Accurate sieving of microparticles

Summary: A novel approach to sieving of sub-millimetre particles is presented that selects a very narrow fraction of sizes and shapes, using an intense sound vibration.

Introduction

Theory of anisotropic sieves

In the following, we approximated the dielectric particles by ellipsoids with three (generally different) half-axes ra < rb < rc. For the purpose of sieving, only the values of the shortest two axes, ra and rb, decide whether the particle can pass through the sieve. The longest ellipsoid axis rc does not affect this, although it may influence the sieving speed. Therefore we can represent each 3-D particle with its projection on the smallest possible ellipse, which is described by its minor axis = 2ra$, and by its major axis = 2rb. For a given shape of a hole in a homogeneous flat sieve, it is easy to determine which values of minor and major axes allow a particle to pass through, and which not. For a square sieve such area in the parameter space forms a disk around the center of origin (Fig. \ref{fg_sieve_pass_notpass}a). It can be shown that when the sieve is diagonally stretched, forming a lozenge hole shape, the area of spheres allowed to pass changes into an ellipse (Fig. \ref{fg_sieve_pass_notpass}b). When the hole shape is circular or elliptical, it is obvious that the area forms a part of a square or of a rectangle, respectively (Fig. \ref{fg_sieve_pass_notpass}c,d).

a) b)

The resonance frequency of a dielectric resonator depends on all three axes, ra < rb < rc. In order to select as narrow size fraction as possible, one has to use double sieving: the above sieve not allowing the fraction of particles too big, the bottom sieve removing the fraction of particles too small. This is where the anisotropic hole shapes become useful - the bottom sieve can exclude also all oblong particles with the difference of ra < rb too big. This effect is illustrated in Fig. \ref{fg_double_sieving}, which also presents a comparison of using more usual sieves of square/lozenge holes with the effect of a couple of sieves of micromachined square/elliptic holes. Obviously, the latter approach better discriminates for the shape of the ellipsoid. This advantage further gains on importance when the anisotropy of the sieve is low.

a) b) }

It shall be noted that although we plotted a binary (pass/not pass) function in Figs. \ref{fg_sieve_pass_notpass} and \ref{fg_double_sieving}, the sieving speed greatly differs for different sizes of particles. This is due to lower probability of a particle passing, if its parameters are near the edge of possible-passing function.

However, this particular fraction of particles is exactly what one is interested in during the high-accuracy sieving! The process must therefore run for long enough time, in the order of days, and with as high sieving speed as possible.

First sieving apparatus

Employing the idea of anisotropic sieves from Fig. \ref{fg_double_sieving}a, we assembled the first prototype based on nylon sieves, as depicted in Fig. \ref{fg_sieving1}. Two glass containers were lathed of a glass tube, and on their bottom, nylon sieves were glued. The side of the sieve holes was 60 μm (+/-5), and while the above sieve was kept isotropic, the bottom one was stretched by ca. 20-25 % in diagonal direction. The nylon mesh was woven, so the threads easily bent aside, allowing oversized particles either to pass or to get stuck permanently, blocking the sieve within few minutes. To resolve the latter problem, two additional narrow glass rings were cut, with much coarser sieves glued on the bottom, to allow little spherical springs bounce beneath the sieves and to loosen the particles that got stuck in the holes. A cover on top prevented the particles to jump out of the above container. Whole stack was carefully lowered into a test tube with a greater diameter, and vibrated by a tiny electric motor glued on the bottom.


Second sieving apparatus

a) A sketch of the acoustic sieving device, and b) a photograph thereof

The partially promising results and, more importantly, obvious deficiencies of the previous apparatus motivated building a second one depicted in Fig. \ref{fg_sieving2}.

Different from any other sieving apparatus known to the author, this one made use of intense vertical acoustic wave for the movement of particles. It consisted of two coaxial glass tubes: The inner tube, with outer diameter of 13 mm, had a round metallic sieve glued to its bottom, and on its upper end it was covered by a 20 mm acoustic transducer. The outer tube (90 mm long, outer diameter 26 mm) surrounded the inner one and had a round bottom, where the particles collected.

The gaskets ensured that whole apparatus was tightly closed, preventing both sieved particles and sound from escaping. The brass ring with the transducer was fixed to a massive aluminum stand, and the rest of the structure was clamped to it by two M3 screws with nuts that allowed for easy disassembly.

The key advantages of this novel approach are the following:

  • The speed of sieving is roughly proportional to the frequency at which the particles hit the sieve. The acoustic frequency of 1 kHz is rouhly two orders of magnitude higher than in usual commercialy available devices. The spheres are moreover continuously stirred, so it is ensured that a layer of over-sized particles does not occupy the sieve.}
  • Upward air pressure pulls out particles that got stuck in the sieve in every period of acoustic vibration. This resolves the major issue of the previous prototype.}
  • Avoiding macroscopic vibrating parts, except the membrane of a small acoustic transducer, allows the device to operate over multiple days without the risk of mechanical failure of any part.}

The outer tube acted as an acoustic resonator, greatly enhancing the effect of the sound when tuned to resonance around 750-900 Hz. These frequencies obviously correspond to the fundamental acoustic resonance, as the quarter-wavelength is the range from 91 to 110 mm. The power of the sinewave feeding the device was limited by the parameters of the acoustic transducer

A practical deficiency of this setup was that the upper opening of the transducer radiated relatively intense sound during operation. We resolved this potential issue by covering whole apparatus by a robust glass bell jar.

With the acoustic power and frequency correctly adjusted, the particles formed a cloud 5-10 mm high. One difficulty arose from that the small particles tend to attach to the surface of glass or metal, probably due to electrostatic charges on their surface. While at an average particle radius ρ = 50 μm this effect was rather marginal and transient, it took only few seconds of sieving for ρ = 20 μm particles to immobilize permanently on any surface. It has however proven efficient to tap the upper brass ring, as the vibration released most spheres, effectively renewing the sieving process. To ensure unattended sieving for a timespan in order of days, we added a little motorized hammer with a timing circuit.

The amount of particles in one batch was limited to ca. 10-20 mm3, otherwise the sieve would be covered with a layer too thick, which could not be efficiently lifted by the acoustic pressure.

It could however be remedied by tilting the apparatus. With a tilt of 5-10 degrees, the bulk of particles then accumulated near one side, leaving most of the sieve surface free for sieving the moving fraction of particles. According to the small amount of particles required for the terahertz spectroscopy measurements, it is however advisable to sort a batch in order of 1-3 mm3.

Automatic determination of microparticle statistics

a) A section of a microphotograph of sample before sieving, b) the corresponding identification of particles in ImageJ

We developed a numerical method to measure the histogram of size distribution of the particles based on a calibrated microphotograph of the sample such as in Fig. \ref{fg_microphoto}1. This enabled to assess the sieving precision and also to predict the realistic signal by simulation.

Laser micro-machining of sieves and fish-net metamaterial layers

a) Laser micromachining the steel sieve, and b) the resulting sieves

To achieve the required precision of sieving, we fabricated the sieves by femtosecond laser drilling of 20 μm thick stainless steel sheets (Fig. \ref{fg_microfab}). %These sieves then were employed in a device that subjected the microsphere sample to acoustic vibrations, improving the speed of the demanding sieving process to acceptable level (Fig. \ref{fg_microfab}b,c).


© Filip Dominec | Last edited: 2015-01-18 | go to index➤