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Fåhræus Effect
The Fåhræus effect is the decrease in average concentration of red blood cells in human blood as the diameter of the glass tube in which it is flowing decreases. In other words, in blood vessels with diameters less than 500 micrometers, the hematocrit decreases with decreasing capillary diameter. The Fåhræus effect definitely influences the Fåhræus–Lindqvist effect, which describes the dependence of apparent viscosity of blood on the capillary size, but the former is not the only cause of the latter. History Robin Fåhræus was a pathologist at the University of Uppsala in Sweden, and his interest in the suspension stability of blood and later in hemorheology was motivated by the desire to understand the clinical effects of abnormalities in the aggregation and flow behavior of the formed elements. The aim was to ascertain whether blood obeyed the law of Poiseuille (Hagen–Poiseuille equation). It was Hess in 1915 who proved that blood obeys the poiseuille law at high f ...
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Non-newtonian Fluid
A non-Newtonian fluid is a fluid that does not follow Newton's law of viscosity, i.e., constant viscosity independent of stress. In non-Newtonian fluids, viscosity can change when under force to either more liquid or more solid. Ketchup, for example, becomes runnier when shaken and is thus a non-Newtonian fluid. Many salt solutions and molten polymers are non-Newtonian fluids, as are many commonly found substances such as custard, toothpaste, starch suspensions, corn starch, paint, blood, melted butter, and shampoo. Most commonly, the viscosity (the gradual deformation by shear or tensile stresses) of non-Newtonian fluids is dependent on shear rate or shear rate history. Some non-Newtonian fluids with shear-independent viscosity, however, still exhibit normal stress-differences or other non-Newtonian behavior. In a Newtonian fluid, the relation between the shear stress and the shear rate is linear, passing through the origin, the constant of proportionality being the coefficient ...
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Hemorheology
Hemorheology, also spelled haemorheology (from Greek ‘αἷμα, ''haima'' 'blood' and rheology, from Greek ῥέω ''rhéō'', ' flow' and -λoγία, ''-logia'' 'study of'), or blood rheology, is the study of flow properties of blood and its elements of plasma and cells. Proper tissue perfusion can occur only when blood's rheological properties are within certain levels. Alterations of these properties play significant roles in disease processes. Blood viscosity is determined by plasma viscosity, hematocrit (volume fraction of red blood cell, which constitute 99.9% of the cellular elements) and mechanical properties of red blood cells. Red blood cells have unique mechanical behavior, which can be discussed under the terms erythrocyte deformability and erythrocyte aggregation. Because of that, blood behaves as a non-Newtonian fluid. As such, the viscosity of blood varies with shear rate. Blood becomes less viscous at high shear rates like those experienced with increased flow ...
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Hemodynamics
Hemodynamics or haemodynamics are the dynamics of blood flow. The circulatory system is controlled by homeostatic mechanisms of autoregulation, just as hydraulic circuits are controlled by control systems. The hemodynamic response continuously monitors and adjusts to conditions in the body and its environment. Hemodynamics explains the physical laws that govern the flow of blood in the blood vessels. Blood flow ensures the transportation of nutrients, hormones, metabolic waste products, oxygen, and carbon dioxide throughout the body to maintain cell-level metabolism, the regulation of the pH, osmotic pressure and temperature of the whole body, and the protection from microbial and mechanical harm. Blood is a non-Newtonian fluid, and is most efficiently studied using rheology rather than hydrodynamics. Because blood vessels are not rigid tubes, classic hydrodynamics and fluids mechanics based on the use of classical viscometers are not capable of explaining haemodynamics. The st ...
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Cell-free Marginal Layer Model
In small capillary hemodynamics, the cell-free layer is a near-wall layer of plasma absent of red blood cells since they are subject to migration to the capillary center in Poiseuille flow. Cell-free marginal layer model is a mathematical model which tries to explain Fåhræus–Lindqvist effect mathematically. Mathematical modeling Governing equations Consider steady flow of blood through a capillary of radius R. The capillary cross section can be divided into a core region and cell-free plasma region near the wall. The governing equations for both regions can be given by the following equations: : \frac=\frac\frac(\mu_c r \frac); 0 \le r\ \le R-\delta\, : \frac=\frac\frac(\mu_p r \frac); R-\delta\le r\ \le R\ \, where: :\Delta P is the pressure drop across the capillary :L is the length of capillary : u_c is velocity in core region : u_p is velocity of plasma in cell-free region : \mu_ is viscosity in core region : \mu_ is viscosity of plasma in cell-free region :\delt ...
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Blood Plasma
Blood plasma is a light amber-colored liquid component of blood in which blood cells are absent, but contains proteins and other constituents of whole blood in suspension. It makes up about 55% of the body's total blood volume. It is the intravascular part of extracellular fluid (all body fluid outside cells). It is mostly water (up to 95% by volume), and contains important dissolved proteins (6–8%; e.g., serum albumins, globulins, and fibrinogen), glucose, clotting factors, electrolytes (, , , , , etc.), hormones, carbon dioxide (plasma being the main medium for excretory product transportation), and oxygen. It plays a vital role in an intravascular osmotic effect that keeps electrolyte concentration balanced and protects the body from infection and other blood-related disorders. Blood plasma is separated from the blood by spinning a vessel of fresh blood containing an anticoagulant in a centrifuge until the blood cells fall to the bottom of the tube. The blood plasma is t ...
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Blood Flow
Hemodynamics or haemodynamics are the dynamics of blood flow. The circulatory system is controlled by homeostatic mechanisms of autoregulation, just as hydraulic circuits are controlled by control systems. The hemodynamic response continuously monitors and adjusts to conditions in the body and its environment. Hemodynamics explains the physical laws that govern the flow of blood in the blood vessels. Blood flow ensures the transportation of nutrients, hormones, metabolic waste products, oxygen, and carbon dioxide throughout the body to maintain cell-level metabolism, the regulation of the pH, osmotic pressure and temperature of the whole body, and the protection from microbial and mechanical harm. Blood is a non-Newtonian fluid, and is most efficiently studied using rheology rather than hydrodynamics. Because blood vessels are not rigid tubes, classic hydrodynamics and fluids mechanics based on the use of classical viscometers are not capable of explaining haemodynamics. The ...
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Laminar Flow
In fluid dynamics, laminar flow is characterized by fluid particles following smooth paths in layers, with each layer moving smoothly past the adjacent layers with little or no mixing. At low velocities, the fluid tends to flow without lateral mixing, and adjacent layers slide past one another like playing cards. There are no cross-currents perpendicular to the direction of flow, nor eddies or swirls of fluids. In laminar flow, the motion of the particles of the fluid is very orderly with particles close to a solid surface moving in straight lines parallel to that surface. Laminar flow is a flow regime characterized by high momentum diffusion and low momentum convection. When a fluid is flowing through a closed channel such as a pipe or between two flat plates, either of two types of flow may occur depending on the velocity and viscosity of the fluid: laminar flow or turbulent flow. Laminar flow occurs at lower velocities, below a threshold at which the flow becomes turbulent. Th ...
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Steady Flow
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modelling fission weapon detonation. Fluid dynamics offers a systematic structure—which underlies these practical disciplines—that embraces empirical and semi-empirical laws derived from flow measurement and used to solve practical problems. The solution to a fluid dynamics problem typically involves the calculation of various properties of the fluid, such as flow velocity, pressure, density, and temperature, as functions of space and time. Be ...
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Colloid
A colloid is a mixture in which one substance consisting of microscopically dispersed insoluble particles is suspended throughout another substance. Some definitions specify that the particles must be dispersed in a liquid, while others extend the definition to include substances like aerosols and gels. The term colloidal suspension refers unambiguously to the overall mixture (although a narrower sense of the word ''suspension'' is distinguished from colloids by larger particle size). A colloid has a dispersed phase (the suspended particles) and a continuous phase (the medium of suspension). The dispersed phase particles have a diameter of approximately 1 nanometre to 1 micrometre. Some colloids are translucent because of the Tyndall effect, which is the scattering of light by particles in the colloid. Other colloids may be opaque or have a slight color. Colloidal suspensions are the subject of interface and colloid science. This field of study was introduced in 1845 by Itali ...
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Rouleaux
Rouleaux (singular is rouleau) are stacks or aggregations of red blood cells (RBCs) that form because of the unique discoid shape of the cells in vertebrates. The flat surface of the discoid RBCs gives them a large surface area to make contact with and stick to each other; thus forming a rouleau. They occur when the plasma protein concentration is high, and, because of them, the ESR (erythrocyte sedimentation rate) is also increased. This is a nonspecific indicator of the presence of disease.Oxford Textbook of Medicine Conversely, the presence of rouleaux is a cause of disease because it will restrict the flow of blood throughout the body because capillaries can only accept free-flowing singular and independent red blood cells. The aggregations, also known as "clumping," form as an allergic reaction to certain antibiotics and not necessarily because of disease. Conditions that cause rouleaux formation include infections, multiple myeloma, Waldenström's macroglobulinemia, infla ...
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Hagen–Poiseuille Equation
In nonideal fluid dynamics, the Hagen–Poiseuille equation, also known as the Hagen–Poiseuille law, Poiseuille law or Poiseuille equation, is a physical law that gives the pressure drop in an incompressible and Newtonian fluid in laminar flow flowing through a long cylindrical pipe of constant cross section. It can be successfully applied to air flow in lung alveoli, or the flow through a drinking straw or through a hypodermic needle. It was experimentally derived independently by Jean Léonard Marie Poiseuille in 1838 and Gotthilf Heinrich Ludwig Hagen, and published by Poiseuille in 1840–41 and 1846. The theoretical justification of the Poiseuille law was given by George Stokes in 1845. The assumptions of the equation are that the fluid is incompressible and Newtonian; the flow is laminar through a pipe of constant circular cross-section that is substantially longer than its diameter; and there is no acceleration of fluid in the pipe. For velocities and pipe diameters a ...
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