The Clausius-Mossotti Factor in Dielectrophoresis: A Critical Appraisal of Its Proposed Role as an 'Electrophysiology Rosetta Stone'.

The Clausius-Mossotti (CM) factor underpins the theoretical description of dielectrophoresis (DEP) and is widely used in micro- and nano-scale systems for frequency-dependent particle and cell manipulation. It has further been proposed as an "electrophysiology Rosetta Stone" capable of linking DEP spectra to intrinsic cellular electrical properties. In this paper, the mathematical foundations and interpretive limits of this proposal are critically examined. By analyzing contrast factors derived from Laplace's equation across multiple physical domains, it is shown that the CM functional form is a universal consequence of geometry, material contrast, and boundary conditions in linear Laplacian fields, rather than a feature unique to biological systems. Key modelling assumptions relevant to DEP are reassessed. Deviations from spherical symmetry lead naturally to tensorial contrast factors through geometry-dependent depolarisation coefficients. Complex, frequency-dependent CM factors and associated relaxation times are shown to inevitably arise from the coexistence of dissipative and storage mechanisms under time-varying forcing, independent of particle composition. Membrane surface charge influences DEP response through modified interfacial boundary conditions and effective transport parameters, rather than by introducing an independent driving mechanism. These results indicate that DEP spectra primarily reflect boundary-controlled field-particle coupling. From an inverse-problem perspective, this places fundamental constraints on parameter identifiability in DEP-based characterization. The CM factor remains a powerful and general modelling tool for micromachines and microfluidic systems, but its interpretive scope must be understood within the limits imposed by Laplacian field theory.