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Micromechanic resonators provide a small-volume and potentially high-throughput method to determine rheological properties of fluids. Here we explore the accuracy in measuring mass density and viscosity of ethanol-water and glycerol-water model solutions, using a simple and easily implemented model to deduce the hydrodynamic effects on resonating cantilevers of various length-to-width aspect ratios. We next show that these measurements can be extended to determine the alcohol percentage of both model solutions and commercial beverages such as beer, wine and liquor. This demonstrates how micromechanical resonators can be used for quality control of every-day drinks.

The dynamic characteristics of cantilever beams strongly depend on the rheological properties of the fluid in which the beams are immersed. Initial investigation into such fluid effects, using millimeter-sized cantilevers, dates back to the 1960s [

Studies into the density and viscosity of petroleum and silicon oils have demonstrated the commercial potential of micromechanical resonators for rheological measurements [^{−3} Pa·s for ultrapure ethanol (compared to the expected 1.35 × 10^{−3} Pa·s) [

Biological applications of nanomechanical rheological sensors have also been investigated, with the characterization of sugar solutions [

One as yet unexplored application of micromechanical resonators is the measurement of ethanol concentration, density and viscosity of alcoholic beverages. Measurements of the ethanol content, density and viscosity of alcoholic drinks are essential for analysis and quality control procedures. Many techniques are currently used in beverage analysis [

Previous studies have investigated to what extent fluid properties and cantilever-length–to-width ratio (aspect ratio) influence the rheological calculations [_{4} and 1-butanol. They found the model to correctly reproduce the frequency response of the cantilevers within an error of 10% for aspect ratio ranges of

Here we focus on the accuracy of such measurements to determine mass density and viscosity of fluids, and in particular to their application for the characterization of commercial beverages. In that context, one of the key parameters is the alcohol percentage. We first compare different aspect ratios of rectangular cantilevers that are clamped at one end, using identical solutions and experimental set-up, to examine the extent by which aspect ratio influences the measurement of density and viscosity. To demonstrate their potential for real-time drinks analysis, we present density and viscosity measurements on a range of commercial drinks, comparing our results to simple aqueous ethanol solutions. We then use these data to determine alcohol content, comparing it to the specifications by the manufacturers. We also investigate the validity of current theory on more viscous liquids, using aqueous glycerol solutions at differing concentrations.

We consider singly clamped rectangular cantilevers of length,

The relevant mathematical framework for describing the resonance behavior of a cantilever with length greatly exceeding its width, and width greatly exceeding its thickness, has been developed by others [^{(}^{n}^{)}_{med}, ρ_{med}, η

When oscillated in a liquid of mass density _{m}^{(n)}_{med}

where ^{(n)}_{vac}_{c}^{(n)}_{med}

According to [

Given the relative simplicity of Γ [^{(n)}_{vac}

Once the mass density and viscosity of the medium have been determined, model solution data can be mapped on the literature values for aqueous ethanol solutions [

For our experiments, the cantilever is mounted in a commercial atomic force microscope (Nanowizard I, JPK Instruments, Berlin, Germany) and submerged in 100–200 μL of liquid, where it is subject to thermal fluctuations, which is the only actuation present in these measurements. Optical beam-deflection is employed to monitor cantilever deflections, owing to its relative simplicity and high lateral resolution. A laser is focused on the free end of the cantilever and reflected back onto the Position Sensitive Detector (PSD). Cantilever motion will consequently change the laser position on the photodiode and therefore the light intensity on each cell. Prior to measurement, the laser spot is aligned in the centre of the PSD, so each segment has equal levels of illumination. Ethanol (ACS reagent, ≥99.5%) and glycerol (ACS reagent, ≥99.5%) used to make the required solutions were obtained from Sigma Aldrich (St. Louis, MO, USA). The resonance behavior of the cantilever is determined from the digitally calculated and averaged Fourier spectrum of the thermal noise of the cantilever. The thermal noise spectrum is then fitted with a simple harmonic oscillator model, via which ^{(n)}^{(n)}

We use tipless uncoated single-crystal silicon cantilevers with dimensions: 500 × 100 × 0.9 μm^{3}, aspect ratio 1:5 [^{3}, aspect ratio 1:10 (NSC12 tipless cantilevers, MikroMasch, Tallin, Estonia); and 400 × 30 × 2 μm^{3}, aspect ratio ∼1:13 (CLFC-NOBO tipless cantilevers, Bruker Probes, Santa Barbara, CA, USA).

We examine the applicability of the described method in determining the density and viscosity of aqueous ethanol and glycerol solutions, alcoholic drinks and also their alcohol percentage. We also examine the influence of differing aspect ratios in the accuracy of the calculation. Success of this method in determining gas properties has been previously reported [

We repeat the procedure for glycerol solutions of the same percentage concentration up to 80%, the results of which are shown in

Above 80% concentration, the solution was too viscous for any resonance behavior to be observed in the thermal noise. Again, the cantilever measurements reproduce the trend expected from the literature values, and—in agreement with previous findings [^{−1} s^{−1} at 60% glycerol concentration, indicating that—for high aspect ratios—the procedure is reasonably accurate up to the point where viscous damping completely suppresses the resonant behavior of the cantilever. Nevertheless, the larger viscosity implies a greater infringence on the assumption

We next apply the procedure to the analysis of commercially available non-alcoholic and alcoholic beverages. As previous results have demonstrated the importance of a high (length-to-width) aspect ratio for the cantilever, we only use cantilevers where the length-to-width ratio is 10:1. For smaller aspect ratios, measurements for both mass density and viscosity will become increasingly inaccurate, as can be observed in

The accuracy of the technique could be further improved by using cantilevers of a higher aspect ratio.

The main scope for improvement in the described technique lies within the readout method. Here cantilever deflection is measured via an optical readout system, limiting the technique to transparent liquids and also reducing its use as a portable device. This could be overcome via the use of piezoelectric or piezoresistive cantilevers, or other schemes that bypass the need of optical detection.

In summary, we have experimentally demonstrated the use of micromechanical cantilever sensors to extract the density and viscosity of simple binary laboratory solutions and of more complex commercial drinks. We have also demonstrated that alcohol content in beverages can be determined from such measurements. As expected, the accuracy of the measurements decreases with decreasing (length to width) aspect ratio of the cantilever. This is important when considering industrial applications, where margin for error is minimal.

We gratefully acknowledge M. Stoneham (deceased) for discussions. This work has been funded by the UK Biotechnology and Biological Sciences Research Council (BB/G011729/1) and Engineering and Physical Sciences Research Council (EP/G036675/1, EP/061599/1).

^{1}

(^{3}, oscillating in water (black, dashed) and ethanol (blue), plotted against a logarithmic scale. The second and third oscillatory modes are shown, with ^{(n)}_{med}^{(n)}_{med}

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