Kim H. Esbensena and Claas Wagnerb
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It is convenient for the present objective to begin by iterating a lesson that was tucked away towards the end of the preceding column, which illustrates a very often used sampler in the laboratory domain, the hand-operated tubular corer (tubular extractor). What is a tubular corer but a (very) small spear designed for forceful insertion in the lot material. This particular sampler is designed so as to allow lot material to be forced into the cylindrical volume as the corer is inserted and forced to greater depths (Figure 1).
The last column laid out in detail WHY the cylindrical corer, used in the one “sample” approach, which is indeed the most often met stipulation, in reality is nothing but grab sampling in disguise (we might call this “cylinder grab sampling”). The singular cylinder extraction approach is in no way able to produce a representative sample of the highly irregular heterogeneity met with in blue cheese—especially if the cylinder is applied in the horizontal direction (left photo). If there is directional spatial heterogeneity in a cheese, it is very likely in the vertical direction, even though this is attempted compensated for by frequent “turning over” of the maturing cheeses. Even though this standard orientation is aiming at reaching all the way to the centre of the lot (a sound objective), there is a marked volumetric over-sampling of the lot material closer to the centre relative to the more peripheral locations (see further below).
The illustration of one or two opposing pie-cuts illustrates the TOS-correct delineation of a circular lot—and takes it further, by expanding the flat lot completely in the third (vertical) direction.
This is the most fundamental issue for all scales. Even if the tubular corer were of the same thickness as the “cheese” in the third, vertical dimension, it would still be at fault. It would still be over-sampling in the central locations (Figure 2). The delineating radius vectors must originate at the central vertical axis through the lot, which is not compatible with the geometry of a cylindrical tubular corer (or the scoop illustrated in Figure 1).
The TOS-correct delineation of a spear sampler used in this geometrical context should have been funnel-like, tapering off towards the centre of the lot, but such a geometry violates against a balanced in-flow of material in the corer. Interestingly then (from a TOS perspective), a corer would appear to have to respect two distinctly different geometrical demands, for vertical vs horizontal insertion, respectively. This is, of course, not so interesting for current practice, which does not distinguish between these two modus operandi. So, the world is left with a plethora of offerings in the form of “universal corers”, none of which able to do correct horizontal coring, but are quite OK for vertical work, so long as they extract a complete core (see further below).
Spear sampling—at all scales
Spear samplers are popular in all walks of science, technology and industry, and at all scales. Spear samplers range in size from the small scale hand-operated tubular extractors used in laboratories, for example in the food and feed industry, certainly not only for cheese as above, but also for minced or mixed meat products, chocolate, butter etc. The main purpose is to extract a sample from the interior of the lot material (and only very rarely also with a view of getting a balanced sample w.r.t. the full lot geometry).
Spear samplers are used extensively also in the meso-scale industrial regimen (1–2 m length) for sampling a wide range of products and commodities, e.g. grain, fly ash, coal fines, chemical products, construction materials etc. and are furthermore much deployed in bulk materials handling, e.g. for sampling bulk minerals and concentrates, ores, coal, wood shards (biomass and bioenergy sectors), and “waste” from other industrial processing that contains valuable elements and compounds that can be recovered at a profit (platinum group metals, Rare Earth Elements (REE), gold, silver etc. ranging in scale from jewellery cuttings to industrial recyclates arriving by the truck or railroad load. In many science and technology areas the characteristics of the target material formally invites specific spear sampling, e.g. agricultural and environmental sampling, i.e. of soil and peat or in pharma. This state of affairs is widespread indeed, e.g. spear sampling from big bags, from product bags, from railroad cars, from truck loads..., spear sampling almost ad infinitum (Figure 3).
All these applications are popular because of the comparative ease with which a column of target material can be extracted. But spear sampling is perhaps mostly popular because of the extremely low capital investment involved, as well as low operator costs. There is actually only one thing wrong with spear samplers in this scenario—they are very, very difficult to make representative!
Against this stands TOS’ dictum: representative sampling must by necessity comply with the Fundamental Sampling Principle (FSP): all virtual increments of a lot must have an identical, non-zero, probability to be extracted, which translates: no physical volume of the lot can be allowed to be out-of-reach of the spear (Figure 4).
From current experience with contemporary practices it is obvious that most spear sampling violates markedly with the FSP demand illustrated below, because spears only rarely are designed or operated to cover the full depth of the lot in question and thus are idiosyncratic w.r.t. the distribution of spatial heterogeneity in the lot, the distributional heterogeneity, DHLOT. The crucial issue is to be able to recover, completely and without loss, a full core length, and in particular the distal bottom part where absolutely no loss is allowed—due to segregation or otherwise. This is the crucial aspect of true spear sampling. Violation of this requirement is the most frequent reason that spear sampling is mostly non-representative (Figure 5).
IF a spear sampler should be able to work in a representative fashion, what might be called a “True Spear Sampler” (TSS), it must by design, manufacturing, usage and maintenance be able to mitigate the deficiencies pointed out:
- For a TSS, the sampling depth must always be able to cover the full depth of the lot (including the “extra” length needed to connect to the driver/engine).
- The TTS is designed to operate in two modi: forced insertion or true coring (drilling).
- The TSS is designed always to recover the complete core, with special focus on the critical bottom part from which no loss is permitted; this demand is not negotiable.
- The TSS must allow all collected material to be recovered; there must be no material adhering to the inner surface of the sampler.
Any TSS must be tested empirically, under deliberately adverse conditions and with materials comprising at least three components with properties representing mass fluxes and concentrations in typical industrial and technological systems, covering both high, intermediate as well as trace concentrations, see, for example, Petersen et al. for description of an extensive experimental design.2 One of the test components should vary significantly in particle shape, aspect ratio and surface roughness and another (preferentially in trace concentrations only) should be prone to particle bouncing and segregation (spillage). Such test systems should be as difficult to sample as possible, in order constitute realistic worst case scenarios.2 Such tests must comply with the stipulations of a proper Replication Experiment (RE).3 Even if a particular TSS is fit-for-purpose and representative for some specific materials, it cannot be universally applied to other types of material—unless similarly tested empirically by RE. Despite many OEM claims, there is no such thing as a “universal sampler” that will work for all materials… because materials have different inherent heterogeneities.
Observe how analysis of “spear sampling” as a generic sampling process is unhampered by special attention to one or some scales only—or to special materials for that matter. The characteristics of spear sampling are principally identical at all scales—it is only the physical size of the spear sampling tool that changes so as to match the physical lot size.
Note also, however, that lot heterogeneity will change independently of the size of the lot and/or the sampling tool. Material heterogeneity is not correlated with lot scale, but is correlated with, is indeed a function of, the fragment/grain/particle size and the local-scale arrangements hereof (the lot unit elements) contributing to the constitutional heterogeneity of the lot, CHLOT. Thus spear sampling is a function of the unit sampling volume, the increment volume. In composite sampling the increment volume must of course be set so as to match CHLOT (influx openings must exceed 3× the largest particle diameter) etc.
The “spear sampler” is a very good, and therefore a very bad example of a very often met with misunderstanding: one type of sampling tool fits all purposes, fits all materials, fit all lots… which it most emphatically does not!
The spear sampler is an example of a perhaps good engineering solution to a problem that unfortunately is not simple and universal: “how to extract a representative sample from the interior of a lot?”, but a problem for which understanding of the full complement of features in TOS is necessary, in particular FSP, CHLOT, DHLOT. In order to deal effectively with the latter, DHLOT, it is necessary to understand and acknowledge the imperative of composite sampling, i.e. applying a sufficient number, Q, of complete top-to-bottom cores of the lot. This is another story already much touched upon in earlier columns (and which needs to be emphasised again below where appropriate).
Representative sampling is not about buying a specific tool with which to take on all the world’s materials, i.e. all the world’s manifestations of heterogeneity. This is futile. Despite many OEM claims, there is no such thing as a “universal sampler” that will work for all materials… precisely because materials have different inherent heterogeneities.
Representative sampling is all about mastering the necessary and sufficient principles laid down by TOS3,4 with which then to make rational choices regarding the most appropriate types of sampling tools needed for a specific task, for a specific material.
Incidentally, the above relates directly to one of the six governing principles of TOS, Sampling Scale Invariance (SSI): when designed, operated (and maintained) correctly (unbiased samplers), the spear sampling principle is identical at absolutely all scales.
- K.H. Esbensen, A.D. Román-Ospino, A. Sanchez and R.J. Romañach, “Adequacy and verifiability of pharmaceutical mixtures and dose units by variographic analysis (Theory of Sampling)—A call for a regulatory paradigm shift”, Int. J. Pharmaceut. 499, 156–174 (2016). doi: http://dx.doi.org/10.1016/j.ijpharm.2015.12.038
- L. Petersen, C. Dahl and K.H. Esbensen, “Representative mass reduction in sampling—a critical survey of techniques and hardware”, in Special Issue: 50 years of Pierre Gy’s Theory of Sampling. Proceedings: First World Conference on Sampling and Blending (WCSB1), Ed by K.H. Esbensen and P. Minkkinen, Chemometr. Intell. Lab. Syst. 74(1), 95–114 (2004). doi: http://dx.doi.org/10.1016/j.chemolab.2004.03.020
- DS 3077. Representative Sampling—Horizontal Standard. Danish Standards (2013). www.ds.dk
- K.H. Esbensen and C. Wagner, “Theory of Sampling (TOS) versus Measurement Uncertainty (MU)—a call for integration”, Trends Anal. Chem. (TrAC) 57, 93–106 (2014). doi: http://dx.doi.org/10.1016/j.trac.2014.02.007