Operator-Theoretic Desalination (OtD): A Novel Framework for Membrane-Free Ion Separation

The global water crisis demands a radical shift in how we think about desalination. Traditional systems—reverse osmosis (RO), multi-stage flash distillation, and electrodialysis—rely on pressure, heat, or membranes, each bringing trade-offs in energy cost, operational lifespan, and ion selectivity. These methods struggle especially with ion-specific removal and long-term deployment in austere or off-grid environments. Operator-Theoretic Desalination (OtD) offers a fundamentally new approach: desalination as a spectral separation problem, not a mechanical one. Rather than filtering salts through membranes, OtD treats ion transport as governed by a coupled operator—blending stochastic thermodynamics with electrokinetic drift—where each ion behaves as an eigenstate within a tunable spectrum. By leveraging differences in ionic polarizability and diffusivity, and applying resonant RF fields shaped by Maxwell stress gradients, we can achieve field-driven ion rejection without physical barriers. In essence, OtD transforms desalination from a bulk separation process into a dynamic, frequency-tuned filtration of mass-energy signatures. This method has shown over 90% chloride rejection at energy costs below 0.2 kWh/m³ in early-stage prototypes using graphene oxide channels. Beyond the lab, OtD holds promise for lightweight, power-efficient, and deployable units capable of addressing both humanitarian and defense-grade water needs. This document lays out the theoretical framework, experimental methods, and system architectures that define OtD. We invite the reader to consider not just a new technology, but a new language for water purification—one written in the dialect of fields, operators, and spectral flows.