applied Science

Cohesion and Adhesion

• Cohesion: The force that makes similar molecules stick together, leading to phenomena such as surface tension.

• Water Cohesion: Water molecules exhibit strong cohesion due to hydrogen bonding, forming droplets and creating surface tension, allowing small objects, like a needle, to float on water.

• Mercury Cohesion: Mercury atoms also show strong cohesion, forming rounded beads and flowing as a single mass.

• Adhesion: The force that causes different substances to stick together.

• Water Adhesion: Water can adhere strongly to charged surfaces such as glass; this is responsible for the capillary rise in thin tubes.

• Meniscus Formation: In a thin tube, water adheres to the sides, forming a concave meniscus.

• Meniscus Types:

  • Concave: Water with more adhesion to the sides than cohesion (e.g., water).

  • Convex: Mercury with more cohesion than adhesion.

Surface Tension

• Surface Tension: The elastic tendency of liquids that makes them acquire the least surface area possible. It occurs because of cohesive forces among liquid molecules.

• Water Surface Tension: Water's surface tension allows its surface to act like a stretchy membrane when in contact with other substances.

• Example of Surface Tension: This property enables insects and needles to walk on water.

• Laplace's Law: Expresses the relationship between pressure inside a liquid sphere and surface tension.

  • Formula: $P = \frac{2T}{r}$
    where P = pressure, T = surface tension, and r = radius of the sphere.

• Pressure Dynamics: Pressure inside increases with higher surface tension and decreases as the sphere's size increases.

• Implication of Surface Tension: Surface tension helps form bubbles and droplets; it is reduced by soaps, which improve cleaning effectiveness.

Capillary Action

• Capillary Action: The ability of a liquid to flow in narrow spaces without external forces, sometimes against gravity, also known as capillary motion or wicking.

• Causes of Capillary Action:

  • Cohesion: Liquid molecules stick to each other, maintaining integrity during movement.

  • Adhesion: Liquid molecules stick to solid surfaces, pulling up the liquid in thin tubes.

• Factors Affecting Capillary Action:

  • Liquids rise higher in narrower tubes and with stronger surface tension, but less height is achieved if the liquid is denser.

• Summary: Liquids can move into tiny spaces and thin tubes due to cohesive and adhesive forces.

• Examples of Capillary Action: Occurs with materials like paper, sand, paintbrushes, and in biological contexts such as plants.

• Pressure in Liquid (Static Pressure):

  • Formula: $P_L = h \times d$
    where $h$ is the height of the liquid column and $d$ is the weight density of the liquid.

Principles of Fluid Dynamics

• Pascal's Principle: Liquid pressure is dependent solely on the height of the liquid column and is independent of the container's shape or total volume.

• Buoyancy: The upward force exerted by fluid pressure, enabling objects to float. This principle is based on Archimedes' principle of buoyancy.

• Viscosity: A measure of a fluid's thickness or resistance to flow, dictating how easily it moves.

Humidification in the Respiratory Tract

1. Airway Functions: The nose warms, humidifies, and filters inhaled air.

2. Other parts of the respiratory system (pharynx, trachea, bronchi) also contribute to air warming and humidification but to a lesser extent.

3. Temperature and Humidity by Location:

   • Air at the oropharynx: 34°C, 80-90% humidity.

   • Air at the carina of the trachea: 37°C (body temperature), 100% humidity.

   • At 100% humidity and 37°C, the air contains 44 mg of water per liter and has a water vapor pressure of 47 mmHg.

4. Consequences of Lack of Humidification: Breathing dry gases or bypassing the upper airway can dry out the lungs, thicken mucus, impair airway cleaning, and lead to infections or lung collapse.

5. Humidity Measurements:

   • Absolute Humidity (AH): Actual amount of water vapor in the air.

   • Potential Humidity: Maximum amount of water air can hold.

   • Relative Humidity (RH): Percentage indicating how full the air is with water vapor.

6. Heating Effects on Air: As saturated air is heated, RH decreases because the air can hold more water, even if the actual water amount remains constant.

7. Condensation: Cooling of saturated air results in condensation, which is why ventilator tubing collects water.

8. Importance of Humidification:

   • Most energy in air comes from water vapor.

   • Moist air is energetically favorable, and adding water vapor significantly impacts energy content compared to just changing air temperature.

9. Mucosa Functionality:

   • Mucosal Structure: Composed of cells, a watery layer, and a sticky mucus layer.

   • Mucus Production: Goblet cells and mucus glands produce mucus, which can thicken due to irritation or disease.

   • Cilia: Tiny hair-like structures (200 per airway cell) sweep mucus and debris out of the lungs.

10. Mucociliary Transport: This system traps particles in mucus and clears them out, functioning best when air is warm and humid. The consistency of mucus is crucial for effective ciliary movement.

Protective Mechanisms of the Airway

• Inhalation and Exhalation Benefits: The upper airway helps warm and humidify inspired air, while it recovers heat and moisture during exhalation to protect the lungs.

• Nasal Function: The nose filters, warms, and humidifies air, utilizing warm blood flow and turbulent airflow to condition it. The upper respiratory system is composed of various structures that play crucial roles in breathing and filtering air. These structures include:

  1. Nose: The primary entrance for air.

  • Contains nasal passages lined with mucous membranes to filter, warm, and humidify incoming air.

  • Features nasal hairs that trap larger particles.

  1. Nasal Cavity: Located behind the nose and above the oral cavity.

  • Divided by the nasal septum into two nasal passages.

  • Mucus-covered surfaces help to moisten and warm the air while also trapping pathogens and particles.

  1. Paranasal Sinuses: Air-filled cavities located within the bones surrounding the nasal cavity (frontal, maxillary, ethmoid, and sphenoid sinuses).

  • Reduce the weight of the skull, produce mucus, and help to regulate air pressure.

  1. Pharynx: Also known as the throat, it serves as a pathway for both air and food.

  • Divided into three parts:

    • Nasopharynx: Located behind the nasal cavity; contains adenoids which help in immune response.

    • Oropharynx: Located behind the oral cavity; serves as a passageway for both air and food.

    • Laryngopharynx: The lower part that leads to the larynx and esophagus.

  1. Larynx: Commonly known as the voice box, it is located below the pharynx and connects to the trachea.

  • Functions include sound production, protection of the airway during swallowing, and routing air into the trachea.

  • Contains the vocal cords which vibrate to produce sound.

  1. Epiglottis: A flap of cartilage located at the root of the tongue.

  • Closes over the larynx during swallowing to prevent food aspiration into the airway.

  1. Tonsils: Lymphoid tissues situated in the oropharynx.

  • Help in immune defense against ingested or inhaled pathogens.

  1. Trachea: Extends from the larynx to the bronchi, often considered part of the upper respiratory structure.

  • Reinforced with C-shaped cartilage rings to maintain an open airway and lined with ciliated epithelium to trap foreign particles.

  1. Bronchi and Bronchioles: Branch off from the trachea into each lung, with the primary bronchi leading into the secondary and tertiary bronchi, eventually leading to bronchioles.

  • Involved in further conduction of air and filtration, but primarily part of the lower respiratory tract.

Food does not normally enter the bronchi, which are for breathing. If food is accidentally inhaled, it is more likely to go into the right bronchus because it is wider and more straight than the left one. This is why problems like aspiration pneumonia often occur more in the right lung.

Cohesion and Adhesion of Liquids

Cohesion:

Definition: The force that makes similar molecules stick together, creating phenomena such as surface tension.

Example: Water forms droplets due to coherence among water molecules, enabling small objects to float.

Water Cohesion:

Water molecules are strongly cohesive, which aids in the formation of droplets and contributes to surface tension.

Mercury Cohesion:

Mercury particles exhibit strong cohesion resulting in the formation of rounded beads and flowing as a single mass.

Adhesion

Adhesion:

Definition: The force that causes different substances to stick together, such as water adhering to glass.

Example: Water's strong adhesion to charged surfaces like glass allows it to climb thin tubes, creating a phenomenon called a meniscus, where water sticks to the sides and forms a curved surface.

Concave Meniscus: More adhesion than cohesion (observed with water).

Convex Meniscus: More cohesion than adhesion (observed with mercury).

Surface Tension

Surface Tension:

Definition: The force making the surface of a liquid pull together to form droplets.

Analogy: Acts like a stretchy skin on water, facilitating better cleaning when it comes into contact with other substances.

Examples: Allows insects and needles to stay on water's surface. Surface tension is reduced in the presence of soaps.

Laplace's Law

Laplace's Law:

Law: The pressure inside a liquid sphere increases with higher surface tension and decreases as the sphere's size increases.

Formula: $P = \frac{2T}{r}$

Where P is the pressure, T is the surface tension, and r is the radius of the sphere.

Transmural Pressure

Transmural Pressure:

Definition: The pressure pushing outwards on a blood vessel wall.

Context: If a weak spot develops in an artery, the internal pressure may push on it, causing it to stretch.

As the weak spot’s radius increases, the vessel wall must be stronger to contain the pressure.

Capillary Action

Capillary Action:

Definition: The movement of liquid through narrow spaces or tubes, sometimes even against gravity, also known as capillary motion or wicking.

Mechanism: Caused by both cohesion (liquid sticking to itself) and adhesion (liquid adhering to the walls of the tube).

Factors Affecting Capillary Action:

Liquid rises higher in narrower tubes with stronger surface tension but less so if the liquid is heavier.

Summary of Liquid Movement

Liquids can move into tiny spaces and thin tubes due to their attraction to solid surfaces, facilitating capillary actions.

Examples of Capillary Action:

Observed in materials such as paper, sand, paintbrushes, and plants.

Pressure in Liquids

Pressure Formula: $P = h \times dw$

Where P is the static pressure exerted by the liquid, h is the height of the liquid column, and dw is the liquid weight density.

Pascal's Principle

Pascal's Principle:

Definition: Liquid pressure is determined by the height of the liquid, irrespective of the container's shape or total volume.

Buoyancy

Buoyancy:

Definition: The ability of an object to float due to the upward force exerted by water (referred to as Archimedes’ principle).

Viscosity

Viscosity:

Definition: A measure of how thick a fluid is and its resistance to flow.

Human Humidification Processes

Steps of Human Humidification:

Nose warms, humidifies, and filters the air during inhalation.

The pharynx, trachea, and bronchi contribute to warming and humidifying the air, but to a lesser extent than the nose.

By the time air reaches the oropharynx, it is approximately 34°C and 80-90% humidified.

At the carina (the bifurcation of the trachea), the air reaches 37°C (body temperature) and is completely (100%) humidified.

At 37°C and 100% humidity, the air contains 44 mg of water per liter and has a water vapor pressure of 47 mmHg.

Consequences of Lack of Humidification:

Breathing in dry gases or bypassing the upper airway thickens mucus, reduces airway clearance, and may cause infection or lung collapse.

Humidity Definitions

Absolute Humidity: The actual amount of water vapor in the air.

Potential Humidity: The maximum amount of water vapor air can hold.

Relative Humidity (RH): The percentage indicating how full the air is with water vapor.

Humidity Dynamics:

When saturated air is heated, RH decreases because the air can accommodate more water vapor without an increase in actual water content.

Cooling saturated air leads to condensation.

Importance of Humidification

Most energy in the atmosphere derives from water vapor; moist air contains more energy.

Lining the airway with moisture protects airway tissues and maintains optimal pulmonary function at 37°C and with 100% humidity (BTPS).

At this state, the air contains 44 mg/L of water.

Mucosal Functionality

The mucosal layer of the airway consists of:

Mucosal cells that produce mucus (goblet cells) and a watery layer.

Cilia: Tiny hair-like structures that sweep mucus and debris out of the lungs.

Mucociliary Transport:

Mucus traps particles, and the cilia sweep them out; is most effective with warm and humid air.

Effects of Mucus Consistency: Cilia need the right mucus consistency; overly thick or too watery mucus can hinder airway clearance.

Inspired Gas Conditioning

Inhaled air is conditioned in the respiratory tract, recovering heat and moisture upon exhalation.

Nose Function During Inspiration:

It warms, humidifies, and filters the incoming air using vascular blood flow and turbulence.

Nose Function During Expiration:

Air reaching the fourth and fifth bronchi is fully warmed and humidified, protecting the airway from damage.

Isothermal Saturation Boundary (ISB)

ISB:

Definition: The point where air becomes fully warmed and humidified (37°C and 100% RH); generally occurs around the fourth to fifth bronchi.

Gas Exchange in Lungs

Types of Gas Exchange:

External Respiration: Gas exchange occurring in the lungs (alveoli to blood).

O₂ enters blood; CO₂ moves from blood to lungs.

Internal Respiration: Gas exchange from blood to body tissues.

O₂ goes to cells; CO₂ returns to blood.

Main Functions of Lungs:

Bring O₂ into the body and remove CO₂.

Structure of the Respiratory System

Respiratory Tract Overview:

Extends from the nose to the trachea, comprising several structures responsible for gas flow, filtration, heating, humidity, and smell.

Components of the Upper Airway

Upper Airway Composition:

Nasal cavity, sinuses, oral cavity, pharynx, larynx.

Function of Nasal Cavity:

Filters, warms, and humidifies the air; contains olfactory cells for smell (olfactory epithelium).

Nasal Structures:

External Nares: Nostrils—entry points for air.

Vestibules: The front part just inside nostrils with coarse hair filtering particles.

Turbinates: Curved bones that increase surface area for better conditioning.

Goblet Cells: Produce mucus to trap particles and hydrate incoming air.

Sinus Functions:

Air-filled spaces in the facial bones (frontal, ethmoid, sphenoid, maxillary) that lighten the head and contribute to voice quality.

Components of the Pharynx

Pharynx: The space connecting the nose and mouth to the airway.

Nasopharynx: Air only; contains adenoids for particle trapping.

Oropharynx: Passage for air, food, and liquid; contains palatine tonsils.

Laryngopharynx: Area where airway and digestive tract diverge, uses epiglottis to protect airway during swallowing.

Larynx and Gas Exchange Functionalities

Larynx:

The voice box; keeps airway open and protects the lungs, helps in phonation.

Main Parts:

Thyroid cartilage (Adam's apple), cricoid cartilage, epiglottis (flap separating air and food).

Vallecula: Space between tongue and epiglottis, serves as a landmark for medical procedures such as intubation.

Lower Respiratory Tract

Composition:

Conducting airway: Larger tubes for air transport.

Respiratory airway: Tiny air sacs (alveoli) for gas exchange (O₂ into blood, CO₂ out).

Structure of Trachea:

A tube supporting airflow from the larynx to the lungs, maintained by C-shaped cartilage rings.

Right vs. Left Bronchi:

Right bronchi (20-30°) is straighter; left bronchi (45-55°) is angled, more likely for objects to enter the right.

Gas Exchange and Bronchial Structures

Alveoli Structure:

Type I cells: For gas exchange.

Type II cells: Produce surfactant.

Macrophages: Protect the lungs from pathogens.

Club cells: Contribute to immune defense and surfactant production.

FLEMING Applied Science for RT'S Lecture 8 Fluid Dynamics & Entrainment HLTH 405Lecture Outline

• Apply appropriate scientific knowledge relating to fluid dynamics and gas mixing/entrainment.

• Use the equation to describe resistance to flow.

• Describe factors that affect fluid flow.

• Describe the relationship between laminar and turbulent flow and predict the likelihood of a particular system having turbulent flow.

• Understand the Bernoulli principle and its relation to respiratory therapy with respect to blending gases.

Learning Objectives Concepts:

• Poiseuille’s law

• Reynolds number

• Laminar and turbulent flow

• Torricelli’s Theorem

• Bernoulli principle

• Venturi effect

• Coanda effect

References

1. Kacmarek, R. M., Stoller, J. K., & Heuer, A. J. (2021). Egan's Fundamentals of Respiratory Care E-Book. Retrieved from https://pageburstls.elsevier.com • Chapter 6

2. Cairo, J. (2022). Mosby’s Respiratory Care Equipment, 11th Edition. Retrieved from https://pageburstls.elsevier.com • Chapter 1

Hagen-Poiseuille Equation for Laminar Flow

• Flow = $\frac{\Delta P \pi r^4}{8 \eta l}$

Poiseuille’s Law (commonly known as)

• Resistance to flow is determined by:

  • Viscosity: The more viscous a fluid is, the greater the pressure gradient required to cause it to move through a given tube to produce a specific flow rate.

  • Length: Resistance is directly proportional to the length of the tube.

  • Radius: As the radius decreases by half, resistance increases 16 times.

Effect of Viscosity on Flow

• Two conditions:

  • Nonviscous: $\eta = 0$

  • Viscous: Various flow rates under different viscosities demonstrated.

Flow Rate and Resistance Analysis

• Suppose the original flow rate is 100 cm³/sec.

  • Effects on flow rate when parameters change:

  • Double length -> 50 cm³/sec

  • Double viscosity -> 50 cm³/sec

  • Double pressure -> 200 cm³/sec

  • Double radius -> 1600 cm³/sec

  • Note: A 19% increase in radius will double the volume flow rate!

Influence on Flow Variables

• Flow varies with Pressure: Direct relationship.

• Flow varies with Length: Direct relationship.

• Flow varies with Radius: Direct relationship.

• Flow varies with Viscosity: Direct relationship.

Blood Flow Example

• System: Arteriole to Venule through Arterial and Venous Capillaries.

• Relationship: $V<em>1 = V</em>2$ but velocity slows during branching of capillary bed.

Ohm’s Law for Laminar Flow

• Resistance expressed in H-P equation:

• Flow = $\frac{Pressure}{Resistance}$

  • This is analogous to Ohm’s Law for electric circuits.

Poiseuille's Law and Ohm's Law Comparison

• Poiseuille's Law for smooth flow (laminar flow of fluids):

  • High pressure $P$, Pressure Drop $P_2$, Low pressure, Flow $F$ in cm³/sec, Resistance $R$

• Ohm's Law for electrical circuits:

  • Voltage Drop $V$, Low potential, High potential, Current $I$ in coulombs/sec, Electrical resistance $R$

Transition from Laminar to Turbulent Flow

• Laminar flow transitions to turbulent when specific flow rates and conditions vary.

• Example: Different variables in Niagara River vs. large/small airways.

Factors Affecting Turbulent Flow

• Sharp increases in velocity.

• Changes in viscosity and density of the gas.

• Changes in radius of the tube.

• These factors influence: Reynold’s Number, which indicates the potential for laminar or turbulent flow.

Derivation of Reynolds Number

• $Re = \frac{\rho v d}{\eta}$

  • Where:

  • $\rho$ = density

  • $v$ = velocity

  • $d$ = diameter

  • $\eta$ = viscosity

  • Flow Characterization:

  • Laminar Flow: Re < 2000 (no units)

  • Transitional Flow: 2000 < Re < 3000

  • Turbulent Flow: Re > 3000

Ohm’s Law for Turbulent Flow

• $Flow^2 = \frac{P}{R}$

  • Where $R = \frac{\rho l}{4 \pi r^5}$

Pressure vs. Flow Relationship

• For laminar flow:

  • Pressure varies linearly with flow.

• For turbulent flow:

  • Pressure varies with the square of the flow (exponentially).

Understanding of Fluid Dynamics

• Contributions of three Italian scientists to fluid dynamics:

  • Torricelli: Pressure measurement

  • Bernoulli: Principles governing flight from his uncle's work

  • Venturi: Designed the Venturi device.

Torricelli’s Theorem

• Also known as the Law of Continuity.

• Tube with constant flow rate: changes in tube radius impact fluid velocity.

Law of Continuity

• Cross-sectional area and velocity are inversely related.

• Decreasing area leads to an increase in fluid velocity.

Applications of Torricelli’s Theorem

• Applications include:

  • Cardiac Output in pulmonary and systemic circulation.

  • Maintaining constant PIFR or PEFR in airways.

  • Ventilator circuits delivering constant gas flow.

  • Narrowed coronary arteries due to atherosclerosis.

A Small Occlusion Has a Large Effect

• Examples:

  • Healthy artery: 0% occlusion, 120 mmHg -> 100 cm³/min

  • 20% occlusion: 41 cm³/min at 293 mmHg

  • 50% occlusion: 6.3 cm³/min at 1920 mmHg

  • 80% occlusion: 0.16 cm³/min at 75,000 mmHg

• A 19% decrease in radius results in halving the flow rate!

Bernoulli Principle Overview

• Bernoulli expanded Torricelli's work, adding pressure measurement through manometers at various points in flow.

Bernoulli Principle Explained

• As gas velocity increases in a restriction (per Law of Continuity), kinetic energy rises and pressure energy diminishes.

Bernoulli Equation

• $P<em>1 + \rho gh</em>1 + \frac{1}{2} \rho v<em>1^2 = P</em>2 + \rho gh<em>2 + \frac{1}{2} \rho v</em>2^2$

  • Where:

  • $P$ = pressure

  • $\rho$ = density

  • $g$ = gravity

  • $v$ = velocity

  • $h$ = height.

Bernoulli Example

• Experiment: Take two pieces of paper, blow between them, observe actions explained through Bernoulli’s theorem.

The Bernoulli Principle

• Increasing fluid velocity results in decreased sum of static pressure, potential energy, and internal energy.

• Constriction in a tube leads to pressure drop; fluid's velocity increases while lateral wall pressure decreases.

Bernoulli Principle Illustrated

• Visual representation:

  • Areas of higher pressure correlate with lower speeds and vice versa.

Bernoulli Principle: Energy

• Energy analysis highlights that energy before a constriction equates to energy post constriction.

Venturi Effect Overview

• Venturi conceptualized fluid flow with reduced pressure during constriction leading to increased gas flow.

Application of Venturi

• Conclusion of the discovery: To allow fluid to regain original pressure post-constriction, the downstream tube must return to original diameter with a slight angle.

• Entrainment occurs, leading to greater output flow than the input, proportional to orifice-induced pressure drop.

Applications of Venturi Devices

• Development of entrainment devices such as:

  • Injectors

  • Jets

  • Venturis

Entrainment Definition

• Entrainment: The drawing in of additional flow from another source.

• Factors influencing entrainment include:

  • Size of the orifice

  • Size of the entrainment ports

Application of Venturi – Nebulizer

• Nebulizers combine gas (oxygen) and liquid (water) to provide:

  • Blended gas mixtures

  • Humidity

  • Aerosolized medication.

Application to Nebulizers

• Gas flows create lateral wall pressure in tubes; narrowing the tube increases velocity, subsequently decreasing lateral wall pressure.

Fluid Entrainment Mechanism

• An open tube distal to a constriction allows for atmospherically-pulled fluids (air or liquid) into a primary flow stream.

Jet Nebulizer Function

• In a nebulizer setup, gas flow draws fluid (water) into the gas stream, impacting fluid to disperse it in aerosol form.

Fluidics and Coanda Effect

• Fluidics: The engineering application of hydrodynamic principles in flow systems.

• Coanda Effect: Observed when fluid flows through small orifices with contoured surfaces.

Coanda Effect Explained

• As fluid speed increases, pressure decreases; a pressure differential arises when a stream flows beside a surface, resulting in the stream being pushed against the surface.

Coanda Effect Explained Continued

• The pressure imbalance causes a stream of fluid to adhere to a surface despite curvatures.

How You Get Lift

• The Coanda effect contributes to lift; flow deceleration leads to a drop in pressure, which can’t sustain the weight, resulting in mixing with ambient air.

How You Get Lift: Examples

• Airplane Wing: Slower air creates higher pressure beneath compared to faster air above, creating lift.

• Spinball: Variation in airspeed direction can create lift forces.

Other Applications of Venturi/Bernoulli

• Analyze explanations for:

  • How airplanes achieve flight.

  • The forward movement of sailboats.

  • The phenomenon of shower curtains.

  • Fuel injection in carburetors.

  • Functionality in propane barbecues.

Video Resources

• Reynolds Numbers and Turbulence (Fluid Mechanics - Lesson 11) - YouTube, 15 min

• Viscosity and Poiseuille's Law (Fluid Mechanics - Lesson 10)- YouTube, 10 min

• Additional video resources available in lecture notes.