Pressure drop coefficient of laminar Newtonian flow in axisymmetric diffusers

The laminar flow of Newtonian fluids in axisymmetric diffusers has been numerically investigated to evaluate the pressure-loss coefficient as a function of Reynolds number, diffusion angle and expansion ratio. The numerical simulations were carried out with a finitevolume based code using non-orthogonal collocated grids and second order accurate differencing schemes to discretize all terms of the transport equations. The calculations were carried out for Reynolds numbers between 2 and 200, diffusion angles from 0 to 90 and expansion ratios of 1.5 and 2 and the data are presented in tabular form and as correlations. A simplified 1D theoretical analysis helped explain the various contributions to the loss coefficient and its difference relative to the reversible pressure variation due to differences between the actual and fully developed friction losses, distortions of the velocity profiles and pressure non-uniformity upstream and downstream of the expansion section

Nanogel formation of polymer solutions flowing through porous media

A gelation process was seen to occur when Boger fluids made from aqueous solutions of polyacrylamide (PAA) and NaCl flowed through porous media with certain characteristics. As these viscoelastic fluids flow through a porous medium, the pressure drop across the bed varies linearly with the flow rate, as also happens with Newtonian fluids. Above a critical flow rate, elastic effects set in and the pressure drop grows above the low-flow-rate linear regime. Increasing further the flow rate, a more dramatic increase in the slope of the pressure drop curve can be observed as a consequence of nanogel formation. In this work, we discuss the reasons for this gelation process based on our measurements using porous media of different sizes, porosity and chemical composition. Additionally, the rheological properties of the fluids were investigated for shear and extensional flows. The fluids were also tested as they flowed through different microfluidic analogues of the porous media. The results indicate that the nanogel inception occurs with the adsorption of PAA molecules on the surface of the porous media particles that contain silica on their surfaces. Subsequently, if the interparticle space is small enough a jamming process occurs leading to flow-induced gel formation

Label-free multi-step microfluidic device for mechanical characterization of blood cells: Diabetes type II

The increasing interest to establish significant correlations between blood cell mechanical measurements and blood diseases, has led to the promotion of microfluidic devices as attractive clinical tools for potential use in diagnosis. A multi-step microfluidic device able to separate red and white blood cells (RBCs and WBCs) from plasma and simultaneously measure blood cells deformability (5 and 20% of hematocrit) is presented in this paper. The device employs passive separation based on the cross-flow filtration principle, introduced at each daughter channel. At the outlets, hyperbolic geometries allow single-cell deformability analysis. The device was tested with blood from five healthy and fifteen diabetic type II voluntary donors. The results have shown that WBCs have lower deformability than RBCs, and no significant differences were observed in WBCs from healthy and pathological blood samples. In contrast, RBCs have shown significant differences, with pathological cells exhibiting lower deformability. Shear rheology has shown that blood from patients with type II diabetes has higher viscosity than blood from healthy donors. This microfluidic device has demonstrated the ability to reduce cell concentration at the outlets down to 1%, an ideal cell concentration for assessing the blood cells deformability, under healthy and pathological conditions. The results provide new insights and quantitative information about the hemodynamics of in vitro type II diabetes mellitus RBCs. Thus, such device can be a promising complement in clinical diagnosis and biological research as part of an integrated blood-on-a-chip system.This work was supported by Projects NORTE-01-0145-FEDER- 028178, NORTE-01-0145-FEDER-029394, NORTE-01-0145-FEDER- 030171 funded by COMPETE2020, NORTE2020, PORTUGAL2020, and FEDER. This work was also supported by Fundação para a Ciência e a Tecnologia (FCT) under the strategic grants UIDB/04077/2020 and UIDB/00532/2020. D. Pinho and V. Faustino acknowledge the Ph.D. scholarships SFRH/BD/89077/2012 and SFRH/BD/99696/2014, respectively, both provided by FCT. Susana Catarino thanks FCT for her contract funding provided through 2020.00215.CEECIND. F. T. Pinho is thankful to FCT for financial support through projects LA/P/0045/2020 of the Associate Laboratory in Chemical Engineering (ALiCE) and projects UIDB/00532/2020 and UIDP/00532/2020 of Centro de Estudos de Fenómenos de Transporte.info:eu-repo/semantics/publishedVersio

Thermocapillary motion of a Newtonian drop in a dilute viscoelastic fluid

In this work we investigate the role played by viscoelasticity on the thermocapillary motion of a deformable Newtonian droplet embedded in an immiscible, otherwise quiescent non-Newtonian fluid. We consider a regime in which inertia and convective transport of energy are both negligible (represented by the limit condition of vanishingly small Reynolds and Marangoni numbers) and free from gravitational effects. A constant temperature gradient is maintained by keeping two opposite sides of the computational domain at different temperatures. Consequently the droplet experiences a motion driven by the mismatch of interfacial stresses induced by the non-uniform temperature distribution on its boundary. The departures from the Newtonian behaviour are quantified via the “thermal” Deborah number, De T and are accounted for by adopting either the Oldroyd-B model, for relatively small De T, or the FENE-CR constitutive law for a larger range of De T. In addition, the effects of model parameters, such as the concentration parameter c=1−β (where β is the viscoelastic viscosity ratio), or the extensibility parameter, L 2, have been studied numerically using a hybrid volume of fluid-level set method. The numerical results show that the steady-state droplet velocity behaves as a monotonically decreasing function of De T, whilst its shape deforms prolately. For increasing values of De T, the viscoelastic stresses show the tendency to be concentrated near the rear stagnation point, contributing to an increase in its local interface curvature

A review of hemorheology : measuring technologies and recent advances

Significant progress has been made over the years on the topic of hemorheology, not only in terms of the development of more accurate and sophisticated techniques, but also in terms of understanding the phenomena associated with blood components, their interactions and impact upon blood properties. The rheological properties of blood are strongly dependent on the interactions and mechanical properties of red blood cells, and a variation of these properties can bring further insight into the human health state and can be an important parameter in clinical diagnosis. In this article, we provide both a reference for hemorheological research and a resource regarding the fundamental concepts in hemorheology. This review is aimed at those starting in the field of hemodynamics, where blood rheology plays a significant role, but also at those in search of the most up-to-date findings (both qualitative and quantitative) in hemorheological measurements and novel techniques used in this context, including technical advances under more extreme conditions such as in large amplitude oscillatory shear flow or under extensional flow, which impose large deformations comparable to those found in the microcirculatory system and in diseased vessels. Given the impressive rate of increase in the available knowledge on blood flow, this review is also intended to identify areas where current knowledge is still incomplete, and which have the potential for new, exciting and useful research. We also discuss the most important parameters that can lead to an alteration of blood rheology, and which as a consequence can have a significant impact on the normal physiological behavior of blood

Label-free multi-step microfluidic device for mechanical characterization of blood cells: diabetes type II

The increasing interest to establish significant correlations between blood cell mechanical measurements and blood diseases, has led to the promotion of microfluidic devices as attractive clinical tools for potential use in diagnosis. A multi-step microfluidic device able to separate red and white blood cells (RBCs and WBCs) from plasma and simultaneously measure blood cells deformability (5 and 20% of hematocrit) is presented in this paper. The device employs passive separation based on the cross-flow filtration principle, introduced at each daughter channel. At the outlets, hyperbolic geometries allow single-cell deformability analysis. The device was tested with blood from five healthy and fifteen diabetic type II voluntary donors. The results have shown that WBCs have lower deformability than RBCs, and no significant differences were observed in WBCs from healthy and pathological blood samples. In contrast, RBCs have shown significant differences, with pathological cells exhibiting lower deformability. Shear rheology has shown that blood from patients with type II diabetes has higher viscosity than blood from healthy donors. This microfluidic device has demonstrated the ability to reduce cell concentration at the outlets down to 1%, an ideal cell concentration for assessing the blood cells deformability, under healthy and pathological conditions. The results provide new insights and quantitative information about the hemodynamics of in vitro type II diabetes mellitus RBCs. Thus, such device can be a promising complement in clinical diagnosis and biological research as part of an integrated blood-on-a-chip system.This work was supported by Projects NORTE-01-0145-FEDER-028178, NORTE-01-0145-FEDER-029394, NORTE-01-0145-FEDER-030171 funded by COMPETE2020, NORTE2020, PORTUGAL2020, and FEDER. This work was also supported by Fundacao para a Ciencia e a Tecnologia (FCT) under the strategic grants UIDB/04077/2020 and UIDB/00532/2020. D. Pinho and V. Faustino acknowledge the Ph.D. scholarships SFRH/BD/89077/2012 and SFRH/BD/99696/2014, respectively, both provided by FCT. Susana Catarino thanks FCT for her contract funding provided through 2020.00215.CEECIND. F. T. Pinho is thankful to FCT for financial support through projects LA/P/0045/2020 of the Associate Laboratory in Chemical Engineering (ALiCE) and pro-jects UIDB/00532/2020 and UIDP/00532/2020 of Centro de Estudos de Fenomenos de Transporte

Effect of polymer melt wall slip on the flow balance of profile extrusion dies

This work describes the implementation of the wall slip boundary condition in an in-house developed 3D numerical code based on the Finite Volume Method. For this purpose, several phenomenological models relating the velocity and the shear stress at the wall were implemented. This new feature is verified using a simple case study, by comparing the numerical results with those obtained through the corresponding analytical solution. Then, the potentialities of the new code are illustrated performing flow simulations of a polymer melt in a complex flow channel. The results obtained show that the slip at the wall influences the flow distribution at the die flow channel outlet. Therefore, and to assess the relevance of slippage in the optimal die geometry, the automatic optimization of a die flow channel, required for the production of a specific thermoplastic profile, is performed using both the no-slip and slip boundary conditions, together with two alternative optimization strategies. It is shown that slip favors the flow balance of the dies and also other issues of its performance.The authors gratefully acknowledge funding from Fundação para a Ciência e Tecnologia, FCT (COMPETE Program) under the projects FCOMP-01-0124 - FEDER-010190 (Ref. PTDC / EME - MFE/102729/2008) and FCOMP-01-0124-FEDER-015126 (Refª. FCT PTDC/EME-MFE/113988/2009), and FEDER, via FCT, under the PEst-C/CTM/LA0025/2011 (Strategic Project - LA 25 - 2011-2012)

Hydrodynamic entrance length for laminar flow in microchannels with rectangular cross section

This work presents a detailed numerical investigation on the required development length (L=L/B) in laminar Newtonian fluid flow in microchannels with rectangular cross section and different aspect ratios (AR). The advent of new microfluidic technologies shifted the practical Reynolds numbers (Re) to the range of unitary (and even lower) orders of magnitude, i.e., creeping flow conditions. Therefore, accurate estimations of L at Re≤O(1) are important for microsystem design. At such low Reynolds numbers, in which inertial forces are less dominant than viscous forces, flow characteristics become necessarily different from those at the macroscale where Re is typically much larger. A judicious choice of mesh refinement and adequate numerical methods allowed obtaining accurate results and a general correlation for estimating L, valid in the ranges 0≤Re≤2000 and 0.1≤AR≤1, thus covering applications in both macro and microfluidics.The authors acknowledge the support by CEFT (Centro de Estudos de Fenómenos de Transporte) and Project PTDC/EMS-ENE/3362/2014—POCI-01-0145-FEDER-016665, funded by FEDER funds through COMPETE2020 “Programa Operacional Competitividade e Internacionaliza” (POCI) and by national funds through FCT “Fundac ao para a Ciência e a Tecnologia”, I.P. L.L. Ferrás would also like to thank FCT for financial support through scholarship SFRH/BPD/100353/2014 and projects UIDB/00013/2020 and UIDP/00013/2020. A. Sucena, A. M. Afonso, M. M. Alves and F. T. Pinho are also grateful to FCT for funding through projects UIDB/00532/2020 and UIDP/00532/2020. A. Sucena thanks FCT for the Ph.D. Grant SFRH/BD/115547/201

Parametric study on the three-dimensional distribution of velocity of a FENE-CR fluid flow through a curved channel

In order to better understand the three-dimensional non-Newtonian flow in an 180 degrees curved duct of square cross-section, simulations were carried out considering an incompressible viscoelastic fluid, which follows the non-linear FENE-CR model, having constant shear viscosity. A fully implicit finite-volume method was used for the solution of the governing equations. Numerical simulations were performed for different Reynolds and Weissenberg numbers, and by varying the model parameters, namely the retardation ratio (beta) and the extensibility (L-2). The aim was to analyse the development and distribution of velocity field in the cross-sections along the curved channel and as a consequence to understand the variation of maximum velocity with these parameters. The results reveal complex changes with increasing extensibility and decreasing retardation parameter, which are associated to transition from one to two pairs of vortices in the secondary flow. Comparison with the literature confirms and reveals that the absence of shear-thinning delays this transition

Flow field of non-Newtonian fluids in impinging jets confined by slopping plane walls

An experimental investigation was carried out to characterize the flow field in a liquid impingingjet confined by slopping plane walls and emanating from a rectangular duct for various non-Newtonianfluids. These jets are frequently found in processes within the food and pharmaceutical industries, and theyare formed when a high velocity fluid impinges a solid surface leading to intense levels of heat and masstransfer. The experimental work is complemented by results from a numerical investigation for purelyviscous fluids. This work continues previous research, Cavadas et al (2006), on the same flow geometry forNewtonian fluids in laminar and turbulent flow regimes. Here detailed measurements of mean flow fieldswere carried out by laser-Doppler anemometry at inlet duct Reynolds numbers of Kozicki (1966) (Re*) of200 pertaining to the laminar flow regime. The two non-Newtonian fluids were aqueous solutions of xanthangum (XG) and polyacrylamide (PAA) at weight concentrations of 0.2% and 0.125%, respectively. ForNewtonian fluids, Cavadas et al (2006) found a characteristic three-dimensional helical flow inside therecirculation, starting at the symmetry plane and evolving towards the flat side walls. This helical floweliminates the separated flow region near the side walls and was also visualized in the non-Newtonian cases.Before reaching the flat side walls, the fluid in helical motion exits the recirculation and joins the main flowstream creating a near-wall jet which can be seen as velocity peaks near the walls in the spanwise profiles ofstreamwise velocity. The numerical simulations investigated the roles of shear-thinning and inertia on themain flow characteristics for purely viscous fluids at Reynolds numbers between 10 and 800. The length ofthe recirculation (XR) is constant in the central portion of the channel and decays to zero before reaching theflat side walls. At high Reynolds numbers a slight increase in XR at the edge of the core of the flow isapparent. As expected, inertia increases the length of the recirculation as for Newtonian fluids, but somewhatsurprisingly it also increases the three-dimensional nature of the flow by reducing the size of the central core.Shear-thinning enhances the role of inertia especially at high Reynolds numbers, whereas at low Reynoldsnumbers the behavior is quite similar for all fluids. All flow fields were found to be symmetric relative to x-zand x-y centre plane