A Unified Spectrum for Turbulence in Microfluidic Flow

TL;DR

This paper introduces a unified spectral model for turbulence-like flows in microfluidics, capturing various regimes with a single expression and enabling predictive design without heavy simulations.

Contribution

It extends Pao's viscous-range closure to include an adaptive inertial-range slope and a physics-specific cutoff, unifying multiple turbulence regimes in microfluidic systems.

Findings

Reproduces spectral slopes and dissipation cutoffs accurately

Requires only global observables for predictions

Unifies different turbulence regimes in microflows

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.