The Peristaltic Pump: Pushing Fluid by Squeezing a Tube

How It Works: Occlusion, Trapping, and Restitution

A peristaltic pump has three functional parts and nothing else in contact with the fluid: a flexible tube or reinforced hose, a rigid track (a circular housing bore, usually 180–360° of wrap), and a rotor carrying two or more rollers (also called shoes on large hose pumps). As the rotor turns, each roller presses the tube flat against the track — full occlusion — squeezing it to zero bore at the pinch point.

• Occlusion: the roller crushes the tube shut, isolating the fluid on the discharge side of that pinch from the fluid on the suction side. This is the sealing 'valve' — a moving pinch instead of a check valve.
• Transport: the sealed slug of fluid between two adjacent rollers (or between a roller and the discharge port) is carried forward at the roller's tangential speed.
• Restitution: behind each roller the elastic tube wall springs back to its round cross-section. That expansion creates a partial vacuum that draws the next charge in from the inlet — this is what makes the pump self-priming and able to lift liquid up a dry suction line.

Because a sealed volume is physically carried from inlet to outlet on every roller pass, the pump is positive displacement: flow is (to first order) proportional to speed and independent of discharge pressure, unlike a centrifugal pump whose flow collapses as head rises.

The Governing Flow Equation

The displaced volume per revolution equals the volume of fluid contained in the tube over the length swept between rollers. If the tube bore is d (inside diameter) and the rotor has n rollers on a pitch circle of radius R, then each revolution sweeps a tube length of roughly the wrapped arc. The clean, textbook form is:

Q = (π·d²/4) · L_swept · N · η_v

where Q is volumetric flow (m³/s), π·d²/4 is the tube's cross-sectional area (m²), L_swept is the tube length displaced per revolution (m), N is rotor speed (rev/s), and η_v is volumetric efficiency (0.85–0.98). The per-revolution product (π·d²/4)·L_swept is the displacement or shot volume per rev — a fixed cubic-per-turn constant that makes the pump a natural metering device.

• Worked example: a 6.4 mm (¼ in) bore tube, L_swept ≈ 0.25 m/rev, at N = 100 rpm (1.667 rev/s), η_v = 0.95: area = π·(0.0064)²/4 = 3.22×10⁻⁵ m²; displacement = 3.22×10⁻⁵ × 0.25 = 8.04×10⁻⁶ m³/rev ≈ 8.0 mL/rev; Q = 8.04×10⁻⁶ × 1.667 × 0.95 ≈ 1.27×10⁻⁵ m³/s ≈ 0.76 L/min.
• Flow scales with d² — doubling tube bore quadruples flow at the same rpm, so pumps span microlitres/min to tens of m³/h by swapping tube size and gearing motor speed.
• Because the shot per rev is constant, a stepper- or servo-driven head can dispense a precise dose by counting a fraction of a turn — the basis of laboratory and IV metering.

Occlusion Ratio, Slip, and Volumetric Efficiency

Perfect displacement assumes the roller crushes the tube to a true zero gap. In practice designers set an occlusion ratio ε = (2t − g)/(2t), where t is wall thickness and g is the roller-to-track gap. Values around ε ≈ 0.1–0.2 (10–20 %, a slight over-squeeze past the point where the walls just meet) give a reliable seal; too little occlusion lets fluid slip backward past the pinch, too much crushes the tube and slashes its fatigue life.

• Slip / backflow: if occlusion is incomplete, discharge pressure drives leakage past the roller. This is the dominant η_v loss and it grows with pressure and with fluid thinness — a low-viscosity fluid at high head slips most. Real η_v therefore droops slightly with rising backpressure even though the pump is 'positive displacement.'
• Tube recovery: at high speed the elastomer may not fully spring back before the next roller arrives (viscoelastic lag), so the swept volume falls short. This caps practical speeds at roughly 100–650 rpm depending on tube durometer and bore.
• Pulsation: flow is delivered in slugs, one per roller pass, so the instantaneous rate ripples. Pulsation frequency = n·N; a two-roller head at 200 rpm pulses at ~6.7 Hz. Adding rollers, using a smoothing/pulse-dampener bore geometry, or a twin-tube 180°-offset head reduces ripple — at the cost of more occlusion cycles per unit volume, i.e. faster tube wear.

Torque, Power, and the Occlusion Penalty

The hydraulic power a pump delivers is P_hyd = Q·Δp, where Δp is the pressure rise (Pa). At Q = 1.27×10⁻⁵ m³/s against Δp = 2 bar (2×10⁵ Pa), P_hyd = 2.5 W — trivially small. The shaft power is dominated not by pumping the fluid but by the mechanical work of squeezing the tube flat against its own stiffness on every roller pass.

• Rotor torque T = P_shaft/ω, and P_shaft = P_hyd/η_overall. Overall efficiency is modest — often 30–60% for tube pumps and higher for large hose pumps — because the elastomer hysteresis (energy lost squashing and un-squashing the wall) is pure loss dissipated as heat.
• That squeeze heat is real: continuous high-speed running warms the tube, softening the elastomer, accelerating creep and fatigue, and in extreme cases the rollers are cooled or the pump duty-cycled. Large industrial hose pumps circulate glycerine or lubricant in the casing partly to carry this heat away and lubricate the hose–shoe contact.
• Starting torque can be high because a stationary rotor may have a roller sitting mid-occlusion; drives are sized with margin, and a worm-gear or planetary reducer commonly sets the low output speed while providing the holding torque and self-locking that keeps a dosing head from creeping backward under discharge pressure.

Tube vs Hose: Two Machines Under One Name

The single most important design split is between low-pressure tube pumps and high-pressure hose pumps, and it is set entirely by the wall.

• Tube pumps use a thin, un-reinforced extruded tube (silicone, PVC/Tygon, Viton, Marprene/Pharmed thermoplastic elastomers). Rollers ride on bearings and roll along the tube. Pressure is limited to ~2–3 bar because a thin wall cannot resist the discharge pushing the pinch open. These are the lab, medical, and OEM-dosing pumps: flows from microlitres to a few L/min, tubes snapped into a cassette and replaced in seconds.
• Hose pumps use a thick, multi-layer reinforced hose (nylon or aramid braid in a rubber matrix) that the pump's shoes slide against inside an oil- or glycerine-flooded casing. The hose's own stiffness provides restitution and the reinforcement lets it hold 8–16 bar. These are the heavy-industry machines: mine tailings, filter-press feed, cement grout, sludge, flows to ~80 m³/h through hoses up to ~100 mm bore. A single hose can cost hundreds of dollars but is the only wear part.
• Material choice tracks chemistry and life: silicone is biocompatible and gas-permeable (great for pharma, poor for solvents); Pharmed/Marprene TPE lasts far longer against flexing fatigue for continuous OEM duty; fluoroelastomers resist aggressive solvents; and abrasion-resistant natural-rubber hoses handle slurry.

Sizing, Selection, and Real Hardware

Selection starts from the required flow and pressure, then works backward to tube bore, rotor speed, and material. Because Q ∝ d²·N, the designer trades a bigger bore (more volume per rev, gentler on the tube, lower speed) against a faster, smaller-bore head (compact, but more occlusion cycles and shorter tube life).

• NPSH and lift: a peristaltic pump self-primes because restitution generates suction, and it can lift a dry column to ~9 m (near one atmosphere). But viscous or high-vapour-pressure fluids limit this — if the tube cannot refill fast enough the slug cavitates and flow starves. Slow the pump or upsize the suction tube.
• Viscosity: the pump handles thick media (pastes, ~10,000+ cP) far better than a centrifugal because displacement is mechanical, but refill time rises, so high-viscosity duties run slow.
• Named hardware: Watson-Marlow (originator of the modern lab pump, still the market reference) and its Bredel line of hose pumps; Cole-Parmer Masterflex with its standardized L/S and I/P tube cassettes; Verderflex, Flowrox/LEWA, ProMinent, and Ragazzini in industrial hose duty. Medical infusion (B. Braun, Baxter) and every dialysis machine's blood pump are peristaltic precisely because the blood touches only a disposable, sterile line.

Limits and Failure Modes

Every strength of the peristaltic pump traces back to the same part — the squeezed tube — and so does every weakness. The tube is a consumable in fatigue, and predicting its life is the central maintenance problem.

• Flexural fatigue / spallation: each roller pass fully flattens then restores the wall, one high-strain fatigue cycle. Life is counted in occlusion cycles, not hours: total cycles ≈ n·N·t. A tube rated for, say, a few million to tens of millions of cycles may last weeks at 100 rpm or hours at 600 rpm. Silicone can 'spall' — shedding micro-fragments of inner wall into the fluid — a real contamination hazard in pharma that drives choice toward TPE tubing.
• Tube rupture: the classic catastrophic failure. When the wall finally cracks through, the pumped fluid escapes into the pump head; industrial pumps add a leak/burst detector and hose pumps contain the spill in the flooded casing. Overtightened occlusion, chemical attack, or over-pressure all shorten time-to-rupture.
• Creep and flow drift: the elastomer takes a permanent set, so bore and restitution shrink over time and delivered flow drifts downward — unacceptable for metering unless the head is re-calibrated or the tube swapped on schedule. Precision dosing systems re-zero periodically or use flow feedback.
• Pressure and temperature ceilings: tube pumps simply cannot make high head — beyond ~3 bar the pinch blows open. Hot fluids soften the wall and cut life. And the inherent pulsation can be unacceptable for coating or analytical feeds without a dampener. These are the hard boundaries that send designers to gear, diaphragm, or centrifugal pumps instead.

Peristaltic (tube vs hose) pumps against other positive-displacement and rotodynamic options

Attribute	Tube (low-pressure) peristaltic	Hose (high-pressure) peristaltic	Gear pump	Centrifugal pump
Max discharge pressure	2–3 bar	8–16 bar	20–200 bar	~10 bar/stage
Max flow	~2 m³/h	~80 m³/h	~100 m³/h	»1000 m³/h
Wetted parts	Tube bore only	Hose bore only	Gears, casing, seal	Impeller, casing, seal
Abrasive slurry handling	Poor–fair	Excellent (to 80% solids)	Very poor (wears gears)	Fair (erodes impeller)
Dry-run / self-prime	Indefinite / yes	Indefinite / yes	Seizes / partial	No / no
Shear on fluid	Very low	Low	High	High