FILM - Flow Instability & Lung Mechanics Simulator

Double soap-bubble experiment

t = 0.0 s

Small radius

3.50 cm

Large radius

10.00 cm

Pressure gradient

0 Pa

Flow rate

0 mL/s

Tube resistance

1.0×

Estimated collapse

~15 s

Bubble and tube geometry and collapse timeline

Young-Laplace + Poiseuille

Predicted observation	Mechanism

Origin of ΔP and factors that control collapse

Pressure correction: for a soap bubble, ΔP means the excess internal pressure over the surrounding external pressure: ΔP = P_inside − P_outside. Between two connected bubbles, the driving pressure is the difference between their internal pressures.

Soap bubble excess pressure: ΔPbubble = Pinside − Poutside = 4γ/R
Driving pressure between connected bubbles: ΔPdrive = 4γ(1/Rsmall − 1/Rlarge)
Poiseuille flow through the connecting tube: Q = πa⁴ΔPdrive / (8ηL)
Single-bubble limit to atmosphere: T = 2ηLR₀⁴ / (a⁴γ)

Connecting tube	Bore	Length	Predicted single-bubble collapse for R₀ = 1 cm

Adult alveolar units: resistance, compliance and time constants

t = 0.0 s

Unit A

Open

Unit B

Open

Airway pressure

5.0

Dynamic / branch R

1.0×

Dynamic τ = R × C

0.35 s

Teaching point

Stabilized

Controls

clinical parallel

Scenario

PEEP 5 cmH2O

Driving pressure 8 cmH2O

Respiratory rate 12/min

Airway segment / generation zone medium conducting

Weibel-inspired weighting: the same local narrowing has different total impact depending on branching generation and parallel cross-sectional area.

Airway diameter 2.0 mm

Airway length 20 mm

Compliance index 1.0×

Tissue tethering 60%

Clinical parallel: halving airway diameter raises local Poiseuille resistance 16-fold. Total airway resistance also depends on airway generation: medium conducting airways contribute disproportionately, whereas very distal narrowing is partly buffered by parallel branching. During expiration in asthma/COPD/emphysema, dynamic airway compression can further increase resistance and prolong τ.

Physiology interpretation

adult lung

Condition	Dominant mechanical change	Interpretation in this simulator
Normal surfactant	Low resistance, normal elastance, normal surfactant.	Units cycle smoothly; surfactant, recoil and interdependence stabilize unit size.
Emphysema	Loss of lung elastance and elastic recoil; high compliance; small-airway collapse during expiration.	Units inflate easily but empty slowly. Low recoil reduces the pressure available for expiration, favoring air trapping, dynamic hyperinflation and auto-PEEP.
Lung fibrosis	High elastance, low compliance, small stiff lung units.	Higher pressure is required to generate the same volume change. Rapid shallow breathing is mechanically favored; excessive driving pressure increases regional stress.
Pulmonary edema	Increased fluid in interstitium/alveoli; reduced compliance; impaired surfactant function; airway narrowing may coexist.	Units become stiff and unstable. Opening pressure rises; fluid-filled or foam-narrowed airways increase resistance and worsen time-constant heterogeneity.
ARDS-like injury	Compliance is often sigmoidal rather than uniformly low: low at low volumes due to atelectasis/derecruitment, relatively better in the recruited baby-lung range, and low again at high volumes due to overdistension. Surfactant dysfunction, edema, regional collapse, and heterogeneous opening pressures coexist.	Some units open late and close early. PEEP may move lung units from the lower flat part of the pressure-volume curve into the recruited middle range, but excessive pressure shifts already-open units toward the upper flat overdistended range.
Pneumoperitoneum	Diaphragm pushed cephalad; chest-wall elastance rises; FRC falls.	The same airway pressure produces less lung expansion. Dependent units approach closing volume earlier, increasing atelectasis risk and ventilation heterogeneity.
Steep Trendelenburg	Abdominal contents load the diaphragm; dependent lung compression increases.	FRC falls further and dependent units derecruit. Higher airway pressure may be needed for ventilation, but the risk of overdistending non-dependent units remains.
Abdominal compartment syndrome	Markedly increased intra-abdominal pressure; severe diaphragm displacement; high chest-wall elastance.	Airway pressures may rise even when transpulmonary distending pressure is inadequate. Ventilation becomes difficult because the respiratory system is stiff from outside the lung.
Morbid obesity	Low FRC, increased chest-wall load, airway closure in dependent regions.	Small reductions in lung volume cause airway closure and atelectasis. Recruitment and PEEP may improve mechanics, but time constants vary across regions.

Separate airway and fluid-overload interpretations

Condition	Primary variable affected	Physiology interpretation
Bronchospasm	Airway radius falls acutely.	Poiseuille resistance rises with 1/r⁴. Even mild narrowing can sharply prolong expiratory time constant and create incomplete emptying before the next breath.
Asthma	Reversible bronchoconstriction plus mucosal edema and secretions.	Severe expiratory flow limitation creates long, uneven time constants. Slow units remain inflated during expiration, causing gas trapping, auto-PEEP and high work of breathing.
COPD	Fixed small-airway disease plus emphysema-related loss of recoil.	Resistance is high and expiratory driving pressure is low. This combination strongly favors dynamic hyperinflation, especially when respiratory rate is high.
Pulmonary edema	Compliance falls; small airways may narrow from peribronchial cuffing and fluid/foam.	This is not pure bronchospasm. The dominant problem is stiff, wet lung units with impaired gas exchange; added airway narrowing increases resistance and heterogeneity.

Model used

Alveolar teaching equation: P = 2T/R
Mead model stress concentration: stress multiplier ≈ max(Vopen/Vsmall, 1)^(2/3)
Weibel model branch-weighted resistance: Rbranch ≈ Wgeneration × (2 mm / d)^4 × (L / 20 mm)
Starling-resistor expiratory compression: Rdynamic = Rbranch × compression factor during expiration
Dynamic expiratory time constant: τdynamic = Rdynamic × C
Elastance = 1 / compliance. Loss of elastance means weak recoil and high compliance; high elastance means stiff, low-compliance lung.
Baseline heterogeneity: Unit B is intentionally initialized about 35% larger than Unit A to represent normal inter-unit size variation and to make regional stress/emptying differences visible.

FILMFlow Instability & Lung Mechanics Simulator