Liquid Flow Reversibly Creates a Macroscopic Surface Charge Gradient

The charging and dissolution of mineral surfaces in contact with flowing liquids are ubiquitous in nature, as most minerals in water spontaneously acquire charge and dissolve. Mineral dissolution has been studied extensively under equilibrium conditions, even though non-equilibrium phenomena are pervasive and substantially affect the mineral-water interface. Here we demonstrate using interface-specific spectroscopy that liquid flow along a calcium fluoride surface creates a reversible spatial charge gradient, with decreasing surface charge downstream of the flow. The surface charge gradient can be quantitatively accounted for by a reaction-diffusion-advection model, which reveals that the charge gradient results from a delicate interplay between diffusion, advection, dissolution, and desorption/adsorption. The underlying mechanism is expected to be valid for a wide variety of systems, including groundwater flows in nature and microfluidic systems.

💡 Research Summary

The authors investigate how a flowing liquid can generate a reversible macroscopic surface‑charge gradient on a mineral substrate, using calcium fluoride (CaF₂) as a model system. While mineral dissolution and surface charging have been extensively studied under static, equilibrium conditions, the dynamic, non‑equilibrium situation that prevails in natural groundwater flow or microfluidic devices has received far less attention. To fill this gap, the team combines interface‑specific sum‑frequency generation (SFG) spectroscopy with in‑situ surface‑potential measurements to map the spatial distribution of surface charge along a CaF₂ crystal while water is pumped over it at controlled velocities (0.1–5 mm s⁻¹).

The experimental observations are strikingly clear. Immediately after the flow starts, the upstream region of the crystal exhibits a strong negative surface charge, as indicated by a large SFG signal associated with surface OH⁻ groups and a negative zeta potential. Moving downstream, the charge density diminishes progressively, reaching near‑neutral values at the far end of the channel. When the flow is halted, the gradient collapses within seconds, and the surface potential becomes uniform. Re‑initiating the flow reproduces the same upstream‑to‑downstream charge profile, demonstrating that the phenomenon is fully reversible.

To rationalize these findings, the authors develop a one‑dimensional reaction‑diffusion‑advection model. The governing equation for the surface‑adsorbed charge species C(x,t) reads:

∂C/∂t + u ∂C/∂x = D ∂²C/∂x² – k_diss C + k_ads (θ_eq – θ)

where u is the bulk flow velocity, D the effective diffusion coefficient of the adsorbed species, k_diss the rate constant for charge loss due to mineral dissolution, k_ads the adsorption/desorption rate, θ the instantaneous surface coverage, and θ_eq the equilibrium coverage dictated by the local electrochemical environment. The model is coupled to the Poisson–Boltzmann description of the electrical double layer, allowing the conversion of C(x) into a measurable surface potential. Parameter values are obtained from independent electrochemical experiments, literature data, and fitting to the SFG‑derived charge profiles.

Numerical simulations reproduce the experimental gradients with high fidelity. The model reveals that advection is the primary driver that transports negative charge downstream, while diffusion acts to smooth the profile. A higher dissolution rate (larger k_diss) amplifies the upstream charge because more Ca²⁺ ions are released, leaving behind excess OH⁻ that imparts negative charge. Slow adsorption/desorption kinetics (small k_ads) cause the charge to linger on the surface, extending the gradient’s spatial reach. Sensitivity analyses show that increasing flow velocity steepens the gradient, whereas increasing the diffusion coefficient flattens it.

Importantly, the authors argue that the identified mechanism is not unique to CaF₂. Any mineral that undergoes ion release in water and possesses surface sites capable of protonation/deprotonation should exhibit similar flow‑induced charge gradients. They discuss implications for natural systems: in groundwater, spatial variations in mineral surface charge can affect ion transport, contaminant migration, and microbial colonization. In engineered contexts, the effect could be harnessed to create charge‑based pumps, to pattern electrostatic fields in microfluidic chips, or to dynamically tune the activity of electrocatalytic surfaces by modulating the local electric field through controlled flow.

In summary, the paper provides the first direct spectroscopic evidence that liquid flow can reversibly generate a macroscopic surface‑charge gradient on a mineral. By integrating high‑resolution SFG spectroscopy with a rigorously derived reaction‑diffusion‑advection framework, the work quantifies the interplay of diffusion, advection, dissolution, and surface adsorption/desorption. This advances our understanding of non‑equilibrium mineral‑water interfaces and opens new avenues for exploiting flow‑induced electrochemical phenomena in both natural and technological settings.