Seminar on

Bio-Fluid Mechanics

Submitted by SupervisorRituparn Singh Dr. Varun Goel14M306 MED

Contents

1. What is bio-fluid mechanics?2. Air flow in lungs3. Blood Rheology4. Flow in Heart5. Flow in Arteries

The Circulation System

Air flow in Lungs

Air flow in Lungs

Blood Rheology

1. Shear models of blood• Bingham• Casson (linear)• Casson (non-linear)• Herschel-Bulkeley

Blood Rheology

2. Blood viscosity models-• Maxwell • Oldroy-B

Fåhræus–Lindqvist effect

region near the wall

1p d dvr

L r dr dr

μc , vc

μp , vp

R

4

411 (1 / ) (1 / )

8 p cp

R pQ R

L

the volume flow

Cell-free marginal layer model

Flow in Heart

Flow in Arteries

• Macrovessels

• Microvessels

Pulsatile Flow

• a flow with periodic variations is known as pulsatile flow

• Womersley number

Wommersley equations• The equation for the motion of a viscous liquid in a cylindrical tube (general form):

• Arterial pulse = periodic function the sum of harmonics

• The solution:

– J0(xi3/2) is a Bessel function of the first kind of order zero and complex argument– y=r/R

2

2

1 1w w p w

r r r z t

3/ 220

2 3/ 20

( )*1

( )i tJ yiA R

w ei J i

The flow velocity pulse and the arterial pressure pulse (femoral artery of a dog).

Heavy physical Mild physical Sedentary work Sleep

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