Physical basis of the dependence of blood viscosity on tube radius

1960 ◽  
Vol 198 (6) ◽  
pp. 1193-1200 ◽  
Author(s):  
Robert H. Haynes
Keyword(s):  
Flow Rate ◽  
Blood Viscosity ◽  
Apparent Viscosity ◽  
Hind Limb ◽  
Marginal Zone ◽  
Tube Wall ◽  
Effective Diameter ◽  
Tube Radius ◽  
Vascular Bed ◽  
A Cell

Two theories are applied to measurements of the decrease in apparent viscosity of blood in narrow tubes (Fahraeus-Lindqvist effect). First, the effect may be attributed to the presence of unsheared laminae in the fluid (sigma phenomenon), and it was found that the thickness of such laminae must vary between 3.5 µ at 10% hematocrit and 34 µ at 80%. Alternatively, the effect may be caused by a cell-free marginal zone adjacent to the tube wall, which would have to be 6 µ thick at 10% hematocrit and 1.5 µ at 80%. There is a slight suggestion in the data that the effect may be reversed as the flow rate approaches zero (i.e. the apparent viscosity rises in small tubes). Finally, a method is proposed for calculating the effective diameter of a vascular bed, and it was found to be 55 µ for a dog's hind limb.

scholarly journals Effects of water salinity on the foam dynamics for EOR application

2021 ◽  
Author(s):  
Svetlana Rudyk ◽  
Sami Al-Khamisi ◽  
Yahya Al-Wahaibi
Keyword(s):  
Flow Rate ◽  
Liquid Flow ◽  
Apparent Viscosity ◽  
Liquid Flow Rate ◽  
Salinity Range ◽  
Porous System ◽  
Foam Formation ◽  
Total Flow ◽  
Total Flow Rate ◽  
Foam Flow

AbstractFactors limiting foam injection for EOR application are exceptionally low rock permeability and exceedingly high salinity of the formation water. In this regard, foam formation using internal olefin sulfonate is investigated over a wide salinity range (1, 5, 8, 10, and 12% NaCl) through 10 mD limestone. The relationships between pressure drop (dP), apparent viscosity, liquid flow rate, total flow rate, salinity, foam texture, and length of foam drops at the outlet used as an indicator of viscosity are studied. Foaming is observed up to 12% NaCl, compared to a maximum of 8% NaCl in similar core-flooding experiments with 50 mD limestone and 255 mD sandstone. Thus, the salinity limit of foam formation has increased significantly due to the low permeability, which can be explained by the fact that the narrow porous system acts like a membrane with smaller holes. Compared to the increasing dP reported for highly permeable rocks, dP linearly decreases in almost the entire range of gas fraction (fg) at 1–10% NaCl. As fg increases, dP at higher total flow rate is higher at all salinities, but the magnitude of dP controls the dependence of apparent viscosity on total flow rate. Low dP is measured at 1% and 10% NaCl, and high dP is measured at 5, 8, and 12% NaCl. In the case of low dP, the apparent viscosity is higher at higher total flow rate with increasing gas fraction, but similar at two total flow rates with increasing liquid flow rate. In the case of high dP, the apparent viscosity is higher at lower total flow rate, both with an increase in the gas fraction and with an increase in the liquid flow rate. A linear correlation is found between dP or apparent viscosity and liquid flow rate, which defines it as a governing factor of foam flow and can be considered when modeling foam flow.

scholarly journals Quantitative Monitoring of Dynamic Blood Flows Using Coflowing Laminar Streams in a Sensorless Approach

2021 ◽  
Vol 11 (16) ◽  
pp. 7260
Author(s):  
Yang Jun Kang
Keyword(s):  
Blood Flow ◽  
Flow Rate ◽  
Blood Viscosity ◽  
Measurement Errors ◽  
Present Method ◽  
Test Fluid ◽  
Constant Flow Rate ◽  
Rbc Aggregation ◽  
Sinusoidal Flow ◽  
Analytical Expressions

Determination of blood viscosity requires consistent measurement of blood flow rates, which leads to measurement errors and presents several issues when there are continuous changes in hematocrit changes. Instead of blood viscosity, a coflowing channel as a pressure sensor is adopted to quantify the dynamic flow of blood. Information on blood (i.e., hematocrit, flow rate, and viscosity) is not provided in advance. Using a discrete circuit model for the coflowing streams, the analytical expressions for four properties (i.e., pressure, shear stress, and two types of work) are then derived to quantify the flow of the test fluid. The analytical expressions are validated through numerical simulations. To demonstrate the method, the four properties are obtained using the present method by varying the flow patterns (i.e., constant flow rate or sinusoidal flow rate) as well as test fluids (i.e., glycerin solutions and blood). Thereafter, the present method is applied to quantify the dynamic flows of RBC aggregation-enhanced blood with a peristaltic pump, where any information regarding the blood is not specific. The experimental results indicate that the present method can quantify dynamic blood flow consistently, where hematocrit changes continuously over time.

Motion of an array of drops through a cylindrical tube

1998 ◽  
Vol 358 ◽  
pp. 1-28 ◽  
Author(s):  
C. COULLIETTE ◽  
C. POZRIKIDIS
Keyword(s):  
Stokes Flow ◽  
Apparent Viscosity ◽  
Numerical Solutions ◽  
Initial Period ◽  
Mathematical Formulation ◽  
Axisymmetric Flow ◽  
Circular Cross Section ◽  
Cylindrical Tube ◽  
Boundary Integral ◽  
Tube Radius

We study the pressure-driven transient motion of a periodic file of deformable liquid drops through a cylindrical tube with circular cross-section, at vanishing Reynolds number. The investigations are based on numerical solutions of the equations of Stokes flow obtained by the boundary-integral method. It is assumed that the viscosity and density of the drops are equal to those of the suspending fluid, and the interfaces have constant tension. The mathematical formulation uses the periodic Green's function of the equations of Stokes flow in a domain that is bounded externally by a cylindrical tube, which is computed by tabulation and interpolation. The surface of each drop is discretized into quadratic triangular elements that form an unstructured interfacial grid, and the tangential velocity of the grid-points is adjusted so that the mesh remains regular for an extended but limited period of time. The results illustrate the nature of drop motion and deformation, and thereby extend previous studies for axisymmetric flow and small-drop small-deformation theories. It is found that when the capillary number is sufficiently small, the drops start deforming from a spherical shape, and then reach slowly evolving quasi-steady shapes. In all cases, the drops migrate radially toward the centreline after an initial period of rapid deformation. The apparent viscosity of the periodic suspension is expressed in terms of the effective pressure gradient necessary to drive the flow at constant flow rate. For a fixed period of separation, the apparent viscosity of a non-axisymmetric file is found to be higher than that of an axisymmetric file. In the case of non-axisymmetric motion, the apparent viscosity reaches a minimum at a certain ratio of the drop separation to tube radius. Drops with large effective radii to tube radius ratios develop slipper shapes, similar to those assumed by red blood cells in flow through capillaries, but only for capillary numbers in excess of a critical value.

scholarly journals Microfluidic-Based Biosensor for Blood Viscosity and Erythrocyte Sedimentation Rate Using Disposable Fluid Delivery System

Micromachines ◽  
2020 ◽  
Vol 11 (2) ◽  
pp. 215
Author(s):  
Yang Jun Kang
Keyword(s):  
Blood Sample ◽  
Erythrocyte Sedimentation Rate ◽  
Flow Rate ◽  
Sedimentation Rate ◽  
Blood Viscosity ◽  
Blood Samples ◽  
Image Intensity ◽  
Fluid Delivery ◽  
Erythrocyte Sedimentation ◽  
Over Time

To quantify the variation of red blood cells (RBCs) or plasma proteins in blood samples effectively, it is necessary to measure blood viscosity and erythrocyte sedimentation rate (ESR) simultaneously. Conventional microfluidic measurement methods require two syringe pumps to control flow rates of both fluids. In this study, instead of two syringe pumps, two air-compressed syringes (ACSs) are newly adopted for delivering blood samples and reference fluid into a T-shaped microfluidic channel. Under fluid delivery with two ACS, the flow rate of each fluid is not specified over time. To obtain velocity fields of reference fluid consistently, RBCs suspended in 40% glycerin solution (hematocrit = 7%) as the reference fluid is newly selected for avoiding RBCs sedimentation in ACS. A calibration curve is obtained by evaluating the relationship between averaged velocity obtained with micro-particle image velocimetry (μPIV) and flow rate of a syringe pump with respect to blood samples and reference fluid. By installing the ACSs horizontally, ESR is obtained by monitoring the image intensity of the blood sample. The averaged velocities of the blood sample and reference fluid (<UB>, <UR>) and the interfacial location in both fluids (αB) are obtained with μPIV and digital image processing, respectively. Blood viscosity is then measured by using a parallel co-flowing method with a correction factor. The ESR is quantified as two indices (tESR, IESR) from image intensity of blood sample (<IB>) over time. As a demonstration, the proposed method is employed to quantify contributions of hematocrit (Hct = 30%, 40%, and 50%), base solution (1× phosphate-buffered saline [PBS], plasma, and dextran solution), and hardened RBCs to blood viscosity and ESR, respectively. Experimental Results of the present method were comparable with those of the previous method. In conclusion, the proposed method has the ability to measure blood viscosity and ESR consistently, under fluid delivery of two ACSs.

Comparison of Geometries for Diffusion-Based Extraction of Dimethyl Sulphoxide From a Cell Suspension

2008 ◽  
Vol 2 (2) ◽  
Author(s):  
Katie Fleming Glass ◽  
Clara Mata ◽  
Ellen K. Longmire ◽  
Allison Hubel
Keyword(s):  
Microfluidic Device ◽  
Flow Rate ◽  
Channel Length ◽  
Dimethyl Sulphoxide ◽  
Hematopoietic Stem ◽  
Cryoprotective Agents ◽  
Multi Stage ◽  
Flow Geometry ◽  
A Cell ◽  
Flow Configurations

Microfluidics can be used in a variety of medical applications. In this study, a microfluidic device is being developed to remove cryoprotective agents from cells post thaw (1–150ml). Hematopoietic stem cells are typically cryopreserved with Dimethyl sulphoxide (DMSO), which is toxic upon infusion. Conventional methods of removing DMSO results in cells losses of 25–30%. The overall objective of this study is to characterize the influence of flow geometry on extraction of DMSO from a cell stream. For all the flow geometries analyzed, flow rate fraction, Peclet Number, and channel geometry had the greatest influence on extraction of DMSO from the cell stream. The range of flow rate fractions that can achieve the desired removal ranges between 0.10 and 0.30. Similarly, the range of Peclet numbers is 250–2500. Distinct differences in channel length could be observed between the different flow configurations studied. The flow rates and channel geometries studied suggest that clinical volumes of cell suspensions (1–100ml) can be processed using a multi-stage microfluidic device in short periods of time (<1hr).

scholarly journals Localization of primordial germ cells or their precursors in stage X blastoderm of chickens and their ability to differentiate into functional gametes in opposite-sex recipient gonads

Reproduction ◽  
2001 ◽  
pp. 547-552 ◽  
Author(s):  
M Naito ◽  
A Sano ◽  
Y Matsubara ◽  
T Harumi ◽  
T Tagami ◽  
...  
Keyword(s):  
Germ Cells ◽  
Marginal Zone ◽  
Primordial Germ Cells ◽  
Donor Cell ◽  
Same Sex ◽  
White Leghorn Chicken ◽  
Central Disc ◽  
Opposite Sex ◽  
A Cell ◽  
Blastodermal Cells

This study was performed to determine the distribution of primordial germ cells and their precursors in stage X blastoderm of chickens. The blastoderm (Barred Plymouth Rock chickens) isolated from the yolk was separated into three portions: the central disc, the marginal zone and the area opaca. The dissociated blastodermal cells derived from the central disc, marginal zone and area opaca were transferred into a recipient blastoderm (White Leghorn chicken) from which a cell cluster was removed from the centre of the central disc. The manipulated embryos were cultured in host eggshells until hatching. The chicks were raised until sexual maturity and test mated with Barred Plymouth Rock chickens to assess the donor cell contribution to the recipient germline. Germline chimaeric chickens were produced efficiently (46.7%, 7/15) when the blastodermal cells derived from the central disc were transferred into recipient embryos of the same sex, whereas no germline chimaeric chickens were produced when the blastodermal cells derived from the marginal zone or area opaca were transferred into recipient embryos of the same sex (0/12). Germline chimaeric chickens were also produced by transfer of blastodermal cells derived from the central disc (6.7%, 1/15), marginal zone (10.0%, 1/10) or area opaca (11.1%, 1/9) into recipient embryos of the opposite sex. It is concluded that primordial germ cells are induced during or shortly after stage X and that the cells derived from the central disc have the highest potential to give rise to germ cells. Cells derived from the marginal zone and area opaca can also give rise to germ cells, although the frequency is low.

Numerical Argumentation of any Factors for Effecting Flow Property of a Power-Law Gel Propellant in a Converging Injector

2012 ◽  
Vol 170-173 ◽  
pp. 2601-2608
Author(s):  
Xue Li Xia ◽  
Hong Fu Qiang ◽  
Wang Guang
Keyword(s):  
Pressure Drop ◽  
Power Law ◽  
Flow Rate ◽  
Apparent Viscosity ◽  
Volumetric Flow Rate ◽  
Flow Property ◽  
Newtonian Viscosity ◽  
Convergence Angle ◽  
The Mean ◽  
Injector Design

To evaluate the effect of a converging injector geometry, volumetric flow rate and gallant content on the pressure drop, the velocity and viscosity fields, the governing equations of the steady, incompressible, isothermal, laminar flow of a Power-Law, shear-thinning gel propellant in a converging injector were formulated, discretized and solved. A SIMPLEC numerical algorithm was applied for the solution of the flow field. The results indicate that the mean apparent viscosity decreases with increasing the volumetric flow rate and increasing the gallant content results in an increase in the viscosity. The results indicate also that the convergence angle can produce additional decrease in the mean apparent viscosity of the fluid. The mean apparent viscosity decreases significantly with increasing the convergence angle of the injector, and its value is limited by the Newtonian viscosity η∞. The effect of the convergence angle on the mean apparent viscosity is more significant than the effect of the volumetric flow rate and the gallant content on the mean apparent viscosity. Additional decreasing the viscosity results in increasing the pressure drop with increasing convergence angle. It is important to injector design that the viscosity decreasing and the pressure drop increasing are took into account together.

Blood viscosity in small tubes: effect of shear rate, aggregation, and sedimentation

1987 ◽  
Vol 253 (3) ◽  
pp. H540-H547 ◽  
Author(s):  
W. Reinke ◽  
P. Gaehtgens ◽  
P. C. Johnson
Keyword(s):  
Shear Rate ◽  
Marginal Zone ◽  
Viscosity Reduction ◽  
Shear Rates ◽  
Glass Tubes ◽  
A Cell ◽  
Vertical Glass ◽  
Vertical Tubes ◽  
Aggregation Tendency ◽  
Cell Free Layer

Apparent viscosity was determined in vertical glass tubes (ID 30.2-132.3 microns) with suspensions of human red cells in A) serum, B) saline containing 0.5 g/100 ml albumin, C) plasma, and D) plasma containing Dextran 250 at a feed hematocrit of 0.45. Pressure-flow relationships were obtained in a range of pseudo-shear rates (mu) between 0.15 and 250 s-1. Relative viscosities in the nonaggregating suspensions (A and B) were found to increase monotonically with decreasing mu. The Fahraeus-Lindqvist effect was present in the entire range of mu. In the two aggregating suspensions (C and D), viscosities increased initially in larger but not small tubes with declining mu and fell in all tubes at some characteristic mu (usually below 10 s-1). Viscosity reduction was greater in the larger tubes and in suspensions with greater aggregation tendency. With suspension D, the Fahraeus-Lindqvist effect was eliminated in the lowermost shear-rate range. The cell-free marginal zone increased in width (to a maximum of approximately 40% of tube radius) as viscosity declined. Measurements of viscosity and cell-free marginal zone were also performed with suspension C in tubes mounted in horizontal position. In contrast to vertical tubes, a monotonic increase in viscosity was found with decreasing mu, associated with cell sedimentation and development of a cell-free layer only in the upper portion of the tubes.

Sign in / Sign up

Export Citation Format

Share Document