Fluids, Surface Tension, Blood Flow

Question 1

Fluids

Answer 1

• Free surface of a liquid is called outside surface contacting with surrounding medium
• The free surface is area on which many specificities of liquids are expressed.

Question 2

Surface Tension

Answer 2

• a force that aspires to screw/decrease the free surface
• At free surface of liquids, surface tension results from the greater attraction of liquid molecules to each other (cohesion interaction) than to the molecules in the air (adhesion interaction)
• The net effect is an inward force at its surface that causes the liquid to behave as if its surface were covered with a stretched elastic membrane
• Thus, the surface becomes under tension from the imbalanced forces
• Surface tension has the dimension of force per unit length, or of energy per unit area

Question 3

Why does water have a high surface tension?

Answer 3

• Because of the relatively high attraction of water molecules for each other through hydrogen bonds
  72. 8 milli newtons per meter at 20 °C
• compared to that of most other liquids. Surface tension is an important factor in the phenomenon of capillarity

Question 4

Surface tension coefficient σ

Answer 4

• The value of σ is specific for a given fluid
• F equals a product of the σ and the length of boundary surface
• σ is equal to the amount of energy required for increase of the boundary surface of the fluid by one unit

F_sur = σ.l

Question 5

Surfactants

Answer 5

• substances that lower surface tension
• Pulmonary surfactant is a surface-active lipoprotein complex (phospholipoprotein) formed by type II alveolar cells
• The proteins and lipids that make up the surfactant have both hydrophilic and hydrophobic regions
• By adsorbing to the air-water interface of alveoli, the main lipid component of surfactant, dipalmitoylphosphatidylcholine (DPPC), reduces surface tension
• Main functions of surfactant are: To increase pulmonary compliance. To prevent atelectasis (collapse of the lung) at the end of expiration

Question 6

Additional pressure (Δp)

Answer 6

• The surface tension is cause for appearance of specific phenomena that arise when liquid is placed in narrow tube or moves within
• Interaction between the liquid and tube causes curvature of the liquid surface
• The curvature determines additional surface pressure
• This pressure is directed perpendicularly to the liquid boundary surface - inward or outward depending on the type of the surface – convex or concave

Question 7

Laplace law

Answer 7

• Additional pressure, Δp, arises on the boundary surface between two fluids if it (boundary) is curved.

Quantitatively additional pressure is measured as:
Δp = 2 σ / r

r– radius of curvature (tube, blood vessel)
σ – coefficient of surface tension – specific property of the given fluid

Question 8

Additional pressure and embolism

Answer 8

• This phenomenon occurs when air bubbles or fat drops enter the blood vessels
• pressure difference that drives blood causes different curvatures on the two opposite sides of the bubble: with smaller radius at low pressure side and bigger at the other side
• Therefore the resulting additional pressure acts against blood stream and at certain value it can equilibrate it causing blockage of vessel.

Question 9

Rheology

Answer 9

• Rheology observes the motion of blood in the cardiovascular system
• Blood belongs to the group of real fluids. These fluids are characterized with changeable density and viscosity.

Question 10

Ideal fluid

Answer 10

Ideal fluid has:

ρ = const.

η=0

ρ = const. η = const. (newtonian)

ρ ≠ const. η ≠ const. (non-newtonian)

Question 11

Motion of fluids

Answer 11

• laminar or turbulent
• each type possesses particular properties such as:
• energy dissipation
• generation of mechanical vibrations
• spatial velocity distribution

Question 12

Laminar blood flow

Answer 12

• Laminar blood flow occurs in most of blood vessels
• It is characterized by:
• Erythrocytes move in parallel layers
• Low energy loss
• No sound is generated

Question 13

Turbulent blood flow

Answer 13

• Vortical motion
• High energy loss
• Sound generation

Turbulent motion is observed in conditions such as:

• Stenosis (blood flow)
• Cardiac shunts (blood flow)
• Upper respiratory tracts inflammation(air flow)

Question 14

Elasticity and blood flow

Answer 14

• Blood vessels are capable to accumulate mechanical energy during blood propagation
• When the heart pumps out a portion of blood, the arterial vessels expand and thus hold potential energy in their walls.
• these expanded walls act upon the blood with elastic forces pushing it toward the capillaries.

Question 15

Reynolds Number, R

Answer 15

• which type of flow will occur depends on the quantity called Reynolds Number, R, evaluated from the fluid properties: density p, velocity v, diameter of stream (cross sectional diameter) d, and the viscosity of fluid η,

R = v. d.p / η

• When viscosity interactions predominate, the motion is smooth – laminar, but if inertial forces determine the stream it will be turbulent. The fluid will move as:

· laminar - when Re < 2000

· transitional - when 2000 < Re < 4000

· turbulent - when Re > 4000

Question 16

Pulse wave

Answer 16

• Elasticity in blood flow provides a smooth time-distribution of energy use up and uniform blood flow
• the elastic deformation propagates along the arterial vessel wall as transverse wave called pulse wave (6-8m/s)

Question 17

Steady flow

Answer 17

steady flow is a fluid flow for which the following relation is satisfied: the product of fluid cross section and velocity is constant along the vessel/pipe.

Question 18

Poisuelle’s law

Answer 18

• At fixed pressure conditions, the flow is dependent on pipe/vessel size only
• small vessels contributes significantly to the flow due to their higher resistance
• Vessel disorders such as stenosis can influence blood stream sizably.
• Regulation of hydrodynamic resistance is accomplished by neuromediators which produce constriction or dilation of small arteries.

Question 19

Flow and pipe/vessel size relation

Answer 19