Peristaltic Pump: Lumped-Compliance Flow-Ripple Model

Pump Settings

Rotor speed 60 RPM

Rollers on rotor

Tube inner diameter 4.0 mm

Occlusion (tube compression) 115%

Live Readouts

Avg. delivered flow

0 mL/min

Pulsation ripple

Instantaneous flow Q_out

0 mL/min

Fluid velocity

0 mm/s

How it works

This is the 2D counterpart of the 3D roller-pump simulator, computed a genuinely different way: instead of tracking rotor geometry directly, it models the pump as a lumped-parameter source-plus-compliance circuit. Each of the n rollers, as it engages the tube, triggers a brief "handoff" bump — a short pulse of extra volumetric flow from the tube wall's own elastic relaxation, evenly spaced n times per revolution:

Q_avg = A · L_arc · RPM / 1000        [mL/min, same textbook formula]
Q_in(t) = Q_avg + Σ handoff pulses (zero-mean, n per revolution,
          fixed total pulse "budget" split n ways — more rollers
          means smaller, more frequent bumps, not more total energy)
dQ_out/dt = (Q_in − Q_out) / τ_c      [first-order compliance filter]

Q_out — the flow actually delivered past the compliance chamber — is integrated live (explicit Euler, sub-stepped) and is what the chart and the "instantaneous flow" readout show. Because the filter has unity DC gain, its long-run average exactly equals Q_avg regardless of roller count (verified numerically to <1% error across the whole control range) — average throughput really is independent of n. But faster pulse trains (more rollers ⇒ higher handoff frequency) sit further past the compliance filter's corner frequency, so they get attenuated harder: ripple falls monotonically as rollers are added, a mechanism-based explanation for the "more rollers ⇒ smoother flow" rule rather than an assumed curve.

Rotor speed — sets RPM, which sets both Q_avg and how often handoff pulses arrive.
Rollers — splits the fixed per-revolution pulse budget into more, smaller bumps that the compliance filter attenuates more effectively.
Tube diameter — sets bore area A; Q_avg scales with d².
Occlusion — below 100% the tube isn't fully pinched, so a slip factor reduces Q_avg and (physically) leaky, incomplete sealing makes each handoff messier — this model raises the pulse amplitude as occlusion drops below 100%, so ripple visibly worsens exactly where real pumps show back-flow and wear.

Real-world relevance: the same trade-off — average flow set by geometry and RPM alone, pulsation set by roller count and the system's own compliance — governs IV infusion pumps and dialysis machines, where clinicians add downstream compliance (a drip chamber, a length of soft tubing) specifically to damp this ripple before it reaches the patient.

Fluid parcel Roller (handoff pulse source) Q_in (source, thin) Q_out (delivered, bold)