Ionic-electrostatic modeling of solid-liquid triboelectric nanogenerators

Relationship between SL-TENG theory and applications

As a multidisciplinary field, SL-TENGs involve coupled processes spanning interfacial electrochemistry, fluid dynamics, electrostatics, and circuit systems. To clarify the interplay between theory and applications, SL-TENG research can be organized into four interconnected aspects: interfacial charge generation and screening physics, theoretical modeling and solution methods, interpretation of experimental phenomena, and device-level design rules. The first two aspects establish the theoretical foundation, while the latter two translate it into practical performance.

First, contact electrification (CE) governs the origin, magnitude, and stability of interfacial charge, and is intrinsically coupled with EDL formation and ionic screening in liquid-contact systems. Second, theoretical modeling aims to map interfacial physics to measurable electrical outputs under realistic geometries and circuit conditions, consistent with the displacement-current framework of TENG operation^[25,26]. Building on this, the proposed model enables quantitative interpretation of key experimental observations, including output behavior that depends on concentration and height^[7,27]. Finally, device and system-level design, such as electrode configuration and load impedance, determines practical performance in energy harvesting and self-powered sensing^[28-30].

Following this theory-to-application framework [Figure 1], this work begins with CE-EDL interfacial physics, develops a measurable induced-charge and circuit model, and translates waveform predictions into design guidelines for SL-TENG systems.

Figure 1. Theoretical framework of SL-TENGs. EDL: Electrical double layer; SL-TENG: solid-liquid triboelectric nanogenerator.

Solid-liquid contact electrification and the CE-EDL framework

Contact electrification and triboelectrification (TE) are closely related but conceptually distinct. TE describes macroscopic charge transfer during frictional motion, whereas CE [Figure 2A] refers to the underlying interfacial process that occurs whenever two phases contact and separate, even without friction; friction mainly enhances the effective interaction^[31]. In SL-TENGs, although the mechanical excitation may involve droplet impact, wave immersion, or flow-driven wetting transitions, the fundamental source process remains CE at the solid-liquid interface. It is followed by electrostatic induction, which converts interfacial charge and time-varying boundary conditions into measurable electrical output.

Figure 2. Mechanism of the CE-EDL framework. (A) Electron cloud model for contact electrification between two materials: (i) before contact, (ii) in contact, (iii) after contact, and (iv) charge release. Adapted with permission^[31], Copyright 2018 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim; (B) Microscopic CE-EDL process: (i) before contact, (ii) contact and electron transfer, (iii) electrons charge the surface, and (iv) EDL formation. Adapted from^[32], licensed under CC BY 4.0. CE: Electrification; EDL: electrical double layer.

A central challenge in SL-TENG theory lies in identifying charge carriers and understanding how a solid-liquid interface becomes charged, because these factors determine surface charge density, stability, and electrolyte/pH dependence. Zhan et al. proposed that solid-liquid CE involves both electron transfer and ion-related processes, rather than purely ion transfer^[21]. Subsequent experiments quantified interfacial charge by measuring the surface charge density on dielectrics and separating removable (electron) and bound (ion) charges via thermionic emission. These results indicate that both electron and ion transfer generally coexist, with their relative contributions governed by liquid composition and surface properties. In particular, solutes tend to suppress electron transfer, while ion transfer is strongly influenced by pH through surface ionization. Surface wettability further modulates the mechanism, with hydrophilic surfaces favoring ion-dominated processes and hydrophobic surfaces favoring electron transfer.

Building on this, Lin et al. proposed a two-step CE-EDL framework [Figure 2B] that directly links interfacial charging to electrical double layer formation^[32]. Initially, contact induces electron transfer and/or surface ionization, leaving the solid surface charged. Subsequently, counterions in the liquid accumulate near the interface under Coulomb attraction, forming an EDL that screens the surface charge. The EDL is therefore not an independent element, but the intrinsic electrostatic response of an ionic liquid to interfacial charging. This CE-EDL framework provides a physical basis for interpreting SL-TENG behavior^{[19,20,33-35]}. For example, the commonly observed attenuation of output with increasing ionic concentration can be understood through two coupled mechanisms: (i) the CE channel, where solutes and surface chemistry regulate the amount and stability of transferred charge, and (ii) the screening channel, where EDL formation reduces the effective electric field reaching the electrode.

The CE-EDL framework highlights two key requirements that guide this work. First, the theoretical description should be divided into two stages. In the initial stage, contact establishes and regulates the effective surface charge density. In the steady stage, no new CE charges are generated. Second, EDL screening should be incorporated into the induction model as a quantitative coupling factor that links water chemistry to macroscopic electromechanical response. Based on these principles, the following sections develop a unified device-level theory that translates interfacial charge states and time-varying wetted area into measurable current and voltage waveforms, and further connects these predictions with experimental observations to inform SL-TENG design for multifunctional applications.

Theoretical modeling geometry and principles of contact-mode SL-TENG

The proposed model builds on Wang’s CE-EDL framework and considers a representative single-droplet contact-mode SL-TENG [Figure 3A]. A dielectric film of thickness d and relative permittivity ε_r is backed by a metallic electrode. A spherical droplet impacts, spreads to a maximum radius, retracts, and eventually detaches. The instantaneous wetted area is defined as

Figure 3. Theoretical model and output characteristics of SL-TENG. (A) Structure and working principle of a contact-mode SL-TENG. Adapted with permission^[16], Copyright 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim; (B) Computed evolution of surface charge with charging time; (C) Computed bipolar current waveform; (D) Computed voltage response as a function of solution concentration, where n denotes the anion-to-cation charge ratio; larger n leads to a faster decay; (E) Computed induced charge as a function of falling height, showing an initial near-linear increase followed by saturation. PTFE: Polytetrafluoroethylene; PMMA: polymethyl methacrylate; Isc: short-circuit current; Voc: open-circuit voltage; Qtr: transferred charge; SL-TENG: solid-liquid triboelectric nanogenerator; n: electrolyte number concentration.

where r(t) is the contact radius. This quantity can be directly measured by high-speed imaging, enabling experimental validation of the scaling between the short-circuit current I(t) and dA/dt. Given the relatively slow droplet dynamics, a quasi-electrostatic approximation is adopted^[36]:

in regions without free volume charge.

This approximation is justified in regions without free volume charge because the characteristic droplet timescale is much longer than the timescales of electromagnetic propagation and charge redistribution. Under extreme conditions, such as high-speed impact or early-time ultrafast dynamics, fully time-dependent electrodynamic effects may become relevant. In such cases, the present formulation should be regarded as the low-frequency limit of a more general treatment.

The operation is described within a two-stage framework. In Stage I (charging stage), early droplet cycles generate net CE, increasing the surface charge density toward saturation. In Stage II (post-saturation stage), no additional net charge is generated, and the output is dominated by electrostatic induction driven by the time-varying wetted area and, for finite electrodes, the droplet position. This separation highlights the distinct roles of charge formation and signal generation. Table 1 summarizes the notation used throughout the model.

Poisson-Boltzmann equation, diffuse-layer differential capacitance and Debye scaling

Following the classical Poisson-Boltzmann (PB)^[37] description of a symmetric electrolyte adjacent to a charged interface, we consider a planar solid-liquid interface at x = 0, with the electrolyte occupying x > 0. Let ψ(x) denote the electrostatic potential in the electrolyte, with ψ(∞) = 0. For a symmetric z:z electrolyte with bulk number density n₀, the ion distributions follow the Boltzmann relation:

Let ψ₀≡ψ(0) denote the surface potential. According to the Grahame relation, the diffuse-layer differential capacitance per unit area is defined as^[37]

where the Debye parameter κ is given by

In the weak-to-moderate potential regime relevant to many practical conditions, cosh(⋅) ≈ 1, yielding

The PB-based description adopted here applies primarily to dilute to moderately concentrated electrolytes (typically ≤ 0.1M for monovalent salts). At higher concentrations, ion-size effects, ion-ion correlations, permittivity reduction, and specific adsorption become significant. In such cases, the present expressions should be interpreted as effective relations, with deviations absorbed into fitted Stern capacitance or other phenomenological parameters^[38].

From EDL to electric output

In the wetted region, two electrostatic storage elements are connected in series: the dielectric layer and the interfacial EDL. The dielectric capacitance per unit area is

Within a minimal Gouy-Chapman-Stern (GCS)^[37] description, the EDL capacitance per unit area is

For device-scale induction, this system can be expressed naturally through a series-capacitance partition:

This partition factor quantifies the fraction of induced charge that effectively penetrates EDL screening and contributes to the electrode response. Physically, in a series stack, the potential drop, and thus the unscreened electric field transmitted through the dielectric, is determined by the relative capacitances. Increasing ionic concentration raises C_EDL, thereby reducing β_EDL and lowering the output amplitude, consistent with experimental observations^[6,21,32]. In sensing applications, this dependence provides a tunable and calibratable link between signal amplitude and electrolyte composition.

Although classical GCS theory was originally developed for metal-electrolyte interfaces, the same interfacial-capacitance framework can be applied here to effectively describe a triboelectrically charged dielectric-liquid interface. In the present SL-TENG, contact electrification establishes a quasi-static surface charge on the dielectric, which is subsequently screened by the formation of a compact Stern-like layer and a diffuse ionic layer in the liquid. Meanwhile, the dielectric itself contributes an additional series capacitance. In this framework, the triboelectrically charged dielectric effectively replaces the externally biased metal as the source of interfacial electrostatic driving.

Let the effective free surface charge density on the dielectric in the wetted region during Stage II be σ_s(t), and define the EDL-screened effective density as

To relate interfacial charge to measurable electrical output, we adopt the electrostatic reciprocity weighting-potential method, which is closely related to the Shockley-Ramo theorem and its electrostatic extensions^[39,40]. The weighting potential ψ_w(r) is defined as the solution of Laplace’s equation in the same geometry, with the target electrode held at 1 V and all other conductors grounded. The induced charge associated with a surface charge distribution over the wetted region Ω(t) is then given by

Here, A(t) denotes the instantaneous droplet contact area. In practical devices, the droplet footprint may be smaller than the electrode or move across finite or segmented electrodes. Neglecting such finite-electrode effects may yield reasonable predictions for central impacts, but it would fail for off-center impacts, electrode arrays, and sensing configurations. The weighting potential formalism isolates geometric effects into a single function ψ_w, which can be computed once for a given electrode design and reused across different conditions.

Under a uniform surface-charge approximation over the wetted region, we define a geometry factor

with

which accounts for electrode size and droplet lateral position. The induced charge then becomes

Let q(t) denote the free charge on the electrode delivered through the external circuit, and C_p the effective terminal capacitance. The terminal voltage is

According to Ohm’s law, for a resistive load R_L, the governing linear ordinary differential equation is established^[41]

The solution is

and thus

Two limiting cases are particularly relevant for interpreting measurements: (1) short circuit (V = 0):

(2) open circuit (I = 0): q(t) remains constant, and for q(0) = 0

Under most resistive-load conditions, the response can be approximated by the short-circuit limit:

Two-stage workflow of SL-TENG

Stage I (charging stage): during the early cycles, the surface charge density σ_s(t) evolves toward a saturation level due to CE, while leakage or ionic compensation leads to charge relaxation. A minimal kinetic model is

Where τ_CE and τ_leak denote the effective charging and decay times, respectively, with τ_leak typically decreasing with ionic strength. If leakage is negligible within a single droplet event, the evolution reduces to

Physically, Stage I corresponds to the buildup of interfacial charge when the liquid contacts the dielectric surface [Figure 3B]. In an idealized picture with an infinitely extended interface, CE generates equal and opposite charges on the solid surface and the liquid interface, while the EDL fully screens the field, resulting in negligible induced current except at the moment of detachment. In realistic situations, however, droplets are finite and their spreading is time-dependent. As a result, charge redistribution extends beyond the immediate contact region, the EDL screening is incomplete, and a weak but finite induced current can be observed during the charging process.

Stage II (post-saturation stage): once the surface charge reaches saturation, no additional net charge transfer occurs upon droplet contact. Within each droplet event, the surface charge density can be approximated as σ_s(t) ≈ σ_sat, and the electrical output is governed by the time-varying wetted area and geometry factor:

In the short-circuit limit,

In many cases, the geometry factor Γ_w is approximately time-independent during a single event,

and for sufficiently large electrodes,

These relations indicate that, after saturation, the current directly follows the time derivative of the wetted area. This provides a clear physical interpretation that is consistent with experimental observations^[6]. Larger contact areas and faster droplet dynamics generally produce higher current output. By contrast, variations in viscosity, surface tension, or temperature influence the signal mainly through their effects on contact-area evolution.

This framework also explains the characteristic bipolar peak waveform [Figure 3C]. During spreading, A(t) increases rapidly, yielding dA/dt < 0 and a first current peak. When the droplet remains on the surface, A(t) is approximately constant and the output approaches zero. During detachment, A(t) decreases sharply, yielding dA/dt > 0 and a polarity-reversed peak^[42]. In practical cases, a mild retraction phase often precedes detachment, leading to a small additional peak of the same polarity. However, this contribution is typically negligible because of its short duration and small amplitude. Overall, the bipolar waveform reflects the fact that the induced charge scales with wetted area, while the current corresponds to its time derivative.

Many droplet-based TENG studies report an initial conditioning phase, where early cycles exhibit evolving charge and waveform characteristics, followed by a stable regime after several impacts^[21]. This behavior naturally corresponds to the transition from Stage I to Stage II. In this framework, Stage I determines the achievable and retained surface charge, whereas Stage II governs how this stored charge is converted into electrical signals through droplet dynamics and geometry.

Closed-form droplet contact-area dynamics and analytical output waveforms

To further quantify the output, we model the droplet contact dynamics^[43] and derive an explicit expression for the wetted area A(t). For a spherical droplet falling from height h, the impact velocity is

Let D₀ denote the droplet diameter and γ the surface tension. The Weber number is defined as^[43]

Combining

the maximum contact radius follows a scaling relation with h:

Within a certain regime, the output increases with falling height, consistent with experimental observations^[16].

To describe the full contact process, we adopt a smooth, closed-form trajectory in which the contact radius evolves sinusoidally. The radius increases to r_max during 0 ≤ t ≤ t_s, retracts to a quasi-static radius R over t_s ≤ t ≤ t_s + t_r, and finally decreases to zero during detachment, t_s + t_r ≤ t ≤ t_s + t_r + t_d:

Here, t_s, t_r, and t_d denote the characteristic durations of spreading, retraction, and detachment, whereas r_max and R represent the maximum and quasi-static contact radii. The spreading time t_s is primarily governed by impact inertia and droplet size, whereas t_r depends on capillarity and contact-line friction or hysteresis. The detachment time t_d is influenced by surface properties such as microstructure and wettability. Substituting this trajectory into the governing equations yields the output expressions:

These results provide a quantitative explanation for the bipolar peak waveform described above.

Furthermore, the peak values can be analytically estimated as

This analysis shows that r_max typically approaches or slightly exceeds R, leading to a negligible retraction peak and a detachment peak slightly larger than the spreading peak. It also highlights two key factors governing SL-TENG output: interfacial screening (β_EDL) and charge retention (σ_sat).

Application in self-powered sensing: concentration-dependent response

Self-powered sensing is a key application of SL-TENGs. The electrical output exhibits a well-defined dependence on electrolyte concentration and is thus used for quantitative sensing^[44-46]. From the preceding analysis, the induced charge can be expressed as

where σ_eff(c) denotes the effective surface charge density after electrolyte screening, and the concentration dependence enters through this term.

For general electrolytes, it is convenient to express the Debye parameter κ in terms of the ionic strength I (mol/L):

which gives (using n₀ = 1,000N_AI in international system of units)

and hence

with

In the Poisson-Boltzmann diffuse-layer limit, the diffuse-layer capacitance follows $$ C_D \propto \sqrt{I} $$. For 1:1 electrolytes (e.g., NaCl, KCl, KNO₃, and NaNO₃), I = c, yielding $$ C_D \propto \sqrt{c} $$. For a 2:1 electrolyte such as CaCl₂, $$ I=\frac{1}{2}(4c+2c)=3c $$, implying stronger screening at the same molar concentration.

In the induction-dominated regime, the electrolyte screens part of the electric field on the liquid side. According to Equations (19,20 and 22), the effective surface charge density coupled to the electrode is

For a fixed mechanical input A(t), the open-circuit peak voltage scales linearly with σ_eff(I):

where V_* collects concentration-independent factors (geometry, A_max, σ_sat, and C_p). Substituting $$ C_{D}(I)=\mid K_{D} \sqrt{I} $$) yields an explicit closed-form expression:

For different electrolytes,

For 1:1 electrolytes, I = c; for a 2:1 electrolyte such as CaCl₂ I = 3c, leading to a faster decay of output with concentration, as shown in Figure 3D.

Two limiting regimes can be identified. Low concentration (diffuse-layer dominated): $$ K_{D} \sqrt{I} \ll C_{\text {Stern }} $$, so $$ C_{EDL}\approx K_{D} \sqrt{I} $$, giving

Thus, for 1:1 electrolytes, V_oc decreases approximately as $$ 1 /(1+\text {const} \cdot \sqrt{c}) $$. High concentration (Stern-layer limited): $$ K_{D} \sqrt{I} \gg C_{\text {Stern }} $$ C_EDL ≈ C_Stern, yielding a concentration-independent plateau:

These trends are consistent with experimental observations^[33].

Interpretation of droplet height h

A key experimental observation is that the transferred charge of SL-TENGs initially increases with droplet falling height h and then approaches saturation^[16]. From the preceding analysis, the charge transferred in a single droplet event can be expressed as

The expression highlights that the height dependence enters through two channels: the effective surface charge density σ_eff and the maximum contact area A_max. The maximum contact area is

which alone would predict

if σ_eff were independent of h.

To account for the height dependence of σ_eff, we analyze the charging dynamics in Stage I. Surface charging is primarily activated during the early impact and spreading phase, where new contact formation and high local pressure occur. This process can be described by a saturating injection law:

where S(h) represents an impact-intensity factor. A physically motivated choice is to relate S(h) to the impact dynamic pressure:

with s₀ as a constant. Importantly, the effective charging duration is not the full contact time, but the spreading timescale t_act, during which rapid contact formation occurs. In the inertia-dominated regime,

With σ(0) = 0, we obtain

Evaluating at t = t_act and using $$ S(h) \propto h $$ and $$ t_{\text {act}} \propto h^{-1/2} $$, we obtain

which implies that, in the regime $$ \kappa \sqrt{h} \ll 1 $$,

Thus, the charging process introduces an additional $$ \sqrt{h} $$ dependence in Q_tr(h) at low heights. Combining both contributions from σ_eff and A_max, we obtain

which explains the experimentally observed near-linear scaling of transferred charge with droplet height.

At sufficiently large h, two independent saturation mechanisms emerge. (1) Charging saturation: σ_eff(h) → σ_sat as h → ∞. (2) Geometric saturation: the maximum contact radius r_max (and thus A_max) cannot increase indefinitely due to finite droplet volume, wettability limits, contact-angle constraints, and electrode nonuniformity. To account for this, we introduce a maximum attainable contact radius r_cap and define

So that A_max(h) → A_cap as h → ∞. Consequently,

In practice, A_max transitions smoothly from a 12 scaling at small heights to a constant value A_cap at large heights. This behavior can be captured by introducing a smooth interpolation:

since $$ 1-e^{-\mu \sqrt{\mathrm{h}} \approx \mu \sqrt{\mathrm{h}}} $$ for small h, where μ is a fitting parameter. Combining these results yields an empirical expression for the overall height dependence of transferred charge:

Two limiting regimes follow directly. $$ \sqrt{(h)} \ll 1 / \kappa $$, 1/μ,

While for $$ \mathrm{h} \gg 1 / \kappa^{2} $$, 1/μ²,

Design rules for device systems

SL-TENG devices often employ finite electrodes, segmented arrays, or distributed sensing geometries. In such configurations, the geometry factor Γ_w(t) varies with droplet lateral motion and partial electrode coverage. By reciprocity, Γ_w(t) is defined as the spatial average of the weighting potential ψ_w(r) over the instantaneous wetted area A(t). Because ψ_w(r) depends only on electrode geometry, it can be computed once for a given layout. Accordingly, Γ_w(t) serves as a compact descriptor of geometric effects that can be reused across different droplet events and operating conditions. Different electrode geometries correspond to distinct Γ_w(t) responses. For an infinitely large planar electrode, Γ_w = 1, whereas for a two-dimensionally infinite strip electrode,

The geometry-dependent output can thus be unified through Γ_w, enabling several sensing modalities. First, droplet position tracking becomes possible because lateral motion across electrodes changes Γ_w, allowing area and position to be encoded simultaneously in the waveform. Second, in water-level and wave sensing, variations in wetted length produce systematic changes in Γ_w, which map directly onto the output amplitude. Third, by combining multiple electrodes with distinct Γ_w(t) responses, the effects of area change and translation can be separated algorithmically. These capabilities are promising for distributed water-level sensing and droplet-position sensing. From a design perspective, electrode geometry should be selected according to the target sensing function. For energy harvesting, a large electrode (Γ_w = 1) maximizes induced charge collection. For position sensing, segmented electrodes with sizes comparable to the droplet footprint enhance sensitivity to lateral motion (dΓ_w/dt). For water-level sensing, vertically distributed strip geometries ensure a monotonic dependence of Γ_w on liquid height. In all cases, the weighting-potential formalism provides a quantitative design framework: one computes ψ_w(r) for the target geometry, evaluates Γ_w under expected droplet dynamics, and optimizes electrode dimensions accordingly.

In many experiments, the measured voltage waveform depends strongly on the external load and the effective measurement impedance. The circuit relation clarifies how the same induced-charge source can produce different voltage and current responses under different electrical conditions. The dynamics are governed by the resistor-capacitor (RC) time constant τ = R_LC_p, where R_L is the external load resistance and C_p is the effective terminal capacitance, including both intrinsic and parasitic contributions. This timescale should be compared with the droplet-event duration T_evt, leading to a key dimensionless parameter R_LC_p/T_evt that determines the operating regime. A convenient performance metric for droplet-based energy harvesting is the energy delivered to a resistive load:

Three regimes can then be identified. In the short-circuit-like regime ($$ R_{L} C_{P} \ll T_{\text{evt}} $$), the current follows the time derivative of the wetted area, and the peak current is governed by spreading and detachment rates. The extracted energy scales approximately with the square of the peak current and is relatively insensitive to R_L. In the open-circuit-like regime ($$ R_{L} C_{P} \gg T_{\text{evt}} $$), the voltage waveform reflects the induced-charge profile, with peak amplitude ~ Q_ind,max/C_p. In this regime, energy extraction depends strongly on downstream power management, because charge accumulates on C_p and must be harvested by switching circuits. In the intermediate regime (R_LC_p ~ T_evt), the output current exhibits exponential decay after each transient peak and can be described analytically via the convolution solution of the circuit equation.

This framework has direct implications for measurement and device design. Peak voltage and peak current cannot be maximized simultaneously: increasing R_L enhances voltage but reduces current. Maximum power is achieved under impedance-matching conditions, highlighting the importance of load optimization for different SL-TENG applications.

For maximizing droplet energy harvesting, the theory suggests three key design levels. (i) Maximizing effective unscreened charge β_EDLσ_sat. The induced-charge source scales with β_EDLσ_sat. Increasing σ_sat requires tribo-negative dielectrics [e.g., polytetrafluoroethylene(PTFE) and fluorinated ethylene propylene(FEP)] and surface treatments such as fluorination or nanostructuring to enhance charge retention. Increasing β_EDL can be achieved by raising the dielectric capacitance C_s, for example through thinner films or higher-permittivity materials. However, reducing the thickness may compromise dielectric strength and long-term reliability, so performance and durability must be balanced. (ii) Maximizing the area-change rate dA/dt. The short-circuit current peak scales with $$ r_{\max }^{2} / t_{s} $$ (spreading) and $$ R_{\max }^{2} / t_{d} $$ (detachment). Increasing r_max, for example through a larger droplet volume or higher falling height h, enhances the output. Reducing t_s and t_d further increases the peak current. Since t_d is governed by wettability and contact-line hysteresis, low-hysteresis surfaces such as superhydrophobic or SLIPS designs enable rapid droplet detachment and improved harvesting^[27]. SLIPS surfaces additionally provide chemical robustness and optical transparency, supporting stable performance in harsh environments. (iii) Engineering the circuit capacitance C_p. The open-circuit voltage scales inversely with the total terminal capacitance C_p, including both intrinsic and parasitic contributions. Minimizing parasitic capacitance (e.g., through compact layouts, short shielded connections, and low-capacitance substrates) effectively enhances the usable charge output. In integrated systems, the input capacitance of rectifiers, storage units, or hybrid energy modules further increases the effective C_p, making co-design of the TENG and power management circuit essential. Recent hybrid systems combining raindrop and solar harvesting^[33-35] suggest that the harvested energy per droplet is ultimately determined not only by device-level optimization, but also by system-level capacitance and impedance matching.

These design principles align with recent experimental advances. In sensing applications, SL-TENGs have progressed from waveform-based concentration detection to practical systems, including self-powered pH monitoring, integrated water metering, and river ecosystem sensing. Performance improvements increasingly rely on surface-morphology engineering and hydrodynamic-interface co-design^[17,45].