[Paper Review] Nano-NMR based flow meter

D. Cohen, Ramil Nigmatullin+4 more|arXiv (Cornell University)|Mar 6, 2019

Microfluidic and Capillary Electrophoresis Applications61 references4 citations

TL;DR

This paper proposes a nano-NMR-based flow meter using nitrogen-vacancy (NV) centers in diamond to non-invasively measure drift velocity and self-diffusion coefficients in microfluidic channels. By detecting magnetic field noise from flowing nuclear spins, the method achieves sub-5% accuracy and outperforms fluorescence-based techniques by orders of magnitude in sensitivity, especially under dominant diffusion effects.

ABSTRACT

Microfludic channels are now a well established platform for many purposes, including bio-medical research and Lab on a Chip applications. However, the nature of flow within these channels is still unclear. There is evidence that the mean drift velocity in these channels deviates from the regular Navier-Stokes solution with `no slip' boundary conditions. Understanding these effects, is not only of value for fundamental fluid mechanics interest, but it also has practical importance for the future development of microfluidic and nanofludic infrastructures. We propose a nano-NMR based setup for measuring the drift velocity near the surface of a microfludic channel in a non-intrusive fashion. We discuss different possible protocols, and provide a detailed analysis of the measurement's sensitivity in each case. We show that the nano-NMR scheme outperforms current fluorescence based techniques.

Motivation & Objective

• To address the lack of accurate, non-invasive experimental techniques for measuring flow velocity near channel walls in micro- and nanofluidic systems.
• To overcome limitations of fluorescence-based velocimetry, including large probe size, poor surface sensitivity, and limited spatial resolution.
• To develop a quantum sensing approach based on nano-NMR that is sensitive to surface flow effects and self-diffusion coefficients.
• To demonstrate that nano-NMR can achieve significantly higher sensitivity than current methods, even when diffusion dominates.
• To validate the method through molecular dynamics simulations of Lennard-Jones fluid flow near an NV center array.

Proposed method

• Utilizes nitrogen-vacancy (NV) centers in diamond as nanoscale magnetometers to detect magnetic field fluctuations generated by flowing nuclear spins in a microfluidic channel.
• Measures the power spectrum of the magnetic field noise at the NV center location via optical detection of the NV spin state.
• Applies the fluctuation-dissipation theorem to relate the power spectrum at zero frequency to the drift velocity and diffusion time scale.
• Employs molecular dynamics simulations with Lennard-Jones potential to model fluid flow and compute the induced magnetic field at the NV center position.
• Uses the Velocity-Verlet integration method with periodic boundary conditions and specular reflections to simulate hydrodynamic flow in a confined geometry.
• Fits the zero-frequency power spectrum to a function of the form $1 + b\sqrt{v} + cv$ to extract velocity sensitivity and validate theoretical predictions.

Experimental results

Research questions

• RQ1 Can nano-NMR using NV centers provide a non-invasive, high-sensitivity measurement of drift velocity in microfluidic channels?
• RQ2 How does the sensitivity of nano-NMR compare to fluorescence-based methods under conditions of dominant diffusion?
• RQ3 To what extent does the power spectrum of magnetic noise at the NV center depend on the drift velocity of nuclear spins?
• RQ4 Can molecular dynamics simulations accurately reproduce the expected scaling of the power spectrum with velocity, validating the theoretical model?
• RQ5 What is the role of surface effects and self-diffusion in the detectability of flow using nano-NMR?

Key findings

• The nano-NMR method achieves a sensitivity that outperforms current fluorescence-based techniques by orders of magnitude, even when diffusion effects are dominant.
• The zero-frequency power spectrum $S(\omega=0)$ scales with drift velocity as $1 + b\sqrt{v} + cv$, with $b = -0.42$ and $c = 0.053$, yielding an $R^2 = 0.9926$ fit to simulation data.
• The simulation results confirm the theoretical prediction that the power spectrum is sensitive to both drift velocity and diffusion time scale $\tau_D$.
• The method is inherently surface-sensitive, as the NV centers are placed near the channel wall, enabling measurement of boundary layer flow.
• The approach is robust to thermal fluctuations and does not require macroscopic polarization, relying only on statistical polarization of nuclear spins.
• The experimental feasibility is verified by existing NV center technology, with no need for strong magnetic field gradients or spin-echo techniques.