1. Methods Of Particle Size Analysis (Some of these are briefly reviewed in Coulson and Richardson 1993) Screening Electronic particle counting (Elzone, Coulter Counter) Sedimentation Optical Methods (i) Microscopy (ii) Laser Diffraction (iii) Dynamic laser light scattering Screening Particles are placed on a screen possessing uniform apertures of given dimensions. Particles capable of passing through the apertures require the opportunity to do so. This is provided by agitation of the load bearing screen for a given period. Particles which pass through this screen can be passed through to a nest of screens of decreasing aperture.
The mass retained by each screen is then gravimetrically determined. Screening efficiency is affected by 1) Sample load. 2) Particle hardness (in comparison with that of the material of the screen). 3) Duration and intensity of agitation. 4) Presence of large particles which prevent access to screen apertures. Screens are available in a variety of standard sizes and are generally used for material >50? m. Screens of smaller aperture are available but these are often mechanically weak or provide a low proportion of surface as apertures. Such systems are often described as membranes.
Classification and separation of many biological particles are performed using membranes. This technology is presented in Bioseparation Processes. Electronic Particle Counting A suspension of particles in an electrolyte medium is drawn (by vacuum) through a (sapphire) aperture (0. 03? 1 mm diameter) across which a direct (constant) current is applied. The overall electrical resistance is determined by the dimensions of the aperture. When electrolyte within the aperture is displaced by a non-conducting particle, in transit through the aperture, the resistance increases and the voltage is increased to maintain the current.
The amplitude (but not the width) of the resulting voltage pulse is measured, classified and counted using a multi-channel analyser. The pulse amplitude is found to be directly ? to the volume of the particle, over a range of diameters from 5 to 40% of the aperture diameter. The residence time in the aperture (and hence pulse width) depends upon particle trajectory. At high concentrations of particles, the probability that they will be counted simultaneously rather than individually increases. At low particle concentrations, electrical noise becomes significant in relation to the total particle count.
The presence of particles with diameters larger than that of the aperture usually leads to blocking and interruption of electrolyte flow. Such events vitiate any analysis in progress at the time of the blockage. The technique provides a size distribution as a function of particle equivalent spherical diameter. Different size ranges can be examined using orifices of various sizes. The necessary use of a conducting electrolyte has implications for the colloidal stability of fine particles. Changes in size distribution of repeat samples from a suspension in such systems usually indicates the operation of these or other processes.
Stirrers are used to maintain particles in suspension in the sample reservoir. Addition of glycerol or other high viscosity substances to the sample is also used to inhibit sedimentation. The technique was originally employed to count and size blood cells in saline media, but has been applied to particle size analysis in industrial and natural environments. Sedimentation Particles are dispersed in a suspending medium and then allowed to settle under gravity in quiescent constant temperature environments.
Particle size and concentration should be such that assumptions associated with Stokes’ law are valid (or appropriate corrections made on a heuristic basis). Typical size ranges in aqueous media for solids density of 2600 kg m3 are 2-32? m. The suspension can be sampled from a given depth below the surface at a variety of times (from the onset of sedimentation) and the solids content of each sample determined, or the settling vessel can be scanned with irradiation and detector systems to provide continuous estimates of the solids content as a function of depth.
The size distribution obtained is related to an equivalent Stokes’ diameter for an assumed or prescribed solid density. Because all particles settle together, a cumulative undersize distribution results directly from the data. Non-instrumental analyses usually take 6 – 8 h after which settling of fine material (< 2? m) is retarded by diffusive motion. No details of this fine end of the distribution are obtained by extending the settling period. Optical Methods Microscopy Particles are examined directly using optical or electron microscopes.
Particles are often seen only in profile and the specimens may not possess truly random orientations of particles. Shadowing techniques allow some indication of hidden dimensions. Various procedures are available which permit a variety of characteristic dimensions to be obtained. Martin’s diameter Feret’s diameter Much of the arduous work associated with the analysis of many individual particles is now performed by computational image analysis, using software that provides comprehensive information about characteristic dimensions and projected particle shape (and up to ~50 other parameters).
Micrographic and photomicrographic video frames or stills images may be used for this purpose. Errors associated with such analyses are usually smaller than those obtained by manual measurement. Laser Diffraction Particles are passed through an expanded laser beam wherein they scatter light which is collected on a detector comprised of an array of photo-diodes. The plane of the detector is positioned normal to the optical axis and a photo-diode at the axis measures unscattered laser light intensity.
The angular dependence of light scattering on particle size is used to construct a size distribution which accounts for the experimentally obtained scattered light distribution. A variety of scattering models is used for the analysis. Fraunhofer theory is adequate for particles > 8? m but below this size Mie theory is more appropriate. Liquid suspensions are passed through the laser beam via a thin (2mm) optical cell with plane windows either side of which (as appropriate) a focusing lens is positioned. The hydrodynamic conditions in the cell and ancillary equipment to some extent determine the outcome of the analysis.
The scattering results from some average cross sectional area that the particles present to the laser beam. This is manipulated (usually using proprietary software) to produce a distribution of their equivalent spherical diameters (on a number, area or volume basis). Dynamic Light Scattering This technique is useful for particles which undergo significant Brownian (diffusive) motion (< 2? m). It is one of the few techniques available to examine particles in this size range within a fluid environment. A fine laser beam is passed through the suspension and the intensity of light scattered to a point (usually at 90i??
) is examined as a function of time using a sampling and auto correlation procedure. The particles behave as an array of mobile scatterers and phase relationships are preserved over the scattering volume. Light intensity fluctuations from minimum to maximum correspond to particles diffusing a distance equivalent to the wavelength of laser light. The average time required for this is determined by correlating the light signal with itself at various time delays. The gradient of the best fit line through the log of this auto-correlation function as a function of the delay time is related to the diffusion coefficient.
The scatter of data about the line indicates polydispersity and the intercept the signal to noise ratio. The resulting particle size (dz) computed from the diffusion coefficient (assuming a Stokes’-Einstein model) is weighted towards those particles whose scattered light predominates at the selected angle. More rigorous analysis of scattering at a variety of angles facilitates identification of the presence of particle populations of different size. General comment There is no absolute standard method of determining particle size distributions.
The methods described exploit and reflect particle properties such as size, shape and density to differing extents. This multi-dimensionality is reduced for convenience to representation by some simple statistics of which process engineers must be aware. Exercise: Consider how you might interpret the output likely to arise from application of the above methods to the analysis of the following system. Gold particles 15 ? 5? m + Micaeous platy sediment 1? 60 ? m Sampling Strategies The success of many particle separation processes is determined using particle size distribution data.
It is necessary that such data be both precise and accurate. Sampling of powders and suspensions should, therefore, be performed in a representative manner. Large powder samples can be sub-divided by a method known as coning and quartering – where a heap of powder is divided into 4, each part of which is mixed and then recombined or discarded. The process is repeated until samples of suitable size are obtained. Sampling of conveyed powders may be performed by devices attached to the conveying system which rapidly traverse the flow and collect all material within an elemental cross section.
Sampling suspensions can be more problematical as some degree of separation spontaneously occurs due to influences of gravity (and of centrifugal motion of stirred suspensions). Sampling of a moving process stream is preferable and if possible several samples of the whole stream should be taken and combined. If continuous sampling is to be employed then this should be isokinetic. This means that the local velocity of the stream should not be significantly affected by the sampling probe inserted into the stream. It is usual for the nozzle of this probe to point into the direction of flow.
Sample aspiration is assisted by application of appropriate negative (relative) pressure. This ensures that sampling of large particles (which are subject to inertial effects) is representative. Small particles tends to follow the fluid streamlines and a representative sample of these should be passed into the nozzle. An inertia parameter (Stokes’ number ? ) is of use in assessing the necessity for isokinetic sampling. This relates the distance (s) in which a particle (of size x, density ? s) can be brought to a standstill, to the diameter (D) of the sampling nozzle.
x2? ss ? = ???  18? D It has been suggested that isokinetic sampling should be employed when 0. 05 < ? < 50. Note that (in comparison with Stokes’ law) the added mass of the particle is neglected and that particle velocity (ds/dt) is that of the stream velocity (u) and retardation du/dt. A variety of sampling systems is available for dry powders (riffle boxes, spinning rifflers etc. (Powders also undergo some spontaneous separation. ) Sampling of suspensions often occurs within size measurement systems and poor design can introduce bias at this stage in the process.
Problem: An electronic particle counter fitted with a 560? m orifice positioned at 20 mm depth in a 120 mm vessel of electrolyte is to be used for determining the size of quartz particles (? s = 2600 kg m? 3 ). What range of particle sizes will be quantitatively detected? How should the analysis be performed to ensure that the data acquired faithfully reflects the size distribution of the solid sample? 3. Efficiency Of Liquid/Solid Separations Some separation equipment can be used for classification of solid materials. Historically this led to a concept of grade efficiency.
This is applicable to continuous operations in solid/fluid separation and solid/solid separation (classification) in a fluid medium. Consider the following definition of a single stage separation (Fig. 2) where M is the mass flow of solids, Q, O and U the volumetric flows of feed overflow and underflow and f and c refer to fine and coarse solids. At steady state M = Mc + Mf [11a] also for any particular size fraction (say between x1 and x2, provided that no agglomeration or comminution occurs) Mx2x1 = (Mc )x2,x1 + (Mf )x2,x1 [11b]by definition the particle size (frequency) distribution provides the fraction of particles of a given size so that MdF = McdFc + Mf dFf [11c] ?? ?? ?? dx dx dx feed overflow (fines) M, dF(x), Q Mf, dFf(x).