Pumps: Principles, Models, and Applications

• Pumps are devices that convert mechanical, pneumatic, thermal, or chemical energy into directed transport, vital for systems from water networks to quantum devices.
• Research employs analytical models, simulations, and optimization techniques to relate drive variables with metrics such as flow rate, pressure, and quantized current.
• Advancements span macro to nanoscale applications, integrating energy efficiency and multi-criteria performance in industrial, microfluidic, and gas-handling pumps.

Pumps are devices or distributed transport structures that generate directed transfer by converting mechanical, pneumatic, thermal, magnetic, electrical, chemical, or internally generated active stresses into sustained motion of a working medium. In the literature represented here, that medium ranges from water in distribution networks and emulsions in electrical submersible pumps to gases in noble-gas recirculation and ultra-high-vacuum systems, liquids in microfluidic architectures, ions in electrochemical cells, and single charges in mesoscopic quantum devices (Wang et al., 2020, Carvalho et al., 2023, Maccarrone et al., 2020, Rossi et al., 2021). Across these domains, pumping is characterized not only by flow rate or current, but also by pressure head, energy cost, radiopurity, quantization accuracy, and the ability to preserve or manipulate the thermodynamic state of the transported medium.

1. Operating principles and conserved quantities

Within hydraulic and microfluidic systems, pumping is commonly formulated through relations between volumetric flow, pressure rise, and energetic expenditure. In water-distribution control, pump hydraulic power is written as $P = (\gamma Q H_p)/(\eta_s \eta_m)$ and interval energy as $E = P \Delta t$, while reciprocating diaphragm pumping is summarized by $Q = \eta_v f V_s$, with $\eta_v$ the volumetric efficiency, $f$ the actuation frequency, and $V_s$ the effective stroke volume. In passive microfluidic architectures, flow is often reduced to a hydraulic-resistance form such as $Q(t)=\Delta P(t)/R_{\mathrm{hyd}}$, which is then coupled to transient capillary, diffusive, or viscoelastic dynamics (Wang et al., 2020, 0802.3070, Alvarez-Braña et al., 2024).

For charge and vacuum pumps, the conserved quantity and the constitutive relation are different but structurally analogous. Single-charge pumps obey the quantization law $I = n e f$, and in parallel operation the total current becomes $I_{\mathrm{total}}=\sum_i n_i e f$ or, for identical devices, $I_{\mathrm{total}} = m n e f$. Ion getter pumps instead are described by throughput and effective pumping speed, with $E = P \Delta t$0 and $E = P \Delta t$1, because the device maintains vacuum by confining electrons in Penning cells and capturing gas species inside the pump body rather than by displacing them to a foreline (Rossi et al., 2021, Yamahata et al., 24 Apr 2025, Maccarrone et al., 2020).

These relations indicate that “pump” is an operational category rather than a single mechanical archetype. Some pumps generate head or displacement by moving membranes, pistons, or impellers; some rectify fluctuations or cyclic drives into directed transport; and some realize quantized particle transfer or permanent gas capture. A plausible implication is that pump theory is unified less by hardware topology than by closure relations linking a drive variable to a transported extensive quantity.

2. Hydraulic and industrial fluid pumps

In large-scale water infrastructure, pumps are embedded in network-constrained optimization and control. Real-time operation of water distribution systems has been posed as a mixed-integer dynamic optimization problem in which the integer number of parallel pumps operating in each station is treated as the control input over a receding horizon. In the Richmond Pruned network, an economic model predictive control formulation minimized total pumping energy cost under time-varying electricity tariffs, tank-level bounds, nodal mass balance, and a switching penalty $E = P \Delta t$2. Closed-loop simulation with EPANET demonstrated tariff-responsive scheduling and reductions in cost per cubic meter ranging from about $E = P \Delta t$3 up to $E = P \Delta t$4 relative to trigger-level control, depending on demand level (Wang et al., 2020).

Centrifugal electrical submersible pumps in oil and gas production are modeled differently because the transported medium is a multiphase mixture whose effective properties vary with water content and emulsion state. A reduced-order ESP model uses the state vector $E = P \Delta t$5 and couples pump flow, shaft dynamics, upstream and downstream line dynamics, and pressure evolution. A physics-informed neural network was used to infer unknown states and parameters such as effective viscosity $E = P \Delta t$6, density $E = P \Delta t$7, bulk modulus $E = P \Delta t$8, and selected pump and pipeline coefficients from intake and discharge pressure measurements. Structural identifiability analysis showed that, with only $E = P \Delta t$9 and $Q = \eta_v f V_s$0 measured, a structurally locally identifiable subset requires prior knowledge of $Q = \eta_v f V_s$1, $Q = \eta_v f V_s$2, and $Q = \eta_v f V_s$3, which places parameter estimation within an explicitly constrained inverse-problem framework rather than a purely data-driven one (Carvalho et al., 2023).

Thermally driven hydraulic pumping also appears in simplified Rankine-like systems. A superheating Rankine pump for possible irrigation use replaces the mechanical pump and turbine of a classical Rankine cycle with a liquid piston and gravity head. In the reported implementation, $Q = \eta_v f V_s$4, the superheated vapor volume was estimated as $Q = \eta_v f V_s$5, hydraulic work per cycle as $Q = \eta_v f V_s$6, and heat input per cycle as $Q = \eta_v f V_s$7 under the paper’s assumptions, implying a thermal-to-hydraulic efficiency of about $Q = \eta_v f V_s$8. With a $Q = \eta_v f V_s$9-minute cycle, the estimated flow rate is about $\eta_v$0, illustrating a low-head, low-complexity pumping mode compatible with concentrated solar heating (Danca, 2018).

3. Microfluidic displacement, peristaltic, and inertial pumps

Membrane and valve mechanics dominate many microscale pumps. A one-side actuating piezoelectric diaphragm micro-pump fabricated in an aluminum case with PDMS valves and diaphragm achieved a measured maximum flow rate of $\eta_v$1 at zero total pump head in the frequency range $\eta_v$2–$\eta_v$3, and a shutoff head of $\eta_v$4 of water for a $\eta_v$5 thick narrow valve. Its performance is governed by the coupled resonance of the diaphragm, the passive PDMS check valves, and the liquid load; experimentally, thinner and narrower valves improved flow, whereas thicker valves reduced displacement and net output (0802.3070).

A pneumatically actuated peristaltic displacement micropump for long-term microfluidic bioreactor perfusion was modeled using Kelvin–Voigt membrane viscoelasticity and channel hydrodynamic resistance. The membrane dynamics were expanded in eigenfunctions, the pressure transients over the chambers were modeled through adiabatic efflux relations, and the instantaneous flow rate was obtained by integrating membrane velocity over the deforming surface. Experimentally, the maximum average output was $\eta_v$6 at $\eta_v$7 and $\eta_v$8, with a chamber diameter of $\eta_v$9, a $f$0 chamber membrane, and $f$1 valves that reduced backflow (Gerasimenko et al., 2016).

At still smaller scales, peristaltic pumping can be implemented without valves through nonreciprocal geometric cycles. A nanoscale design with two localized actuator regions executes a four-step sequence in the two-dimensional shape space $f$2, yielding a net per-cycle flow

$f$3

with $f$4 and $f$5. Coarse-grained molecular dynamics confirmed the predicted directionality and showed an example average flow rate of $f$6, together with an optimal actuation delay. A different soft-matter realization, the magneto-elastic hysteresis peristaltic pump, generates a phase-shifted occlusion sequence from a single pneumatic input; its quasi-static model exhibits a critical hysteresis parameter $f$7, below which the pressure–displacement curve becomes non-monotonic and supports the left-to-right peristaltic phase lag (Farahpour et al., 2013, Park et al., 23 Apr 2026).

Thermal inertial pumps extend the displacement principle into networked microfluidics. In H-shaped silicon/SU8 switchboards, each leg contains a thermal inkjet resistor that nucleates a vapor bubble and produces a per-pulse displaced volume. The network response is captured by a pump matrix $f$8, where the symmetric H geometry reduces $f$9 to two parameters, $V_s$0 and $V_s$1. An experimentally symmetrized matrix yielded $V_s$2 and $V_s$3, allowing dynamic valving, quantitative two-fluid dilution, and three-fluid routing through simple frequency programming. Because the matrix is singular by volume conservation, one pump frequency remains a free parameter in inverse routing problems (Hayes et al., 2018).

4. Passive, active, and evaporation-driven pumps

A recurrent misconception is that pumps necessarily require bulky external power trains. Several microfluidic studies instead use stored thermodynamic, capillary, or biochemical free energy. PDMS degassing-driven micropumps exploit gas reabsorption into vacuum-degassed polymer blocks; for epoxy-coated pumps that suppress leakage through external faces, the front dynamics follow

$V_s$4

and an EPX-S device sustained autonomous flow for $V_s$5 hours, advanced a fluid front by $V_s$6 through a channel of cross-sectional area $V_s$7, moved $V_s$8 in total, and had an average flow rate of about $V_s$9 (Alvarez-Braña et al., 2024).

Evaporation-assisted capillary pumps use a different passive mechanism. A leaf-mimicking micropump combines branched PDMS microchannels, which emulate veins, with a microporous cellulose support, which emulates the mesophyll and stomata. The architecture increased volumetric pumping rate by about sixfold relative to a single-capillary control, achieving $Q(t)=\Delta P(t)/R_{\mathrm{hyd}}$0, corresponding to about $Q(t)=\Delta P(t)/R_{\mathrm{hyd}}$1, and sustaining a pressure head of about $Q(t)=\Delta P(t)/R_{\mathrm{hyd}}$2 of water before cavitation. The paper attributes this gain to distributed irrigation of a large evaporative area, not to a change in the capillary-pressure formula itself (Kumar et al., 2018).

Active-matter pumps replace external hardware with internally generated stress. In active nematic gels composed of microtubules, kinesin motor clusters, ATP fuel, and PEG-induced quasi-2D ordering, triangular hydrogel inclusions break fore–aft symmetry and stabilize a lattice of counter-rotating vortices. The resulting wall-free virtual channels pump in the direction antiparallel to the triangle orientation. Performance collapses when lengths are normalized by the defect spacing $Q(t)=\Delta P(t)/R_{\mathrm{hyd}}$3, with optimum operation near $Q(t)=\Delta P(t)/R_{\mathrm{hyd}}$4 and $Q(t)=\Delta P(t)/R_{\mathrm{hyd}}$5; at least a $Q(t)=\Delta P(t)/R_{\mathrm{hyd}}$6 array is required for robust pumping, disorder beyond about $Q(t)=\Delta P(t)/R_{\mathrm{hyd}}$7 extinguishes it, and the mixing parameter $Q(t)=\Delta P(t)/R_{\mathrm{hyd}}$8 decays from $Q(t)=\Delta P(t)/R_{\mathrm{hyd}}$9 to about $I = n e f$0 after roughly $I = n e f$1 pumping elements (Vélez-Ceron et al., 2024).

Catalytically active pores extend this idea to chemically generated slip. A semi-analytical model of self-diffusioosmotic transport in active pores includes advective transport and an inverse chemical reaction that consumes solute. In fore–aft symmetric pores, pumping can emerge through spontaneous symmetry breaking; when asymmetry is introduced through pore shape or catalytic coating, the flow rate displays discontinuous jumps and hysteresis loops as the asymmetry parameters are tuned. This suggests that catalytic patterning and geometry play coupled roles analogous to valve timing and chamber asymmetry in more conventional pumps (Antunes et al., 2023).

5. Gas recirculation and vacuum pumps

For noble-gas detectors and other ultra-clean gas systems, the dominant pump design problem is not only throughput but containment, outgassing, and radiopurity. A magnetically driven piston pump for EXO-200 used an external ring magnet on a linear actuator to drive an internal sealed magnetized piston through a stainless-steel cylinder, thereby eliminating dynamic seals to atmosphere. Using sprung UHMWPE gaskets, the pump was capable of more than $I = n e f$2 of xenon gas at $I = n e f$3 differential pressure, while supporting detector purity requirements below $I = n e f$4 $I = n e f$5-equivalent. The UHMWPE gasket implementation showed no loss of performance in the first $I = n e f$6 hours of operation (LePort et al., 2011).

Later magnetically coupled noble-gas pumps extended this architecture in force, flow, and cleanliness. A high-purity gas pump with alternating-polarity ring magnets measured a magnetic restoring force of $I = n e f$7 and delivered more than $I = n e f$8 with argon and more than $I = n e f$9 with xenon while maintaining a compression of up to $I_{\mathrm{total}}=\sum_i n_i e f$0. A subsequent ultra-clean radon-free four-cylinder system used a measured piston coupling force of $I_{\mathrm{total}}=\sum_i n_i e f$1, achieved xenon flows of $I_{\mathrm{total}}=\sum_i n_i e f$2 at a pressure difference of $I_{\mathrm{total}}=\sum_i n_i e f$3, and reduced single-cylinder radon emanation to $I_{\mathrm{total}}=\sum_i n_i e f$4. Phase-shifted synchronization reduced flow fluctuations by up to $I_{\mathrm{total}}=\sum_i n_i e f$5 and pressure fluctuations by up to $I_{\mathrm{total}}=\sum_i n_i e f$6 in four-pump operation (Brown et al., 2018, Schulte et al., 2021).

Ion getter pumps occupy a different part of the gas-pumping landscape. They are static capture pumps for ultra-high vacuum, built from Penning cells operated at about $I_{\mathrm{total}}=\sum_i n_i e f$7–$I_{\mathrm{total}}=\sum_i n_i e f$8 and $I_{\mathrm{total}}=\sum_i n_i e f$9–$I_{\mathrm{total}} = m n e f$0. Electrons are confined by crossed electric and magnetic fields, ionize residual gas, and the resulting ions are either implanted or chemically gettered onto titanium surfaces. Properly prepared systems can operate well below $I_{\mathrm{total}} = m n e f$1 and, with sufficiently low outgassing, down to $I_{\mathrm{total}} = m n e f$2. When pressures lower than $I_{\mathrm{total}} = m n e f$3 are required, the whole vacuum system must typically be baked at about $I_{\mathrm{total}} = m n e f$4–$I_{\mathrm{total}} = m n e f$5 for $I_{\mathrm{total}} = m n e f$6–$I_{\mathrm{total}} = m n e f$7 hours, and leakage current must be accounted for if pump current is used as a pressure proxy (Maccarrone et al., 2020).

6. Charge, ion, and quantum pumps

In quantum metrology and mesoscopic transport, pumps transfer discrete charge packets rather than fluid volumes. A single-hole pump in germanium uses a tunable-barrier quantum dot at a Ge/SiGe heterostructure interface and a single sinusoidal drive applied to the entrance barrier. Its defining relation is $I_{\mathrm{total}} = m n e f$8, and the experiment established robust $I_{\mathrm{total}} = m n e f$9 plateaux with $E = P \Delta t$00 up to $E = P \Delta t$01, corresponding to about $E = P \Delta t$02 at $E = P \Delta t$03, $E = P \Delta t$04 at $E = P \Delta t$05, and $E = P \Delta t$06 at $E = P \Delta t$07. The device was limited by accidental multiple-dot formation and random charge fluctuations, so it remained a proof of principle rather than a metrological standard (Rossi et al., 2021).

Parallelization in silicon addresses the low-current limitation of single pumps. A scalable split-source architecture for tunable-barrier single-electron pumps arranged eight silicon nanowire devices in parallel with shared entrance and exit gates but independent source electrodes. By tuning source voltages, four pumps were parallelized at $E = P \Delta t$08 to produce a clear $E = P \Delta t$09 plateau of about $E = P \Delta t$10, while three pumps at $E = P \Delta t$11 were set to $E = P \Delta t$12, yielding a current plateau exceeding $E = P \Delta t$13, specifically about $E = P \Delta t$14. This result is important because nanoampere-level currents are required for sub-$E = P \Delta t$15 ppm quantum current standards and quantum metrology triangle experiments (Yamahata et al., 24 Apr 2025).

A Josephson quantum electron pump realizes a conceptually different quantum cycle. An unbiased InAs nanowire embedded in a SQUID experiences cyclic modulation of the superconducting phases at different contacts through the ac Josephson effect, thereby generating pumping through time-dependent Andreev-reflection amplitudes. At $E = P \Delta t$16, currents exceeding $E = P \Delta t$17 were measured, and the antisymmetry of the current with respect to enclosed flux served as a discriminating signature against rectification. The pumped charge per cycle was only a fraction of an electron, but the experiment established pumping without Coulomb blockade in an open hybrid conductor (Giazotto et al., 2011).

Ion pumps in electrochemical systems again alter the transported entity while preserving the logic of cyclic rectification. Ratchet-based ion pumps built from Au-coated nanoporous alumina membranes modulate an asymmetric electric field with a square-wave input of $E = P \Delta t$18 at $E = P \Delta t$19. In hydrochloric-acid cells with Pt electrodes, the ratchet accelerated or inhibited the hydrogen evolution reaction depending on duty cycle and cell configuration, with ratchet-induced current changes up to about $E = P \Delta t$20 and overpotential shifts of the order of tens of millivolts, including an increase of approximately $E = P \Delta t$21 in one configuration. A crucial result was that applying a constant DC bias equal to the time average of the square wave did not reproduce the effect, showing that dynamic flashing rather than mean bias generated the pumping (Amichay et al., 18 Feb 2025).

7. Modeling, optimization, and recurrent themes

Pump analysis in these studies is strongly model-based, but the relevant model class depends on scale and transport mechanism. Water-network pumping is framed as mixed-integer economic MPC with a receding horizon and state feedback; ESP monitoring combines reduced-order nonlinear ODEs with structural and practical identifiability constraints inside a physics-informed neural network; inertial microfluidic switchboards use a linear pump matrix $E = P \Delta t$22; and pneumatically actuated micropumps use modal solutions of viscoelastic plate equations coupled to hydraulic resistance. Even active-nematic pumps collapse onto reduced variables when velocities are normalized by $E = P \Delta t$23 and lengths by $E = P \Delta t$24, indicating that dimensional reduction, rather than brute-force simulation alone, remains central to pump design across scales (Wang et al., 2020, Carvalho et al., 2023, Hayes et al., 2018, Gerasimenko et al., 2016, Vélez-Ceron et al., 2024).

A second recurrent theme is that pump performance is intrinsically multi-criteria. In water infrastructure, the relevant output is not simply volumetric throughput but cost per cubic meter under time-of-use tariffs. In noble-gas handling, radiopurity, outgassing, and hermeticity are coequal with flow and compression. In quantum pumps, plateau flatness, uncertainty, and stability against charge noise dominate over raw current amplitude. In self-powered microfluidics, duration, predictability of decay, and compatibility with disposable cartridges can be more important than peak pressure. These examples also correct two common misconceptions. First, pumping does not require external mechanical machinery: degassing-driven PDMS blocks, evaporation-assisted leaf mimics, active nematics, catalytic pores, and flashing ratchet ion pumps all generate transport through stored or continuously supplied non-mechanical free energy. Second, “pump” does not denote a fluid-only device: the same term now includes architectures whose primary observable is current, overpotential shift, or vacuum throughput rather than discharge head or volumetric rate (Alvarez-Braña et al., 2024, Vélez-Ceron et al., 2024, Schulte et al., 2021, Rossi et al., 2021, Amichay et al., 18 Feb 2025).

Taken together, these studies suggest that contemporary pump research is less a single engineering discipline than a family of transport problems unified by directed flux generation under constraints. The outstanding frontiers identified across the corpus include uncertainty-aware control for real-time network operation, better explicit hydraulic constraints in reduced-order optimization, improved material quality and noise suppression in quantum charge pumps, long-term durability in soft peristaltic devices, and scalable architectures that preserve either purity or quantization while increasing throughput.