Presented by:
Anup Paul
C.Sundarraj

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Fluid flow in Biological system
Introduction
• What is blood?
• “Everybody Has It, Every Body Needs It”
• William Harvey in early 16th century focused much of his research on the mechanics of blood flow in the human body.
• blood is essentially the carrier of nutrients and waste to and from the cells, among which oxygen and carbon dioxide are two fundamental components of cellular function
• Blood also has a fundamental participation in the thermal control of the body, by convecting heat to and from the skin.
• Blood circulation in human body is a closed loop. Within this loop, blood requires to be pumped for flowing. Pumping requires energy (pressure-drop), which is provided by the heart
• Do you know?
• In a child, there are 60,000 miles of blood vessels. An adult has 100,000 miles of blood vessels. The blood circulates through the body 1,000 times a day.
• The body contains about 50% water. Blood is 83% water, muscles are 75% water, the brain 74% water, and the bones contain 22% water
• It takes about 20 seconds for a red blood cell to circle the whole body.
• About 8 million blood cells die in the human body every second, and the same number are born each second.
• The human brain contains about 85% water
• Is blood a Non-Newtonian fluid?
• Blood flow has its peculiarities.
• A fundamental property of blood is the viscosity
• Blood affects the power required from the heart to circulate the blood throughout the body
• In some circumstances, blood does not behave as a Newtonian fluid !
• Viscosity of blood changes
depending on size of capillary
it flows through.
• Because of the heterogeneous
character, blood viscosity
behaves differently from
the viscosity of simple liquids.
Apparent blood viscosity, in centiPoise, as function
of blood vessel diameter for 40 % hematocrit. (from [3])
• Is blood a Non-Newtonian fluid?
….continued
• when flowing through very large vessels, much larger than the size of the components of blood, the blood will look like a homogeneous fluid, and present a Newtonian characteristic.
• The blood viscosity varies with the concentration of components (e.g., amount of red blood cells), and with the diameter of the blood vessel
• For laminar flow of a liquid with average velocity U (m/s) through pipes of length L, with circular cross section of diameter D, one could write

Poiseuille’s relationship for viscosity
or ,
the measured viscosity is independent of the capillary size (length or diameter), volume flow rate and applied pressure-drop
• Fahraeus – Lindqvist effect
• Poiseuille’s relationship for viscosity doesn’t hold for blood flow in capillaries, at least in a range of capillary diameters. This is called the Fahraeus – Lindqvist effect,
named after Swedish
haematologists Robert
Sanno Fahraeus and
Johan Torsten Lindqvist
• Fahraeus – Lindqvist effect
…..continued
Result:
• Below a diameter of about 0.3 mm, the viscosity decreases strongly with reduced diameter of the tube.
because of decrease in average concentration of RBC in human blood as the diameter of the capillary in which it is flowing decreases.
• The blood viscosity through 0.03 mm diameter capillary is almost 50% that of 0.3 mm diameter capillary.
• They found the viscosity decreases in small vessels (diameter D < 300μm) to a minimum of 1cP at D = 8μm.
• Amazingly, for further reduction in capillary diameter, for capillaries with D ≤ 8μm, the blood viscosity increases.
because, the RBCs are unable to squeeze through the narrow vessel and restrict the blood flow.
Eye-facts
• The eyes are constantly in motion, even during sleep. Dreaming sleep especially is characterized by constant eye movement known as Rapid Eye Movement or "REM". Tears are normally secreted through two canals near the inner corner of the eyes.
• Your eye will focus on about 50 things per second
Fluid in eye
• The anterior segment of eye is filled with a transparent fluid, aqueous humor and the posterior segment (vitreous body) is occupied by a fluid, vitreous humor.
• Aqueous humor
• ±2.4 microlitre min−1
• Aqueous humor occupying the anterior chamber provides a transparent medium for its optical function
• Regulates the intraocular pressure(2000-2600 Pa).
• pathway for topically applied drugs and for
• nutritional supply to and metabolites removal from avascular cornea.
.Flow in AH
Thermally induced buoyant force
• The basis for AH flow is a temperature difference across the chamber, with a cooler anterior surface (the cornea) and a warmer posterior surface (the iris). Thus, the conventional flow in the anterior chamber is caused by thermal processes
• The fluid dynamics within the eye have an important role in governing the eye’s visual functions. The disturbance in fluid dynamics of the eye contributes to the development of several pathological states
• Temperature distribution through the eye at steady state
Exposure to Radiation
• Eye tissue contains a lot of water, easy to absorb electromagnetic radiation power,
• Under the action of electromagnetic radiation, the temperature of the eye may be raised which may lead to disorders in eye.
• In addition, long-term role of low-intensity electromagnetic radiation, can contribute to visual fatigue, eye discomfort and a sense of dry eyes such phenomena as
Vitreous humor
• Water content to be about 99% by weight.
• The gel structure is produced by a combination of collagen fibers and mucopolysaccharide.
• In most of the studies, it is assumed to be stagnant. But aqueous actually permeates through it.
Mathematical model
• Natural convectional flow of aqueous humor in the anterior chamber of a human eye is treated the flow as viscosity dominated due to its low Reynolds number and driven by buoyancy affects because of the temperature gradient (though small but significant) across the anterior chamber.
• The fluid may be assumed to be a linear viscous fluid with a viscosity, density and expansivity identical to that of water.
• The fluid flow and heat transfer in the anterior chamber is assumed to be governed by the Navier–Stokes equations together with the energy equation with the following restrictions: steady state, laminar flow, constant physical properties, density variations relevant only in the buoyancy terms of the momentum equations (Boussinesq approximation), and fluid Newtonian behavior.
Research
• Fluid flow in eye is predominantly studied to enhance the drug delivery techniques.
• Posterior segment eye diseases are difficult to be cured since it is complicated to reach the drug over there.