Flow Profile Research Articles

Flow dynamics over cylinder in two‐dimensional benchmark problem: A finite element approximation

This research investigates 2D benchmark flow around a circular cylinder, utilizing the incompressible Navier–Stokes equations alongside the continuity and energy equations. The numerical solution is achieved through finite element discretization for space variable, combined with a second‐order Crank–Nicolson scheme for time integration. The computational results are derived using the FEATFLOW finite element based library package. Our study focuses on the dimensionless form of the flow equations and examines three key dimensionless parameters: drag, lift, and pressure drop. Upon applying finite element method (FEM) discretization, the system is converted into a set of linear or nonlinear ordinary differential equations or algebraic equations for steady‐state scenarios. We then apply the Newton–Raphson method as the outer nonlinear solver, and the multigrid method for efficiently resolving the linear subproblems. To ensure numerical accuracy, we evaluated the and errors, confirming that the experimental order of convergence matches the theoretical predictions. Flow profiles were both graphically represented and tabulated, offering a detailed understanding of the simulation results.

Invariant regimes of Spencer scaling law for magnetic compression of rotating FRC plasma

Abstract The scaling laws for the magnetic compression of a toroidally rotating field reversed configuration (FRC) have been investigated in this work. The magnetohydrodynamics (MHD) simulations of the magnetic compression on rotating FRCs employing the NIMROD code (Sovinec et al 2004 J. Comput. Phys. 195 355), are compared with the Spencer’s one-dimensional (1D) theory (Spencer et al 1983 Phys. Fluids 26 1564) for a wide range of initial flow speeds and profiles. The toroidal flow can influence the scalings directly through the alteration of the compressional work as also evidenced in the 1D adiabatic model, and indirectly by reshaping the initial equilibrium. However, in comparison to the static initial FRC equilibrium cases, the pressure and the radius scalings remain invariant for the magnetic compression ratio B w 2 / B w 1 up to 6 in presence of the initial equilibrium flow, suggesting a broader applicable regime of the Spencer scaling law for FRC magnetic compression. The invariant scaling has been proven a natural consequence of the conservation of angular momentum of both fluid and magnetic field during the dynamic compression process.

DC Electric Fields Promote Biodegradation of Waterborne Naphthalene in Biofilter Systems.

Biofiltration is a simple and low-cost method for the cleanup of contaminated water. However, the reduced availability of dissolved chemicals to surface-attached degrader bacteria may limit its efficient use at certain hydraulic loadings. When a direct current (DC) electric field is applied to an immersed packed bed, it invokes electrokinetic processes, such as electroosmotic water flow (EOF). EOF is a surface-charge-induced plug-flow-shaped movement of pore fluids. It acts at a nanometer distance above surfaces and allows the change of microscale pressure-driven flow profiles and, hence, the availability of dissolved contaminants to microbial degraders. In laboratory percolation columns, we assessed the effects of a weak DC electric field (E = 0.5 V·cm-1) on the biodegradation of waterborne naphthalene (NAH) by surface-attached Pseudomonas fluorescens LP6a. To vary NAH bioavailability, we used different NAH concentrations (C0 = 2.7, 5.1, or 7.8 × 10-5 mol·L-1) and Darcy velocities typical for biofiltration ( = 0.2-1.2 × 10-4 m·s-1). In DC-free controls, we observed higher specific degradation rates (qc) at higher NAH concentrations. The qc depended on , suggesting bioavailability restrictions depending on the hydraulic residence times. DC fields consistently increased qc and resulted in linearly increasing benefits up to 55% with rising hydraulic loadings relative to controls. We explain these biodegradation benefits by EOF-altered microscale flow profiles allowing for better NAH provision to bacteria attached to the collectors even though the EOF was calculated to be 100-800 times smaller than bulk water flow. Our data suggest that electrokinetic approaches may give rise to future technical applications that allow regulating biodegradation, for example, in response to fluctuating hydraulic loadings.

Hybrid Radial‐Axial Flow for Enhanced Thermal Performance in Packed Bed Energy Storage

ABSTRACTIn this work, a hybrid radial‐axial (HRA) system is used to store thermal energy in a packed bed. The heat transfer fluid (HTF) is delivered via a perforated radial pipe placed at the center of the packed bed along the axial length. Hot fluid flows from the center toward the wall through the holes (like other radial systems), but then leaves via the traditional axial flow exit, creating the HRA flow configuration. A computational fluid dynamics (CFD) model is used to analyze the thermal performance of the packed bed during the charging process utilizing the new HRA system. Alumina beads of 6 mm were filler materials and air was HTF with inlet temperature of 75°C for proof of concept. The present paper focuses on two aims: (1) utilizing CFD models to analyze flow and temperature profiles in the packed bed; (2) comparing the model results to experimental results published in a previous HRA flow study and to traditional axial flow. Two HRA configurations were considered based on previous experimental designs, one with uniform holes in the central pipe (R1) and one with gradients in the hole sizes to promote even flow from the central pipe into the bed (R2). The numerical results agree with the experimental results in both cases. The HRA system performance depends on the flow profile created by the hole designs, and it can perform better than the axial flow depending on the design of the radial pipe. Design R2, which promotes even flow from the central pipe into the bed, has higher charging efficiency than standard axial flow methods. For HRA design R2 at 0.0048 m3/s (7 SCFM, standard cubic feet per minute), numerical results for charging efficiency were 75.5% versus 73.8% for traditional axial flow. For HRA design R2 at 0.0061 m3/s (9 SCFM), numerical charging efficiency was 80.5% versus 78.1% for traditional axial flow. These results are consistent with experimental data.

Exploring swirling flow dynamics: Unsupervised machine learning in Maxwell hybrid nanofluid convection over an exponentially stretching cylinder with non-linear radiation effects

This article analyses the flow of Maxwell hybrid nanofluid induced by an exponentially stretching and rotating cylinder. The presence of non-linear convection, non-linear radiation, and magnetic field is also assumed. The factors covered in the study has a wide spectrum of application in various disciplines, and therefore we analyse the influence of different flow parameters after numerically solving the set of modelled differential equations. A data-free physics-informed neural network using a wavelet activation function is used to approximate the numerical solution. The reliability of the used methodology is validated by comparing the results of the limiting case with the available results. The paper demonstrates the effectiveness of using PINN in an unsupervised fashion to tackle fluid flow problems, showcasing their ability to provide reliable and accurate solutions without the need for extensive datasets. This approach highlights the potential of PINN to address complex fluid dynamics problems by utilizing physical laws within the neural network framework. From the numerical study, it is observed that hybrid nanofluid has a better rate of heat transfer compared to the nanofluid. Furthermore, radiation parameter and maxwell flow parameter is seen to exhibit significant impact of the flow profiles.

Flow Profiling Analysis of a Refractured Tight Oil Well Using Distributed Temperature Sensing

Flow Profiling Analysis of a Refractured Tight Oil Well Using Distributed Temperature Sensing

Melting rheology of Prandtl Eyring hybrid nanofluid flow with slip condition past a Riga Wedge through Darcy-Forchheimer medium

The current matter examines the 2D flow of Prandtl Eyring hybrid (Al2O3+Cu/SA) nanoliquid through a porous media with a velocity slip mechanism along the melted Riga wedge. A combination of Alumina (Al2O3) and Copper (Cu) nanoparticles in a sodium alginate (SA) base liquid is called a hybrid nanofluid. Furthermore, the physical meaning of the flow behavior is explored with Darcy-Forchheimer. Heat sink/source, nonlinear thermal energy, and viscous dissipation, applications all need the computation of heat transference. The current flow problem is modelled in the system of highly nonlinear PDEs based on flow assumptions. We use an appropriate similarity transformation to turn these PDEs into ODEs. We simulate the obtained paired nonlinear higher-order ODEs employing the ideas from the bvp4c Matlab scheme. With the help of the graphics, several physical dimensionless factors are discussed and their unique effects on the flow profile are shown. One of the study's most notable findings is that applying boundary slip and Riga impact can increase velocity because of weak electromagnetic forces. At lower velocities, wedge flow through a Darcy-Forchheimer medium is primarily driven by viscous resistance under Darcy's law, with little in the way of inertial forces. It is also noteworthy that the temperature differential, thermal radiation, nanoparticle volume percentage, and Eckert number all enhance the nanoliquid thermal profile in both Prandtl Eyring fluid and hybrid nanofluid. The Nusselt number is increased for both the melting and fluid parameters.

Superb microvascular imaging for assessment of post‐cesarean myometrial blood flow from 1 to 4 weeks after operation: A preliminary study

AbstractPurposeTo evaluate superb microvascular imaging for measuring puerperal myometrial microvascular blood flows at incisional sites following cesarean delivery.MethodsTwenty postpartum women (singleton births) were studied: 10 with cesarean and 10 with transvaginal deliveries. All cesarean cases were first operational delivery with lower uterine incision, repaired with double‐layer suture. At 1 and 4 weeks postpartum, the uterus was delineated using transvaginal ultrasonography with superb microvascular imaging. Separate regions of interest were created for anterior myometrium of the isthmus and the body. The microvascular flow profile in three circular sampling points placed in a region of interest was quantified and expressed as vascular density. The vascular density ratio of the uterine isthmus to the body was compared between one and four weeks for both groups. Wilcoxon's signed‐rank test was used to assess statistical significance (set at p < 0.05).ResultsIn cesarean deliveries, the vascular density ratio of the uterine isthmus to the body increased from 1 (median: 0.51, range: 0.30–0.68) to 4 weeks (0.99, 0.85–1.60), whereas no changes were noted in transvaginal deliveries.ConclusionSuperb microvascular imaging can effectively measure myometrial microvascular blood flow recovery at cesarean incision sites, indicating its potential as a tool for monitoring postpartum wound healing.

Numerical investigation on the VIV response of the flexible cylindrical structures subjected to non-linearly varying shear flow

Vortex-induced vibration (VIV) of flexible cylinders is an important phenomenon in ocean structures, which may cause fatigue damage and structural failure of offshore structures. Much literature has extensively explored VIV of flexible cylinders under various flow conditions, such as uniform and linearly varying shear flow. However, real scenarios in most cases involve non-uniform, non-linearly varying shear flow profiles. Hence, it is important to investigate the VIV response of the flexible cylindrical structures subjected to non-linearly varying shear flow profiles. This study employs a wake oscillator model (WOM) that simulates the VIV response of the flexible cylinder under the action of non-linearly varying shear flow velocity profiles. The flexible cylinder subjected to linearly varying sheared flow velocity profiles not only overpredicts but also underpredicts the VIV responses compared to the non-linearly varying sheared flow profile, which represents the real scenario. The VIV mode number for the flexible cylinder subjected to non-linear shear flow was found to have a non-linear relationship with that of linear shear flow. The VIV response of the flexible cylinder subjected to a linearly varying shear flow profile exhibits more travelling wave behaviour compared to non-linear shear flow. The location of the maximum VIV response of the structure having the same aspect ratio (L/D) and shear parameter (β), was different for linear and non-linear flow profiles across the span. The time and frequency domain responses showed a shift in the frequency band. The results obtained from the numerical simulations give better insights into the vibrational behaviour of flexible cylinders in realistic flow environments.

Different Types of Milk Flow Curves and Factors Affecting Milkability in Buffalo Species

Buffaloes are characterized by longer teats and teat canals and stronger muscular resistance of the teat wall than cattle; it is necessary to have a high vacuum level to open the teat canal and begin milk ejection. In buffalo milking management, milk yield, and flow profiles are essential parameters to record and evaluate. The milking machine is a critical point, and the characteristics of the milking vacuum and the pulsation rate are closely related to milk flow observations. In Italy, the most used vacuum levels are 44-46 kPa (range 40-53 kPa). The data on the milkability traits of the Mediterranean Italian breed made it possible to classify eight different types of milk flow curves due to anatomical, physiological, and management differences. This study aims to evaluate the main factors influencing milkability in dairy buffaloes. The results suggest the detachment of the milking cluster to reduce the decreasing and blind phases with the following advantages: reduction of the total milking time and consequently of the worker's time, improvement of the farmer's profitability and milk quality through decreasing the incidence of mastitis. Milk ability is influenced by physiological, sanitary, management, and genetic factors. In Mediterranean Italian buffaloes milked with the Automatic Milking System (AMS), a considerable variation in milk ejection and, consequently, in the milk flow curve was found compared to the conventional one, with better pre-stimulation, independent milk ejection for each teat, optimal milking of all quarters. In conclusion, continuous milkability monitoring will help optimize milking practices by reducing labor time and increasing farmers’ income through better milk quality. In addition, the identification of buffaloes with desirable types of milk flow curves could be helpful for buffalo breeders’ associations to address farmer management and to define potential new breeding objectives.

STEAM INDUCED SHOCKWAVE INTERACTION WITH A SUBMERGED PLATE CONFIGURED AT A RANGE OF INCLINATIONS FROM VERTICAL

Interaction of shock wave and the shear induced vortex across the steam-water layer has been vital in several transportation and chemical industrial processes. Experiments were conducted using a facility including a rectangular chamber, which housed a shock tube in it. Steam was injected into the tube to induce shock wave by bursting the Aluminum diaphragm disk and the shock wave surrounding by the steam-water shear layer induced vortex, exited the shock tube and struck the rectangular steel plate. PIV setup along with the pressure and acoustic emissions sensors were used to characterize the propagation and impingement of the shock wave on the plate as well as the behavior of the reflected shock wave and the vortex ring. In case of a vertical rectangular steel sheet stationed in front of the exit of the shock tube, the central part of the shock wave was found to interact with the central part of the vortex structure and the external part of the shock wave came into contact with the outer part of the vortex structure. Whereas in case of inclined sheet, the shockwave reflected from the sheet, came into collision with the rebound shockwave as well as with the lower portion of the vortex ring largely. However, with the further variation in the angle of inclination (i.e. 30o and larger) fromvertical axis, no further appreciable change was observed in the flow profile except the vortex ring interacted earlier with the rebounded shockwave in the lower region within the neighborhood of the plate than the interaction of the vortex ring with the rebounded shock wave in the upper region of the inclined plate. The pressure and acoustic emission measurements were symmetric with the vertical plate, however, the pressure data was asymmetric when the plate was inclined from vertical. When the angle of inclination changes to 30 degrees from the vertical, the flow becomes more asymmetric as the shockwave and the consequent vortices impinged on the surface of the plate much earlier than the 15 degrees’ inclination case.

Combination of two-fluid model and delayed equilibrium model for the critical flow in a slit

Accurately predicting the mass flux, pressure profile, and velocity profile of the critical flow in a slit is essential for analyzing the breaking process of the liquid phase and calculating the aerosol source term for leak-before-break (LBB) monitoring and Loss of Coolant Accident (LOCA) risk analysis. A new critical flow model combining Two-fluid Model (TFM) and Delayed Equilibrium Model (DEM) is built to get accurate profiles while avoiding the same phase velocity in DEM and the arbitrary critical flow criterion in TFM. The new model is verified using past experiments of the critical flow in a slit. It proves to be accurate in mass flux but not in critical pressure, with maximum relative errors of around 25% in mass flux and around 80% in critical pressure. The new model is optimized for higher accuracy in critical pressure. The empirical equation of saturated phase mass flow rate fraction gradient is optimized by conducting approximate pressure profile calculation and regression analysis. The maximum relative error decreases little while the ratio of critical pressure relative errors lying in the range of ±40% increases after optimization. In contrast, the difference in the average abstract relative error of pressure between original TFM-DEM and DEM is much larger, for the maximum relative error of mass flux and critical pressure are around 25% and 110%. The comparison between the original and optimized TFM-DEM proves that the new critical flow model is accurate in mass flux and can be optimized to raise pressure calculation accuracy. The comparison between the original TFM-DEM and DEM proves that the phase velocity difference is the major source of accuracy improvement in the pressure profile.

Formation of a uniform velocity profile in the section of a profiled channel of a reference installation

The velocity profiles in gravity and pressure channels of flow diverters in reference installations in the field of liquid flow and quantity measurements are studied. The design shortcomings of reference installations that do not allow obtaining a flow velocity profile close to uniform in the sections of pressure nozzles over a long period of reference installation operation are described. It is shown that the placement of various straightening devices in the profiled channels and pressure nozzles of flow diverters of reference installations does not lead to obtaining a flow velocity profile close to uniform. An approach to profiling the gravity channel of the flow diverter is proposed, which allows obtaining a velocity profile close to uniform. An experimental justification of the hydraulic efficiency of the geometry of the flow part of the profiled channel of the flow diverter of the EU-3 reference installation from the State Primary Special Standard of Units of Mass and Volume of Liquid in a Flow, Mass and Volume Flow Rates of Liquid GET 63-2019 is presented. The influence of the flow velocity profile shape in the section of the profiled channel of the flow switch and the stability of the main hydro- and thermodynamic parameters of the water flow (flow rate, absolute pressure and temperature) in the pressure pipeline on the metrological characteristics of the reference installation is substantiated. Experimental studies of the velocity profile of the free-flow water flow in the section of the profiled channel are performed using high-speed total pressure meters and Pitot tubes. Close to uniform water flow velocity profiles in the section of a profiled channel were obtained for free flow in the range of investigated Reynolds numbers Re=(35...300)·103. The results of maintaining the stability of the specified value of the mass flow rate of water over a long period of time are presented. The equations for calculating the mass of water during transient processes are written down, taking into account the change in the thickness of the water flow and flow rate from zero to specified values. The presented approach and the obtained results are useful for manufacturers of reference installations and are relevant in the design, creation and modernization of profiled channels of flow switches of reference installations.

Pectin-chitosan hydrogels with modified properties for the encapsulation of strawberry phenolic compounds

Pectin-chitosan hydrogels with blends of low (50–190 kDa) and medium (310–395 KDa) molecular weight (MW) chitosan (LC and MC, respectively) were developed, and their characteristics were investigated before and after the encapsulation of an aqueous strawberry extract. The pectin to total chitosan mass ratio, the composition of the strawberry extract and the MW of chitosan greatly affected the interactions between pectin and chitosan at different pH values. More specifically, blends of low and medium MW chitosan improved the stability of the strawberry-gels in acidic conditions compared to their corresponding MC-gels, showed better flow and texture profiles, as well as slower release of phenolic compounds during in vitro digestion compared to the only stable LC-gel. Therefore, by manipulating the length range of chitosan chains would allow the formation of pectin-chitosan hydrogels with improved properties for the development of functional food products.

Role of the constriction angle on the clogging by bridging of suspensions of particles

Confined flows of particles can lead to clogging, and therefore failure, of various fluidic systems across many applications. As a result, design guidelines need to be developed to ensure that clogging is prevented or at least delayed. In this Letter, we investigate the influence of the angle of reduction in the cross section of the channel on the bridging of semidilute and dense non-Brownian suspensions of spherical particles. We observe a decrease of the clogging probability with the reduction of the constriction angle. This effect is more pronounced for dense suspensions close to the maximum packing fraction where particles are in contact in contrast to semidilute suspensions. We rationalize this difference in terms of arch selection. We describe the role of the constriction angle and the flow profile, providing insights into the distinct behavior of semidilute and dense suspensions. Published by the American Physical Society 2024

Thermophoretic particle deposition and double-diffusive mixed convection flow in non-Newtonian hybrid nanofluids past a vertical deformable sheet

PurposeThermophoresis deposition of particles is a crucial stage in the spread of microparticles over temperature gradients and is significant for aerosol and electrical technologies. To track changes in mass deposition, the effect of particle thermophoresis is therefore seen in a mixed convective flow of Williamson hybrid nanofluids upon a stretching/shrinking sheet.Design/methodology/approachThe PDEs are transformed into ordinary differential equations (ODEs) using the similarity technique and then the bvp4c solver is employed for the altered transformed equations. The main factors influencing the heat, mass and flow profiles are displayed graphically.FindingsThe findings imply that the larger effects of the thermophoretic parameter cause the mass transfer rate to drop for both solutions. In addition, the suggested hybrid nanoparticles significantly increase the heat transfer rate in both outcomes. Hybrid nanoparticles work well for producing the most energy possible. They are essential in causing the flow to accelerate at a high pace.Practical implicationsThe consistent results of this analysis have the potential to boost the competence of thermal energy systems.Originality/valueIt has not yet been attempted to incorporate hybrid nanofluids and thermophoretic particle deposition impact across a vertical stretching/shrinking sheet subject to double-diffusive mixed convection flow in a Williamson model. The numerical method has been validated by comparing the generated numerical results with the published work.

Antagonistic behavior of brain networks mediated by low-frequency oscillations: electrophysiological dynamics during internal–external attention switching

Antagonistic activity of brain networks likely plays a fundamental role in how the brain optimizes its performance by efficient allocation of computational resources. A prominent example involves externally/internally oriented attention tasks, implicating two anticorrelated, intrinsic brain networks: the default mode network (DMN) and the dorsal attention network (DAN). To elucidate electrophysiological underpinnings and causal interplay during attention switching, we recorded intracranial EEG (iEEG) from 25 epilepsy patients with electrode contacts localized in the DMN and DAN. We show antagonistic network dynamics of activation-related changes in high-frequency (> 50 Hz) and low-frequency (< 30 Hz) power. The temporal profile of information flow between the networks estimated by functional connectivity suggests that the activated network inhibits the other one, gating its activity by increasing the amplitude of the low-frequency oscillations. Insights about inter-network communication may have profound implications for various brain disorders in which these dynamics are compromised.

9 to 5 or a new‐normal? Cluster analysis of pre and post pandemic vehicle and cycle diurnal flow profiles

AbstractCommuting traffic associated with the “9 to 5” workday shaped the morning and evening peaks across the world. The COVID‐19 pandemic led to unprecedented changes in travel behaviour such as an increase in cyclists and telecommuting, where employees worked from home during lockdown periods. Transport modellers, planners and policy makers need to know whether the 9 to 5 has returned, or we have entered a “New‐normal” of more flexible working arrangements and increased cycling, key for delivering sustainability targets. In this research, the unsupervised machine learning technique k‐means clustering investigates temporal patterns across the day and week, comparing the pre‐ and post‐pandemic era across both motorised vehicles and bicycles. Results show that the total daily traffic flow has returned to pre‐pandemic volumes, but more spread across the day. Mondays and Fridays have less‐pronounced peaks compared to pre‐pandemic, having implications for air quality modelling and assessment, traffic management and transport planning. Meanwhile, cycling has increased in volume and the time‐of‐day people are travelling has changed. Policy makers need to consider whether the additional capacity on the road, brought about by reduced peak traffic, could be reallocated to make roads safer for and reduce delay to cyclists, contributing towards net zero goals.

Computational fluid dynamics modeling of gas bubble separation efficiency in downhole separators and vertical / inclined annulus: An experimental validation and analysis

This study presents a comprehensive investigation into gas bubble separation efficiency in a vertical downhole separator using computational fluid dynamics (CFD) modeling, which is validated with experimental data. The research aims to provide detailed insights into the separation mechanisms and the factors affecting them, such as liquid velocity, gas bubble sizes, and positions. Using an Euler-Lagrange multiphase model, the behavior of individual gas bubbles within the liquid-gas mixture was simulated. The results demonstrate that separation efficiency decreases as the liquid flow rate increases. This reduction in efficiency occurs because the increased liquid flow rate drags more bubbles within the stream, making it harder for them to separate. The separation process is primarily driven by the buoyancy force acting on the bubbles and the velocity profile of the liquid flow. Smaller bubbles, which tend to be near the casing wall, separate more efficiently, while larger bubbles are predominantly located between the second and third quarters of the annulus space. The "quarters" refer to radial divisions from the casing wall to the tubing wall, with the first quarter closest to the casing wall and the fourth quarter closest to the tubing wall. The study introduces a nonlinear regression model based on the numerical results to predict liquid slug separation efficiency. This model, validated against experimental data, accurately predicts separation efficiency and offers a robust methodology for estimating the efficiency of gravity-driven gas-liquid separators. This methodology is crucial for refining separator design and improving the operational efficiency of downhole separation systems, which are vital for enhancing the performance of pumping systems in oil and gas wells. The contributions of this study include a deeper understanding of the downhole separation process, the development of a simplified model for assessing bubble separation efficiency, and the potential application of the proposed methodology to different gas-liquid separator designs and inclination angles, thereby informing the design and operation of downhole separation systems.

Development of a local wall concentration model for the design of single pass tangential flow filtration (SPTFF) systems with viral vector surrogates

Recent advances in the use of viral vectors for gene therapy has created a need for efficient downstream processing of these novel therapeutics. Single-pass tangential flow filtration (SPTFF) can potentially improve final product quality via reductions in shear, and it can increase manufacturing productivity via simple implementation into continuous/intensified processes. This study investigated the impact of variations in pressure and flow rate along the length of the membrane on overall SPTFF performance. Constant-flux filtration experiments at feed fluxes from 14 to 420 L/m2/h (Reynolds numbers <20) were performed using Pellicon® 3 TFF cassettes with fluorescent nanoparticles as model viral vectors. The location of nanoparticle accumulation shifted towards the filter outlet at high conversion and was also a function of the permeate flow configuration. These phenomena were explained using a newly developed concentration polarization model that predicts the distribution in local wall concentration over the length of the membrane. The model accurately captured the observed nanoparticle accumulation trends, including the effects of the permeate flow profile (co-current, divergent, or convergent flow) on nanoparticle accumulation within the SPTFF module. Nanoparticle accumulation at moderate conversion was more uniform using convergent flow, but nanoparticle accumulation at 80 % conversion (5x concentration factor) can be minimized using a divergent flow configuration. The local wall concentration model was also used to evaluate the critical flux by assuming that fouling occurs when the nanoparticle concentration at any point along the membrane surface exceeds 15 % by volume. These results provide important insights for the design and operation of SPTFF technology for inline concentration of viral vectors.