A Unified Spectrum for Turbulence in Microfluidic Flow

Abstract

We present a predictive master spectrum describing turbulence-like flows in microfluidic systems. Extending Pao's viscous-range closure, the model introduces (i) an adaptive inertial-range slope dependent on measurable dimensionless numbers and (ii) a physics-specific cutoff that captures entropy-producing sinks such as electrokinetic forcing, compliant walls, active stresses, and interfacial tension. This formulation unifies turbulence regimes -- electrokinetic, active, interfacial, and compressible -- within one compact expression. Comparison with reported data reproduces both spectral slopes and dissipation cutoffs while requiring only global observables (velocity, viscosity, Taylor microscale, and forcing strength). The framework provides a design-level predictive tool for turbulent microflows prior to computationally heavy DNS or CFD.