1. Introduction
Consistency is a quantification of the structural integrity of a material that exhibits both fluid- and solid-like behavior. Such materials include non-Newtonian fluids, viscoelastic materials, dispersions, structured liquids, soft solids, semi-fluids, semi-solids, and more. Some of these terms are organized in
Figure 1. Such a chart should only be used for a basic understanding of the subject, as many materials do not neatly fit within the organizational structure given due to the overlapping scopes of many of the terms contained within. Because of this ambiguity, the present authors adopt the term “rheological material” to include all materials for which the term “consistency” applies in a mechanical sense. These materials are used in a vast range of fields, such as food/dairy, pharmaceutical, cosmetic, lubricating grease, cement/concrete, grout/mortar, bitumen, paints/coatings, paper pulp, printing ink, toothpaste, blood tests, drilling mud, sewage, and soil analysis [
1,
2,
3,
4,
5,
6,
7].
Across these areas, there are various definitions and vastly different methods for testing material consistency. A review of the existing literature shows that there is no unifying definition and method for the quantification of consistency. Rather, there are individual definitions that apply to a specific situation. Numerous explicit and implicit definitions of consistency and the context for which they apply are given in
Table 1.
Most of these definitions are quite similar and could be combined to form a definition for consistency, such as “the ability of a material to resist movement when subjected to stress”. This is quite similar to shear viscosity, which is generally regarded as the most important material function in an industrial context [
8]. What differentiates consistency from viscosity is that it applies to a wider range of materials and contexts where a simple viscosity cannot be calculated. According to ASTM F1080 [
9], a device called the Bostwick consistometer (later discussed in
Section 4) is used because viscosity measurements cannot predict consistency “due to surface tension and density effects”. There are clearly properties other than viscosity that determine consistency.
Overall, McGuigan [
10] broadly defines consistency as “a subjective term descriptive of the flow properties of a liquid usually measured in an empirical manner and in arbitrary units.” To add to this, the notes for ASTM D907 indicate that “consistency is not a fundamental property” but is instead “composed of viscosity, plasticity, and other phenomena” [
11]. Thus, one could say that consistency is not a permanent feature of a rheological material; instead, it is a representation of how the material behaves at a particular point in time under a particular set of conditions. As the underlying fundamental properties that make up consistency change with time, so too does consistency.
Table 1.
Definitions of consistency across various industries
Table 1.
Definitions of consistency across various industries
Context | Definition of Consistency |
---|
Cementitious mixtures | “Relative mobility or ability to flow” [12] |
Soil | “Relative ease with which a soil can be deformed” [13] |
Lubricating grease | Degree of resistance to movement by force [14,15] |
Relative stiffness or hardness [16,17] |
Cohesiveness [18] |
Self-flowing castable refractories | “Degree of mobility under its own weight” [19] |
Liquid adhesives | “Material’s ability to resist deformation” [11] |
Food | Degree of mobility down a ramp due to gravity [9] |
Force or deformation needed to cause yielding [20] |
Average size of food particles [21] |
Subjective texture [22] |
Many different industries arbitrarily define consistency as the result of a particular test. For lubricating grease, consistency is defined by the cone penetration test [
23]. For concrete, consistency is measured by the slump test [
24]. Other tests are sometimes used in these cases, but they have not seen widespread acceptance. However, in all contexts, consistency may be determined by some combination of more fundamental properties such as apparent viscosity, viscoelasticity, adhesiveness, density, thixotropy, yield stress, crossover stress, surface tension, elastic modulus, particle size, particle agglomeration, and tackiness. A more thorough discussion of these properties is provided later.
A quantification of consistency may be needed for safety purposes in foods and medications or even in concrete to ensure correct structural properties. There may also be quality control purposes for quantifying consistency in products such as lotions, foods, and cosmetics to give a certain brand a competitive subjective advantage. Further, there may be efficiency improvements that can be made by optimizing the consistency of a product to match a specific application, such as lubricating grease or drilling mud. In such industries, a batch of product with the wrong consistency may need to be discarded, generally with significant financial impact. Thus, an understanding of the mechanics of consistency during manufacturing [
25] and appropriate test methods to ensure proper consistency are critical.
In this paper, the fundamental mechanics of consistency are described in
Section 2, covering the microscopic and macroscopic interactions that lead to consistency.
Section 3 covers concepts in the field of rheology that are useful in understanding and modelling consistency.
Section 4 covers the main empirical tests currently used across a wide range of industries with a focus on applications.
Section 5 then covers rheological tests useful in measuring the fundamental parameters that give rise to consistency. These parameters are summarized in
Section 6. Then, conclusions and recommendations for future work are given in
Section 7.
4. Quantifying Consistency: Industry Tests
Though the idea of consistency is broadly similar across various industries, there are different ways of quantifying it depending on the industry. These different methods are expected to provide slightly different results that do not exactly correlate with each other. As McGuigan notes [
10], most consistency tests are empirical with results presented in arbitrary units. Such tests include a wide range of deformation tests, flow tests, penetration tests, and other similar tests. Each is generally used within a specific industry because the test is simple to perform, provides a reasonable degree of reproducibility, and has at least some capacity to dictate a material’s suitability to a given application.
Because there are fundamentally different consistency tests across a wide range of industries, they are grouped together here by the core concept of the test. The main concepts include deformation by a material’s own weight, forced deformation with minimal constraints, penetration by a foreign object, flow through a fixed geometry, simple viscosity tests, and other tests that are designed to be simple.
The first consistency test concept that will be covered is where a material’s own weight is used to induce flow. Such methods generally test how much a material’s density overpowers cohesive (and to a lesser extent, adhesive) forces when allowed to flow starting from an unstable formation. Such tests include the Bostwick consistometer test [
18], castable refractory consistency test [
19], concrete slump test [
24], and controlled low-strength material (CLSM) flow consistency test [
69].
The Bostwick consistometer test [
9] measures the distance a material flows down a ramp over a given amount of time. This is primarily used for food products, but it may also be used to measure paint, cosmetics, or other chemicals. This test is used because of its simplicity and ability to be used with a wide range of materials.
The castable refractory consistency test [
19] is applied to materials that are often used to construct heat-resistant structures such as ovens and kilns. An appropriate mix of dry castable and mixing liquid is placed into a cone-shaped mold. The mold is then removed from the partially cured refractory mixture, causing it to deform and flow under its own weight. The change to the diameter of the base of the cone is used as the measurement of consistency and can be used to calculate the “percent self-flow”.
A similar test exists for measuring controlled low strength materials (CLSM), such as soil, aggregates, and cementitious material [
69]. The procedure is quite similar, and the end result is a disc whose diameter is measured in various places and is averaged to produce an indication of consistency.
These differ slightly from the concrete slump test [
24], which uses a similar procedure, but the final height of a slumped cone of concrete is used rather than the diameter of its base. Nevertheless, this test once again measures the change in geometry of a material when left to deform under its own weight from an unstable initial state.
Similar to these tests is the second concept, where the test sample is forced to deform, but there are minimal restrictions on its motion. This means that the initial formation is not necessarily unstable, but the results are less dependent on density than the preceding tests. Two examples are the flow table test for mortar consistency [
70] and the vibratory table test for concrete [
71].
The mortar consistency test is similar to the castable refractory test and CLSM test, except the sample is on a table that is dropped repeatedly, leading to repeated impacts. Clearly, this causes more deformation than if the sample were left alone.
In the vibratory table test, a stiff concrete mix is placed in a cone mold on a vibratory table. The mold is removed, and a weight is placed on top of it. The table then vibrates until the sample is flat and the time it takes for this to happen is recorded as the consistency.
The third test concept involves penetration of the test sample by a foreign object such as a cone, rod, or needle. This applies to industries such as grease [
23,
72], petroleum waxes [
73], petrolatum [
74], bituminous materials [
75], cement paste [
76], and/or mortars [
77,
78,
79]. These tests have differences in preparation of the samples, geometry of the penetrating tool, and other details, but the overall idea is similar across all of them. In most cases, the penetrating tool is allowed to fall into the sample and the depth it reaches in some amount of time is used as an indication of the consistency. In other cases, the tool is allowed to penetrate until it reaches a steady state. The deeper the tool penetrates, the less firm the consistency. Mechanics of the grease cone penetration test are discussed in detail in other papers focused on grease consistency [
80,
81].
The fourth general test concept discussed in this paper is the flow of a material through a fixed geometry. This may be through a cone in the case of grout [
82] or a syringe in the case of food [
21] and lubricating grease [
83]. They use gravity or a plunger to force the sample through the fixed geometry and the rate of flow or flow resistance is measured and used to quantify consistency. This is akin to pumpability, where the results depend on properties such as apparent viscosity, wall effects, plug formation, and yield stress. However, if gravity is used as the driving force, the results depend more strongly on density.
The fifth test concept explored here is the testing of a material’s apparent viscosity. This concept mainly applies to materials such as paint, coatings, and slurries. This may be performed with a commercial viscometer [
84,
85,
86] or in the case of slurries, a special machine that is effectively a large-scale viscometer [
87]. In this case, a measurement tool with a specific geometry—typically a cylinder or paddle—rotates within a container of the sample and the resistive torque imposed on it is used to calculate the apparent viscosity. Because most of the materials relevant in this paper are not Newtonian fluids, the apparent viscosity depends on the exact conditions imposed by the test.
The last section of tests are qualitative tests used because of their simplicity. Often these are used for field testing or where results only need to be an approximation. Such tests include the ball-in-hand test of refractories [
88] and various food tests, including the spoon tilt test, fork drip test, and fork pressure test [
89].
The ball-in-hand test of refractories [
88] involves forming a ball of the refractory in the practitioner’s hand and visually inspecting consistency by seeing how much flows between the practitioner’s fingers after tossing the ball in the air and catching it.
The International Dysphagia Diet Standardization Initiative outlines various simple tests that can be easily carried out to examine food consistency, including the fork drip test, spoon tilt test, fork or spoon pressure test, chopstick test, and finger test [
21,
89]. Understanding food consistency is important for the safety of children or those with disabilities, yet a rigorous quantitative test is impractical and not necessary. Using a 10 mL syringe for drinks and standard eating utensils for food allows for anyone to test food consistency quickly and easily.
Overall, consistency is generally quantified with arbitrary measurements that are meant as a way of comparing different samples. This generally means there is some freedom in determining exactly how consistency should be measured. For example, ASTM D1338 [
90] demands a consistency test for evaluating adhesive materials, but states that “any means of measuring the viscosity or consistency of the adhesive can be selected.” Because of the high variance in methods, the units of consistency can be distance, time, force, viscosity, or nothing at all because the test is qualitative. Nevertheless, the list of tests provided in this section (summarized in
Table 5) is not exhaustive; instead, it is meant to provide an overview of the range of possible tests for quantifying consistency across the wide range of industries for which the concept is relevant.
Table 5.
Common consistency tests across various industries.
Table 5.
Common consistency tests across various industries.
Test Type | Relevant Properties | Tests Available | Fields Where Relevant |
---|
Deformation under own weight | Density, apparent viscosity, yield stress, thixotropy | Bostwick consistometer [9], slump test [24], refractory consistency [19], CLSM consistency [69] | Food, concrete, soil, cement, mortar |
Minimally constrained forced deformation | Apparent viscosity, yield stress, thixotropy, density | Concrete vibratory table [71], mortar consistency flow table [70] | Concrete, mortar |
Penetration test | Apparent viscosity, yield stress, adhesiveness, density | Cone penetration [23,72,74,77,78], needle penetration [73,75], rod penetration [76] | Grease, bitumen, petrolatum, soil, cement, mortar |
Flow through fixed geometry | Apparent viscosity, yield stress, adhesiveness, density | Grout flow cone [82], food syringe test [21], grease die extrusion [83] | Grout, food, grease |
Viscosity test | Apparent viscosity | Stormer viscometer [86], API paddle [87] | Paint, coatings, slurries |
Qualitative tests | Density, adhesiveness, apparent viscosity | Spoon tilt/fork drip food tests [21], ball-in-hand refractory test [88] | Food, refractories |
6. Fundamental Parameters That Determine Consistency
Consistency is a macroscopic property that is made up of numerous fundamental properties, including those outlined in
Table 8. In fact, one may think of consistency as a practical simplification of complex behavior that can be measured relatively easily and used to assess a material’s suitability for a given application. The balance of fundamental properties that makes up consistency depends on one’s interpretation of consistency, meaning one must identify the particular parameters that are relevant for a given material in a particular application. Once identified, these parameters may be individually measured and used together to detail exactly how consistency is being defined and how sensitive it is to changes in these properties. Unfortunately, these fundamental parameters are generally not distinct from one another.
Parameters that may be used include apparent viscosity, adhesion, thixotropy, yield stress, crossover stress, wall depletion, particle shape and size, particle agglomeration tendency, density, tackiness, elastic modulus, creep response, relaxation behavior, surface tension, relaxation time, zero-shear viscosity, and more. Apparent viscosity is generally the most important component of consistency but does not entirely capture the behavior of materials. Most of these parameters may be measured by rheological tests, allowing for almost all the aspects of consistency across a wide range of domains to be measured by a rheometer using different geometries. Many industries, such as cosmetic and pharmaceutical industries, are absent from
Section 4, as they mostly use penetration tests and rheological tests to quantify behavior rather than the specific setups of the industry-focused tests discussed.
Pumpability is one way of interpreting consistency but is dependent on apparent viscosity, wall effects, plug formation, yield stress, and thixotropy for many rheological materials, while this is simply a function of viscosity and density for a Newtonian fluid. These properties, particularly thixotropy, govern behavior in materials such as grease and coal suspensions during start/stop pumping. Such a consideration is also relevant in food systems that can lose their suspension properties, causing sedimentation or creaming.
The tests to measure some of these fundamental properties do not necessarily involve rheology. For instance, surface tension and density are relevant parameters in modelling consistency. The magnitude of surface tension, sometimes measured by observing the contact angle of a water droplet [
127], means that the materials used to construct test equipment could potentially have a significant effect on the results due to wetting behavior. Awareness of the impact of such variables is needed as methods for quantifying consistency are refined.
7. Conclusions and Future Work
An understanding of consistency and its fundamental underlying parameters has a significant appeal to a wide variety of industries. Though there are numerous ways of defining consistency, every definition refers to the structural integrity of a material in some way. In an industrial context, this structural integrity is measured in a wide variety of manners, each of which is intended on providing a close match to the end application. However, by more closely understanding the end application and the test methods used, the underlying fundamental parameters may be measured individually and used to model the performance of a material more thoughtfully and to design more meaningful consistency tests. Such parameters include apparent viscosity, adhesion, thixotropy, yield stress, crossover stress, wall depletion, particle shape and size, particle agglomeration tendency, density, tackiness, elastic modulus, creep response, relaxation behavior, surface tension, and zero-shear viscosity. Many of these are measured using rheological techniques that can be more thoroughly understood at a fundamental level than specific industry tests. In addition, results of some of these tests have already been found to correlate quite well with some measures of consistency [
80,
81,
128,
129,
130,
131].
A key consideration of consistency is the need to have measurement conditions resemble application conditions since different behaviors may manifest in different regimes. Therefore, steady state measurements may fully characterize a material in one situation, while being completely irrelevant for another situation. Another consideration is that materials that have consistency are generally not homogeneous and have different phases that may separate. Therefore, the specific sample measured may not be indicative of the bulk. For these cases, standardized methods for collecting samples [
132,
133] should be used to obtain a sample most representative of a larger quantity.
A further understanding of consistency may also be useful in interpreting and designing consistency tests. For instance, results of a cone penetration test have a strong dependence on apparent viscosity and yield stress, but a weak dependence on creep and relaxation due to how short the test generally is. If the test time were extended, these characteristics would become more significant.
Consistency is generally not well defined across all industries and similar concepts arise, such as the idea of workability in concrete. Workability of concrete is suitability for a given context (the ease with which it can be put in its final form for a particular job without segregation), while consistency is considered a material property. The slump test directly measures consistency, indirectly measuring workability. The overall idea of workability is not completely distinct from consistency, meaning they have some overlap. Similar situations of overlapping terminologies exist across many industries where rheological materials are used and are partly responsible for the imprecise definitions of consistency.
Ultimately, consistency is only one macroscopic property of a material and may or may not be relevant when assessing a material’s performance in a certain context. Measuring some of the more fundamental properties that make up consistency may be a better choice, as these may be quantified using generalized methods. As noted before, consistency is simply a characterization of a material at a given point in time under a given set of conditions. Especially for lubricants, these conditions generally change with time, potentially resulting in dramatically different consistency over time. In many cases, understanding and modeling this change is crucial for accurately matching a product to an application.