Particle Mass and Size from Archimedes' Principle
At the heart of ARCHIMEDES is the relationship between the frequency shift of the microchannel resonator, and the physical properties of a particle. To understand this relationship, consider Archimedes' Principle: the buoyant force on an object is equal to the weight of the fluid it displaces. This can be used to define the "buoyant mass" as the mass of a particle over that of the fluid it displaces. The buoyant mass is related to a particle's "dry" mass via the relationship shown at right.
During a measurement, ARCHIMEDES "feels" the buoyant mass of a particle as it passes through the microchannel resonator. Note that the buoyant mass increases with the density mismatch between the particle and fluid. Also, consider that if the particle density and fluid density were the same, the resonator's overall mass would not change as the particle passed through.
These relationships can be used to determine a particle's mass and size:
The first step relates the frequency excursion for a particle to its buoyant mass. This is done using the microchannel resonator’s “sensitivity” S, which relates the frequency excursion to buoyant mass with s simple constant with units [mHz/fg]. The sensitivity S is a fixed value for each resonator, reflecting a simple linear relationship over the entire range of measurable particles. The sensitivity is is determined by a simple calibration procedure.
As shown above, the dry mass, volume, and “equivalent sphere” diameter can then be calculated. Note that these values are determined for each particle individually. The resulting lists can then be cast as histograms giving a statistical picture of the particle population. Because information is available for each particle, more detailed sample profiles can be obtained than is the case for ensemble techniques, such as light scattering, that average over many thousands of particles.