a branch of superadiabatic flames with small radii, a branch of subadiabatic flames with large radii, and an intermediate connecting branch where the velocity increases with increasing flame size. Numerical integrations for flames propagating in channels yield solutions along the intermediate branch, suggesting that the other two branches may be artifacts of the asymptotic analysis. The numerical results confirm the existence of a continuum of flame solutions, with velocities and radii closely matching the theoretical predictions. Novelty and significance statement A new theoretical description of nearly circular premixed flames propagating between two parallel plates is derived through low-Péclet-number and large-activation-energy limits. The complete two-dimensional description – subject to conductive heat losses to the confining walls – provides analytical closure relations between the size, temperature, and propagation speed of the flame structure. Although a continuum of steady-state solutions, divided into three distinguished branches, is obtained from the theoretical analysis, numerical simulations confirm the validity of the intermediate branch only. This subset indicates that ring-like flames can exist in a range of sizes and propagating speeds for small enough Lewis numbers of the fuel. The significance of this finding is underscored by the ongoing interest in accurately understanding the physical phenomena governing fuel storage, handling, and the mitigation of hazardous scenarios in applications using highly diffusive fuels like hydrogen.

The hydrodynamic theory of flame propagation in closed vessels is extended here to configurations involving nonuniform initial distributions of temperature and composition, admitting arbitrary steady-planar-deflagration chemical kinetics not considered in previous publications. The analysis addresses planar, cylindrical, and spherical configurations in the high-Péclet-number limit in which a thin premixed flame separates fresh-mixture and burnt-gas regions that are free from diffusive transport in the first asymptotic approximation. The simplified approach reduces the problem to solving a system of ordinary differential equations in time for the Euler-equation descriptions of the hydrodynamics in the fresh and burnt gases, along with the motion of the deflagration separating them. Planar hydrogen-air flames with a detailed chemical-kinetic description are selected to illustrate the simplified computational procedure and to expose the influences of the nonuniform initial distributions admitted by the new general formulation. The good accuracy of the simplified approach is supported by favorable agreement with a full numerical integration of the problem as originally formulated, prior to imposition of the asymptotic simplifications. The new method may facilitate future investigations of stratified-charge and unexpected-accident scenarios. Novelty and significance statement This work presents a reduced-order formulation of the evolution of flames in closed vessels, taking into account nonuniform initial distributions of temperature and reactant concentrations for the first time. It is significant in that it facilitates investigations of flame propagation under conditions that may arise in many real-world situations.

The optimization of intrathecal drug delivery procedures requires a deeper understanding of flow and transport in the spinal canal. Numerical modeling of drug dispersion is challenging due to the disparity in time scales: dispersion occurs over 1 hour, while cerebrospinal fluid pulsations driven by cardiac motion occur on a 1-second scale. Patient-specific predictions in clinical settings demand simplified descriptions that focus on drug-dispersion times, bypassing the rapid concentration oscillations caused by cyclic motion. A previously derived reduced-order model involving convective transport driven by mean Lagrangian drift is tested here through comparisons with MRI-informed direct numerical simulations (DNS) of drug dispersion in a cervical-canal model featuring nerve rootlets and denticulate ligaments. The comparisons demonstrate that the reduced model is able to describe precisely drug transport, enabling drug-dispersion predictions at a fraction of the computational cost involved in the DNS. Approximate descriptions assuming convective transport to be governed by the mean Eulerian velocity are found to significantly underpredict drug dispersion, highlighting the critical role of mean Lagrangian motion. Our results also confirm the substantial influence of microanatomical features on drug dispersion, consistent with earlier analyses. A key additional finding from the DNS is that molecular diffusion has a negligible impact on drug dispersion, with the mean drift of fluid particles primarily dictating the evolution of the drug distribution-an insight valuable for future modeling efforts.

Clearance of waste material from the brain by the glymphatic system results from net flow of cerebrospinal fluid (CSF) through perivascular spaces surrounding veins and arteries. In periarterial spaces, this bulk flow is directed from the cranial subarachnoid space towards the brain's interior. The precise pumping mechanism explaining this net inflow remains unclear. While in vivo experiments have shown that the pulsatile motion in periarterial spaces is synchronized with arterial pulsations, peristalsis alone has been deemed insufficient to explain bulk flow. In this study we examine an alternative mechanism based on the interaction between arterial pulsations and fluctuations in transmantle pressure. Previously studied using pressure data from a hydrocephalus patient, this mechanism is analyzed here in healthy subjects using in vivo flow measurements obtained via phase-contrast magnetic resonance imaging. Arterial pulsations are derived from flow-rate measurements of arterial blood entering the cranial cavity, while transmantle-pressure fluctuations are computed using measurements of CSF flow in the cerebral aqueduct. The two synchronized waveforms are integrated into a canonical multi-branch model of the periarterial spaces, yielding a closed-form expression for the bulk flow. The results confirm that the dynamic interactions between arterial pulsations and transmantle pressure are sufficient to generate a positive inflow along periarterial spaces.

Developed in this study is a theoretical description of squeeze-film lubrication systems that involve the flexural oscillation of a thin plate near a parallel wall. Such systems were discovered in recent experiments to produce load-bearing attractive forces that are a thousandfold stronger than those generated by rigid oscillators, which typically favour repulsion. Analyses of squeeze-film gas flow driven by a presumed plate deformation reproduce the observed magnification of attractive load capacity, but exhibit serious discrepancies with crucial aspects of the experimental measurements – most importantly, the precise distribution of air pressure along the film. The discrepancies are resolved in this study by accounting for the presence of two-way-coupled fluid–structure interactions whereby the undulations of the plate, modelled here with use of the classical Kirchhoff–Love equation, are affected non-negligibly by the evolving pressure, described by a modified Reynolds lubrication equation that accounts for compressibility. The resulting problem of elastohydrodynamic lubrication is solved with use of perturbation methods that exploit the limit of small oscillation amplitudes. The analysis ultimately provides an explicit expression specifying the attractive load capacity of a squeeze-film system as a function of relevant operating parameters – including, in particular, the amplitude and frequency of the localized excitation force exerted on the plate. The rudimentary theory derived here may be readily generalized to guide the analysis and development of a wide variety of emerging engineering systems that exploit the vibration-induced squeeze-film effect – such as wall-climbing soft robots and contactless grippers.

Design and analysis are presented for a new device to test the response of endothelial cells to the simultaneous action of cyclic shear stresses and pressure fluctuations. The design consists of four pulsatile-flow chambers connected in series, where shear stress is identical in all four chambers and pressure amplitude decreases in successive chambers. Each flow chamber is bounded above and below by two parallel plates separated by a small gap. The design of the chamber planform must ensure that cells within the testing region experience spatially uniform time-periodic shear stress. For conditions typically encountered in applications, the viscous unsteady flow exhibits order-unity values of the associated Womersley number. The corresponding solution to the unsteady lubrication problem, with general nonsinusoidal flowrate, is formulated in terms of a stream function satisfying Laplace's equation, which can be integrated numerically to determine the spatial distribution of shear stresses for chambers of general planform. The results are used to optimize the design of a device with a hexagonal planform. Accompanying experiments using particle tracking velocimetry (PTV) in a fabricated chamber were conducted to validate theoretical predictions. Pressure readings indicate that intrachamber pressure variations associated with viscous pressure losses and acoustic fluctuations are relatively small, so that all cells in a given testing region experience nearly equal pressure forces.

Starting with a detailed-chemistry description involving 20 elementary steps for hydrogen oxidation and 40 elementary steps for ammonia oxidation, it is shown that systematic application of sensitivity analyses of premixed flames under typical gas-turbine combustion conditions reduces the description to 12 elementary steps for hydrogen oxidation, 4 of them being reversible, and an additional 19 steps for ammonia oxidation, 6 of them being reversible, yielding reasonable predictions for auto-ignition and deflagration processes. Subsequent introduction of steady-state approximations for chemical intermediates, afforded by the high-pressure conditions existing in gas-turbine combustion chambers, effectively reduces the fuel-oxidation description in systems utilizing H 2 -NH 3 fuel mixtures to two global steps for deflagrations, namely, 2H 2 + O 2 ⇌ 2H 2 O and 4NH 3 ＋ 3O 2 ⇌ 2N 2 + 6 H 2 O. Analytical expressions for the associated overall rates, involving the local temperature and the O 2 , H 2 , NH 3 , N 2 , and H 2 O concentrations, are derived through selective truncation of the steady-state expressions, resulting in a simplified chemistry description that can facilitate future numerical analyses based on direct-numerical and large-eddy simulations. Novelty and significance statement A new short mechanism involving only 31 elementary reactions between 16 reactive species has been derived for hydrogen-ammonia oxidation under conditions of pressure, temperature and dilution typically found in gas-turbine burners. Introduction of steady-state assumptions for all intermediate species leads to a two-step mechanism that is shown to predict burning rates with sufficient accuracy. The proposed mechanism can significantly reduce computational times in future direct-numerical and large-eddy simulations.

This paper investigates the transport of drugs delivered by direct injection into the cerebrospinal fluid (CSF) that fills the intrathecal space surrounding the spinal cord. Because of the small drug diffusivity, the dispersion of neutrally buoyant drugs has been shown in previous work to rely mainly on the mean Lagrangian flow associated with the CSF oscillatory motion. Attention is given here to effects of buoyancy, arising when the drug density differs from the CSF density. For the typical density differences found in applications, the associated Richardson number is shown to be of order unity, so that the Lagrangian drift includes a buoyancy-induced component that depends on the spatial distribution of the drug, resulting in a slowly evolving cycle-averaged flow problem that can be analysed with two-time scale methods. The asymptotic analysis leads to a nonlinear integro-differential equation for the spatiotemporal solute evolution that describes accurately drug dispersion at a fraction of the cost involved in direct numerical simulations of the oscillatory flow. The model equation is used to predict drug dispersion of positively and negatively buoyant drugs in an anatomically correct spinal canal, with separate attention given to drug delivery via bolus injection and constant infusion.

study aims at clarifying the relation between the oscillatory flow of cerebrospinal fluid (CSF) in the cerebral aqueduct, a narrow conduit connecting the third and fourth ventricles, and the corresponding interventricular pressure difference. Dimensional analysis is used in designing an anatomically correct scaled model of the aqueduct flow, with physical similarity maintained by adjusting the flow frequency and the properties of the working fluid. The time-varying pressure difference across the aqueduct corresponding to a given oscillatory flow rate is measured in parametric ranges covering the range of flow conditions commonly encountered in healthy subjects. Parametric dependences are delineated for the time-averaged pressure fluctuations and for the phase lag between the transaqueductal pressure difference and the flow rate, both having clinical relevance. The results are validated through comparisons with predictions obtained with a previously derived computational model. The parametric quantification in this study enables the derivation of a simple formula for the relation between the transaqueductal pressure and the stroke volume. This relationship can be useful in the quantification of transmantle pressure differences based on non-invasive magnetic-resonance-velocimetry measurements of aqueduct flow for investigation of CSF-related disorders.

A simple two-dimensional fluid–structure interaction problem, involving viscous oscillatory flow in a channel separated by an elastic membrane from a fluid-filled slender cavity, is analysed to shed light on the flow dynamics pertaining to syringomyelia, a neurological disorder characterized by the appearance of a large tubular cavity (syrinx) within the spinal cord. The focus is on configurations in which the velocity induced in the cavity, representing the syrinx, is comparable to that found in the channel, representing the subarachnoid space surrounding the spinal cord, both flows being coupled through a linear elastic equation describing the membrane deformation. An asymptotic analysis for small stroke lengths leads to closed-form expressions for the leading-order oscillatory flow, and also for the stationary flow associated with the first-order corrections, the latter involving a steady distribution of transmembrane pressure. The magnitude of the induced flow is found to depend strongly on the frequency, with the result that for channel flow rates of non-sinusoidal waveform, as those found in the spinal canal, higher harmonics can dominate the sloshing motion in the cavity, in agreement with previous in vivo observations. Under some conditions, the cycle-averaged transmembrane pressure, also showing a marked dependence on the frequency, changes sign on increasing the cavity transverse dimension (i.e. orthogonal to the cord axis), underscoring the importance of cavity size in connection with the underlying hydrodynamics. The analytic results presented here can be instrumental in guiding future numerical investigations, needed to clarify the pathogenesis of syringomyelia cavities.

Directional fluid flow in perivascular spaces surrounding cerebral arteries is hypothesized to play a key role in brain solute transport and clearance. While various drivers for a pulsatile flow, such as cardiac or respiratory pulsations, are well quantified, the question remains as to which mechanisms could induce a directional flow within physiological regimes. To address this question, we develop theoretical and numerical reduced-order models to quantify the directional (net) flow induceable by peristaltic pumping in periarterial networks. Each periarterial element is modeled as a slender annular space bounded internally by a circular tube supporting a periodic traveling (peristaltic) wave. Under reasonable assumptions of a small Reynolds number flow, small radii, and small-amplitude peristaltic waves, we use lubrication theory and regular perturbation methods to derive theoretical expressions for the directional net flow and pressure distribution in the perivascular network. The reduced model is used to derive closed-form analytical expressions for the net flow for simple network configurations of interest, including single elements, two elements in tandem, and a three element bifurcation, with results compared with numerical predictions. In particular, we provide a computable theoretical estimate of the net flow induced by peristaltic motion in perivascular networks as a function of physiological parameters, notably, wave length, frequency, amplitude, and perivascular dimensions. Quantifying the maximal net flow for specific physiological regimes, we find that vasomotion may induce net pial periarterial flow velocities on the order of a few to tens of μm/s and that sleep-related changes in vasomotion pulsatility may drive a threefold flow increase.

Robots capable of generating adhesion forces that can achieve free movement in application environments while overcoming their own gravity are a subject of interest for researchers. A robot with controllable adhesion could be useful in many engineered systems. Materials processing equipment, robots that climb walls, and pick-and-place machines are some examples. However, most adhesion methods either require a large energy supply system or are limited by the properties of the contact plane. For example, electromagnetic adhesion requires a ferromagnetic surface and pneumatic adhesion requires a flat surface. Furthermore, nearly all existing approaches are only used to generate adhesion forces and often require additional mechanisms to remove the adhesive component from the surface. In this study, we aimed to develop a simpler method of adhering to a surface while simultaneously moving in directions parallel to the surface, using multiple vibration sources to generate normal adhesion and propulsion. To test our approach, we constructed circular and elliptical models and conducted experiments with various inputs and model parameters. Our results show that such a gas-lubricated adhesive disk could achieve adhesive rotation and displacement in the plane without requiring any auxiliary operating system. Using only vibration sources, we were able to generate the necessary adhesion and propulsion forces to achieve the desired motion of the robot. This work represents a step towards the construction of a small-sized tetherless robot that can overcome gravity and move freely in a general environment.

We are grateful to have been asked to edit this Special Issue of Combustion Science and Technology to honor Paul Libby’s life, his service to the journal, and his lifelong contributions to the fiel...

Axisymmetric numerical simulations are used to assess the swirl-induced stabilization of low-Mach-number non-premixed jet flames at a moderate Reynolds number (Re=200). Using a one-step model chemistry describing methane-air partially premixed combustion, we carry out a parametric investigation of the coupling between vortex breakdown and laminar flame liftoff/blowoff in a concentric jet configuration involving a central non-swirling methane jet surrounded by a swirling annular air jet issuing from a pipe with radius RA′ rotating with angular speed Ω′. The analysis considers order-unity values of the two relevant controlling parameters, namely, the Damköhler number DN, defined as the square of the ratio of the stoichiometric methane-air flame-propagation velocity to the mean air-jet velocity UA′, and the swirl number S=Ω′RA′/UA′. As the Damköhler number DN is decreased the attached edge flame lifts off from the injector rim. The resulting lifted triple flame migrates downstream on further decreasing DN until a critical blowoff value DN,b is reached. Results for fixed S=1 exhibit lower values DN,b than the corresponding simulations with fixed S=0. For a fixed Damköhler number, it is found that increasing S results in increased entrainment and reduced liftoff heights. At a critical value SB* of the swirl number, equal to SB*=1.2 for DN=0.35, a recirculation zone abruptly forms upstream of the lifted triple flame, enhancing the mixing and facilitating flame stabilization closer to the injector.

Directional fluid flow in perivascular spaces surrounding cerebral arteries is hypothesized to play a key role in brain solute transport and clearance. While various drivers for pulsatile flow, such as cardiac or respiratory pulsations, are well quantified, the question remains as to which mechanisms could induce directional flow within physiological regimes. To address this question, we develop theoretical and numerical reduced-order models to quantify the directional (net) flow induceable by peristaltic pumping in periarterial networks. Each periarterial element is modeled as a slender annular space bounded internally by a circular tube supporting a periodic traveling (peristaltic) wave. Under the reasonable assumptions of small Reynolds number flow, small radii, and small-amplitude peristaltic waves, we use lubrication theory and regular perturbation methods to derive theoretical expressions for the directional net flow and pressure distribution in the perivascular network. The reduced model is used to derive closed-form analytical expressions for the net flow for simple network configurations of interest, including single elements, two elements in tandem, and a three element bifurcation, with results compared with numerical predictions. In particular, we provide a computable theoretical estimate of the net flow induced by peristaltic motion in perivascular networks as a function of physiological parameters, notably wave length, frequency, amplitude and perivascular dimensions. Quantifying the maximal net flow for specific physiological regimes, we find that vasomotion may induce net pial periarterial flow velocities on the order of a few to tens of mum/s and that sleep-related changes in vasomotion pulsatility may drive a threefold flow increase.

The classical problem of secondary flow driven by a sinusoidally varying pressure gradient is extended here to address periodic pressure gradients of complex waveform, which are present in many oscillatory physiological flows. A slender two-dimensional wavy-walled channel is selected as a canonical model problem. Following standard steady-streaming analyses, valid for small values of the ratio ε of the stroke length of the pulsatile motion to the channel wavelength, the spatially periodic flow is described in terms of power-law expansions of ε, with the Womersley number assumed to be of order unity. The solution found at leading order involves a time-periodic velocity with a zero time-averaged value at any given point. As in the case of a sinusoidal pressure gradient, effects of inertia enter at the following order to induce a steady flow in the form of recirculating vortices with zero net flow rate. An improved two-term asymptotic description of this secondary flow is sought by carrying the analysis to the following order. It is found that, when the pressure gradient has a waveform with multiple harmonics, the resulting velocity corrections display a nonzero flow rate, not present in the single-frequency case, which enables stationary convective transport along the channel. Direct numerical simulations for values of ε of order unity are used to investigate effects of inertia and delineate the range of validity of the asymptotic limit ε≪1. The comparisons of the time-averaged velocity obtained numerically with the two-term asymptotic description reveals that the latter remains remarkably accurate for values of ε exceeding 0.5. As an illustrative example, the results of the model problem are used to investigate the cerebrospinal-fluid flow driven along the spinal canal by the cardiac and respiratory cycles, characterized by markedly non-sinusoidal waveforms.

This paper presents results of an experimental investigation of solute transport in a simplified model of the spinal canal. The work aims to provide increased understanding of the mechanisms responsible for drug dispersion in intrathecal drug delivery (ITDD) procedures. The model consists of an annular channel bounded externally by a rigid transparent tube of circular section, representing the dura mater, and internally by an eccentric cylindrical compliant insert, representing the spinal cord. The tube, closed at one end, is connected to a rigid acrylic reservoir, representing the cranial cavity. The system is filled with water, whose properties are almost identical to those of the cerebrospinal fluid. A programmable peristaltic pump is employed to generate oscillatory motion at frequencies that are representative of those induced by the cardiac and respiratory cycles. Laser induced fluorescence is used to characterize the dispersion of fluorescent dye along the canal and into the cranial cavity for different values of the relevant Womersley number and different eccentricities of the annular section. The present work corroborates experimentally, for the first time, the existence of a steady bulk flow, associated with the mean Lagrangian motion, which plays a key role in the transport of the solute along the spinal canal. The measurements of solute dispersion are found to be in excellent agreement with theoretical predictions obtained using a simplified transport equation derived earlier on the basis of a two-timescale asymptotic analysis. The experimental results underscore the importance of the eccentricity and its variations along the canal and identifies changes in the flow topology associated with differences in the Womersley number, with potential implications in guiding future designs of ITDD protocols.

Abstract Background: The cerebrospinal fluid filling the ventricles of the brain moves with a cyclic velocity driven by the transmantle pressure, or instantaneous pressure difference between the lateral ventricles and the cerebral subarachnoid space. This dynamic phenomenon is of particular interest for understanding ventriculomegaly in cases of normal pressure hydrocephalus (NPH). The magnitude of the transmantle pressure is small, on the order of a few Pascals, thereby hindering direct in vivo measurements. To complement previous computational efforts, we perform here, for the first time, in vitro experiments involving an MRI-informed experimental model of the cerebral aqueduct flow. Methods: Dimensional analysis is used in designing a scaled-up model of the aqueduct flow, with physical similarity maintained by adjusting the flow frequency and the properties of the working fluid. High-resolution MRI images are used to generate a 3D-printed anatomically correct aqueduct model. A programmable pump is used to generate a pulsatile flow rate signal measured from phase-contrast MRI. Extensive experiments are performed to investigate the relation between the cyclic fluctuations of the aqueduct flow rate and the transmantle pressure fluctuation over the range of flow conditions commonly encountered in healthy subjects. The time-dependent pressure measurements are validated through comparisons with predictions obtained with a previously derived computational model. Results: Parametric dependences of the pressure-fluctuation amplitude and its phase lag relative to the flow rate are delineated. The results indicate, for example, that the phase lag is nearly independent on the stroke volume. A simple expression relating the mean amplitude of the interventricular pressure difference (between third and fourth ventricle) with the stroke volume of the oscillatory flow is established. Conclusions: MRI-informed in-vitro experiments using an anatomically correct model of the cerebral aqueduct and a realistic flow rate have been used to characterize transmantle pressure. The quantitative results can be useful in enabling quick clinical assessments of transmantle pressure to be made from noninvasive phase contrast MRI measurements of aqueduct flow rates. The scaled-up experimental facility provides the ability to conduct future experiments specifically aimed at investigating altered CSF flow and associated transmantle pressure, as needed in connection with NPH studies.

This paper addresses the viscous flow developing about an array of equally spaced identical circular cylinders aligned with an incompressible fluid stream whose velocity oscillates periodically in time. The focus of the analysis is on harmonically oscillating flows with stroke lengths that are comparable to or smaller than the cylinder radius, such that the flow remains two-dimensional, time-periodic and symmetric with respect to the centreline. Specific consideration is given to the limit of asymptotically small stroke lengths, in which the flow is harmonic at leading order, with the first-order corrections exhibiting a steady-streaming component, which is computed here along with the accompanying Stokes drift. As in the familiar case of oscillating flow over a single cylinder, for small stroke lengths, the associated time-averaged Lagrangian velocity field, given by the sum of the steady-streaming and Stokes-drift components, displays recirculating vortices, which are quantified for different values of the two relevant controlling parameters, namely, the Womersley number and the ratio of the inter-cylinder distance to the cylinder radius. Comparisons with results of direct numerical simulations indicate that the description of the Lagrangian mean flow for infinitesimally small values of the stroke length remains reasonably accurate even when the stroke length is comparable to the cylinder radius. The numerical integrations are also used to quantify the streamwise flow rate induced by the presence of the cylinder array in cases where the periodic surrounding motion is driven by an anharmonic pressure gradient, a problem of interest in connection with the oscillating flow of cerebrospinal fluid around the nerve roots located along the spinal canal.

A previously derived one-step reduced chemical-kinetic mechanism, describing hydrogen flames under near-limit conditions involving peak temperature not far from the crossover temperature, is used in computations of hydrogen-air flamelets at elevated pressures typical of gas-turbine combustion. Besides freely propagating laminar deflagrations with compositions spanning the whole range of flammability conditions, the calculations address strained premixed and nonpremixed flames as well as partially premixed propagating fronts. The comparisons with results of detailed-chemistry computations reveal that, for most purposes, the one-step mechanism provides sufficiently accurate predictions of burning rates under all conditions of interest for gas-turbine combustion. The reduced-chemistry model, featuring an explicit analytic expression for the hydrogen oxidation rate in terms of the local temperature and the O2, H2, and H2O concentrations, can be easily implemented in numerical codes, thereby facilitating future numerical analyses based on direct-numerical and large-eddy simulations.

Developed in this paper is a theoretical description of the fluid flow involved in contactless transport systems that operate using squeeze-film levitation. Regular perturbation methods are employed to solve the appropriate Reynolds equation that governs the viscous, compressible flow of air in the slender film separating the oscillator and the levitated object. The resulting reduced formulation allows efficient computation of the time-averaged levitation force and moment induced by fluid pressure, as well as the accompanying quasistatic thrust force that accounts additionally for shear stresses. Investigated, in particular, is the possibility of combining two distinct methods of thrust generation that have been experimentally demonstrated in previous studies – (i) inclination of the levitated body and (ii) generation of asymmetrical flexural deformations, such as travelling waves, on the oscillator surface – the latter of which is shown to allow a transition from the typically repulsive levitation force to one that is attractive. Computations reveal that systematic control of the inclination angle can provide significant performance benefits for squeeze-film transport systems. In the case of attractive levitation, the amount of improvement that can be obtained appears to correlate closely with the degree of lateral asymmetry exhibited by the flexural oscillations.