Underwater wireless communication via TENG-generated Maxwell's displacement current

The paper addresses the long-standing challenge of robust underwater wireless communication in complex and confined environments. Traditional approaches—acoustic, optical, and electromagnetic—each have limitations: acoustic links suffer from multipath, Doppler, environmental dependence, and echoes/reverberation; optical links face absorption, scattering, beam divergence, and ambient light interference; high-frequency EM waves are strongly attenuated in water, while low-frequency EM requires very large antennas and offers limited practicality. Inspired by Maxwell’s equations, especially the displacement current term ∂P/∂t associated with medium polarization, and prior work connecting TENG outputs to ∂P/∂t, the authors hypothesize that a TENG-generated polarization electric field can enable reliable underwater communication less sensitive to conventional underwater disturbances. They propose and investigate an approach converting airborne sound to underwater electrical signals via an acoustic-driven triboelectric nanogenerator (TENG), transmitting through water as polarization fields and receiving via an electrode connected to an electrometer.

The authors review underwater communication modalities: (1) Acoustic is prevalent due to relatively low absorption in water but suffers from significant delays, temperature/pressure/salinity dependence, multipath, Doppler shifts, and echo/reverberation challenges in confined spaces (pipes, tunnels, caves). (2) Optical can provide high data rates but is limited by absorption, scattering, beam divergence, and ambient-light interference. (3) Electromagnetic-based approaches face strong absorption of high-frequency waves; low-frequency EM can propagate but requires kilometer-scale antennas. They highlight displacement-current-based communication, noting prior demonstrations in air using TENGs to create alternating electric fields for wireless sensing/communication. Given water’s high dielectric constant relative to air, they posit improved propagation of polarization fields (∂P/∂t). Prior theory by Wang (Maxwell-based first principles of nanogenerators) links TENG output current to the ∂P/∂t term of displacement current, suggesting feasibility of underwater communication leveraging TENGs.

Concept and theory: The system models the transmitting and receiving electrodes as plates of a capacitor with water as the dielectric. A TENG connected to the transmitting electrode generates a time-varying electric field E0 in water; medium polarization produces P0, giving a displacement current density JP = ∂P0/∂t = ((εr − 1)/εr) ∂E0/∂t. The received current at a distant electrode is induced by polarization charges without relying on direct electron exchange with water. Analytical framing uses Gauss’s law ∇·D = ρ, D = ε0E + P, and discussions of displacement vs conduction current dominance (εω > σ) for the employed frequencies. Experimental setup: An acoustic-driven Helmholtz-resonator TENG (HR-TENG) comprising a resonant cavity (73×73×40 mm), aluminum film (45×45×0.1 mm) with 440 holes, and FEP film (12.5 μm) with conductive ink electrode, was mounted with a loudspeaker driven by a function generator. One TENG electrode is grounded; the other connects to the immersed transmitting electrode (wire or copper plate). The receiving electrode connects to a Keithley 6514 electrometer. The TENG operates in single-electrode mode to enhance output via ground charge acquisition. Measurements included short-circuit current at the TENG electrode and received current at various distances, water volumes, electrode geometries/orientations, salinities, turbidity, temperature, and presence of obstacles. Pipeline tests used a 100 m PVC pipe (13 mm inner diameter), with a DC pump controlling flow; both straight and spiral configurations were evaluated, including oil–water mixtures. Signal processing: Signals were modulated using on–off keying (OOK): a ‘1’ encoded as longer intervals (50 ms), ‘0’ as shorter intervals (25 ms), with 25 ms separations; fundamental TENG frequency ~80 Hz; digital symbol rate ~16 Hz (16 bit/s). Demodulation and decoding were implemented in MATLAB/LabVIEW; frequency-domain analyses employed Fourier transform. For voice control, a microphone-style TENG produced signals for classification (via short-time Fourier transforms and a neural network) and actuation of underwater lights through a microcontroller-controlled relay. A touch/button-type TENG demonstration controlled an independent underwater system (weak-current acquisition board, MCU, relay, light). Basin-scale test: A sandwich-like multi-layer TENG (S-TENG) delivering ~60 μA was deployed in a 50 m × 30 m × 5 m basin; received signals at 3–5 m were acquired and sent via WiFi for real-time display. Simulations: COMSOL Multiphysics (Electrostatics, transient) modeled polarization field distributions and terminal charges, with ultra-fine meshing. 2D simulations examined long-distance attenuation; 3D models (≤15 m size) explored field distribution and distance scaling, comparing cases with/without receiving electrodes to assess field perturbations.

• Signal integrity and waveform preservation: Received current waveforms in water remain consistent with TENG outputs across 1–3 m in a 3×2×0.4 m tank; Fourier spectra match, indicating negligible distortion. Signals persist even when the transmitting electrode is insulated (Kapton) and across gas/liquid interfaces, confirming field-mediated coupling. Grounding the tank reduces amplitude but not waveform.
• Attenuation with water volume and distance: Increasing water volume to 6 m³ reduces peak current by ~30% due to energy density scaling (W = ∫ 0.5 εr ε0 E² dV). In a 100 m saltwater pipe, peak current decreases by ~66% while waveforms remain undistorted. Simulation distance dependence follows P ∝ x^a (a ≈ −1 in 2D, ≈ −2 in 3D) and terminal charge Q ≈ k2 ln x + k3.
• Electrode geometry effects: Using a 10×5 cm receiving plate increases peak current by ~18% versus a thin wire, attributable to increased ion contact area. Electrode plate angle has minimal effect in the tank configuration. The receiving electrode perturbs and enhances local polarization field distribution, consistent with a near-zero potential terminal.
• Environmental robustness: Salinity boosts signal amplitude up to a point: at 5 g·L⁻¹ NaCl, peak current increases by ~40% over pure water; above 15 g·L⁻¹, further increases are negligible. Deviations of pH from 7 (more ions) increase received currents. Signals are robust to obstacles and turbidity—waveforms remain essentially identical to originals. Signals are insensitive to water temperature and ambient light levels. In pipelines, straight vs spiral (curved) configurations yield similar signals; oil–water mixtures and varying flow states still permit reception.
• Displacement vs conduction current regime: For the employed low-frequency operation, εω > σ, indicating displacement-current-dominated propagation over relevant distances; conduction currents dominate only at very short ranges. Rayleigh distance for the electrode is negligible, consistent with near-field polarization coupling.
• Data transmission: OOK-modulated digital signals transmit texts and images at 16 bits/s. A 2.7 KB image was transmitted in 1353 s with no bit errors across ~20,000 bits (~100,000 TENG cycles). The system shows water-channel bandwidth >85 kHz (power spectral analysis), and externally applied AC can enable kHz-rate modulation via the same channel.
• Wireless control demos: Voice-driven TENG signals (‘red’, ‘green’) were classified via STFT + neural net to control underwater lights in real time; an independent submerged control unit was actuated via touch TENG pulses. Basin-scale S-TENG tests (50×30×5 m) demonstrated real-time signal acquisition and display at 3–5 m distances.
• Representative magnitudes: TENG short-circuit current ~14.9 μA (air) and ~14.5 μA received at 2 m in water under 80 Hz, 80 dB acoustic drive; S-TENG output ~60 μA in basin tests. Open-circuit voltage drops from 28.5 V (air) to 13 V (water).

The results demonstrate that underwater communication based on the polarization component (∂P/∂t) of Maxwell’s displacement current, generated by TENGs, is feasible and robust in complex aqueous environments. Unlike high-frequency EM waves, which attenuate rapidly in water, and unlike acoustics/optics, which suffer from environmental sensitivity, the polarization field requires a dielectric medium and couples effectively through water. The experiments show that signal waveforms are preserved over meters in tanks and across 100 m in pipelines with only amplitude attenuation, confirming suitability for reliable information transfer. Environmental disturbances—salinity, turbidity, obstacles, temperature, light—have limited impact on waveform integrity, and increased ionic content can enhance signal strength up to a saturation point. The channel supports low-frequency modulation and is capable of higher-frequency operation when driven by appropriate sources, suggesting scalability of data rate. Practical demonstrations (text/image transmission, voice-controlled lighting, basin-scale sensing) illustrate applicability to scenarios such as pipeline inspection, confined spaces (pipes, caves), and underwater sensor/robot communications where acoustics or optics may falter. Theoretical and simulation analyses (field distributions, displacement vs conduction regimes, distance scaling) align with measurements and provide a foundation for system design and optimization.

The study introduces and validates an underwater wireless communication method leveraging TENG-generated Maxwell’s displacement current (∂P/∂t). An acoustic-driven TENG produces a time-varying polarization electric field in water, enabling current induction at a distant receiver. Signals maintain waveform fidelity over distances (meters in tanks; 100 m in pipes with ~66% amplitude reduction), are resilient to salinity, turbidity, obstacles, and temperature/light variations, and can traverse complex pipelines without distortion. Using simple OOK, the system transmits text and images at 16 bits/s with zero errors over ~20,000 bits, and supports real-time voice-based control of underwater devices. Basin-scale tests with an S-TENG further confirm practicality. This displacement-current approach offers a promising alternative to acoustic and optical techniques for challenging underwater environments. Future work could focus on: (1) increasing data rates via higher-frequency TENGs or external drive waveforms and advanced modulation/coding; (2) optimizing electrode geometries and arrays for extended range and directionality control; (3) channel characterization in open-water scenarios and varying salinity/temperature profiles; (4) integration with low-power embedded receivers and protocol stacks for multi-node networks; and (5) co-design of energy harvesting and communication for self-powered underwater systems.

• Data rate is limited by the TENG’s fundamental frequency in the presented self-powered setup (16 bits/s demonstrated); while kHz modulation is possible with external AC drive, fully self-powered high-rate operation requires higher-frequency, higher-output TENGs.
• Signal amplitude decreases with increased water volume and distance; practical long-range deployments will require optimization of transmitter output, electrode size/placement, and receiver sensitivity.
• Demonstrations were primarily in tanks/basins and pipes; open-water, large-scale ocean trials are inferred theoretically but not experimentally validated here.
• System relies on conductive coupling within a continuous water body; grounding conditions and boundary effects can affect amplitude (though not waveform), necessitating careful system grounding design in field deployments.
• Environmental enhancements (e.g., increased salinity or pH deviation) improve amplitude up to a saturation point; performance in highly variable natural waters may require adaptive calibration.