Agricultural Engineering · Post-Harvest, Food & Process Engineering · also Engineering Properties of Biological Materials, Biomaterials Properties
The physical, frictional, aerodynamic, thermal, rheological and electrical properties of grains, fruits and foods that every machine and process is designed around.
In the exams: GATE AG Section 6 (first syllabus line; rheology in 4 of 8 papers 2019–26); ICAR AICE subject 41 Unit 1; NCEES PE properties of biological materials
Engineering properties of agricultural produce are the measurable physical, mechanical, thermal, aerodynamic, frictional, electrical, optical and moisture-related characteristics of grains, seeds, fruits, vegetables and foods. Every machine and process in post-harvest engineering is sized around them. The screen aperture of a grader comes from kernel dimensions; the capacity of a bin comes from bulk density; the fan of a dryer is chosen from the porosity and airflow resistance of the grain mass; the air speed in a cleaner sits between the terminal velocities of chaff and grain; the hopper wall angle comes from the friction of grain on steel; the heating time of a retort comes from thermal diffusivity; the pump for a fruit purée comes from its flow behaviour; and the shelf life of a dried product comes from its water activity.
Biological materials are not like steel or concrete. They are variable (two kernels from the same ear differ), anisotropic, alive or recently alive, and they change with moisture content, temperature, maturity and time. A property value is therefore meaningful only when the moisture content, temperature, variety and method of measurement are stated with it. This manual teaches the definitions, the standard measurement methods and the equations, and repeatedly warns where values vary by crop, variety, country and method.
The subject is examined worldwide. In India it is the first line of the Agricultural Process Engineering section of GATE AG, Unit 1 of the ICAR AICE-JRF/SRF Processing and Food Engineering syllabus, and part of Unit VI of ICAR AIEEA-PG; rheology and water activity questions recur in GATE. The NCEES PE Agricultural and Biological Engineering examination tests properties of biological materials within Processing Systems, using supplied standards. Engineers Canada lists physical properties of biological materials and foods as a Group A examination subject.
A biological material is a product of growth. Its cells contain water held in vacuoles, cell walls and capillaries, and its structure differs along and across the grain, fibre or fruit axis. Three consequences matter for the engineer. First, variability: dimensions, mass and strength vary between individuals, so properties are reported as a mean with a standard deviation or as a frequency distribution, and a machine must handle the spread, not only the mean. Second, dependence on state: almost every property changes with moisture content, temperature, maturity and storage time, and many depend on the rate at which load is applied. Third, the material can be damaged: a fruit that is bruised or a seed whose embryo is cracked has lost value even if it looks whole, so the engineer designs for the onset of damage, not for ultimate failure. Sampling must also be representative: grain in a truck or bin is drawn with probes at several points, then mixed and divided before any property is measured.
Moisture content is the single most important state variable. On wet basis, M_wb = mass of water / total mass (water plus dry matter). On dry basis, M_db = mass of water / mass of dry matter. Wet basis is used in trade and in most grain standards; dry basis is used in drying calculations because the dry matter does not change while water is removed. The conversions are M_db = M_wb / (1 - M_wb) and M_wb = M_db / (1 + M_db), with both as decimals. Wet basis cannot exceed 100 percent; dry basis can, and fresh fruit and vegetables often exceed 400 percent dry basis.
The mass of water removed when a material is dried from M1 to M2 (both wet basis) is found by holding dry matter constant: final mass = initial mass × (1 - M1) / (1 - M2). For example, drying 1000 kg of paddy from 20 percent to 14 percent wet basis gives 1000 × 0.80 / 0.86 = 930.2 kg, so 69.8 kg of water is removed, not 60 kg.
Moisture is measured by direct methods (air-oven drying at a stated temperature and time, vacuum oven, distillation with an immiscible solvent, and chemical titration) and by indirect methods calibrated against them (electrical resistance and capacitance meters, near-infrared reflectance, microwave and nuclear magnetic resonance methods).
Size of an irregular particle is described by three mutually perpendicular dimensions: the length L (major diameter, the longest), the width W (intermediate) and the thickness T (minor). They are measured with a micrometer or vernier calliper on a sample of individual kernels, or today by image analysis, which also gives projected area and perimeter. For each dimension, the mean, standard deviation and range are reported, because a grader or a metering plate must accept the whole distribution.
Two equivalent diameters are used. The arithmetic mean diameter is D_a = (L + W + T) / 3. The geometric mean diameter is D_g = (L × W × T)^(1/3); it is the diameter of a sphere whose volume equals that of the triaxial ellipsoid with the same axes (the ellipsoid volume is π L W T / 6). The surface area of a grain is often approximated as S = π D_g², the area of the sphere with diameter D_g, while the volume as an ellipsoid is V = π L W T / 6. The aspect ratio R_a = W / L describes elongation; a value near 1 indicates a rounder outline, which tends to roll rather than slide on a surface.
For ground material (feed mash, flour), size is a distribution measured by sieving. The ASABE method computes a geometric mean diameter by mass, d_gw = antilog [Σ(W_i log d̄_i) / Σ W_i], where W_i is the mass on sieve i and d̄_i is the geometric mean of the apertures of the sieve and the one above it.
Sphericity expresses how close a shape is to a sphere; a sphere has sphericity 1 and every other shape less. Three definitions are in use, and examination questions say which one they mean.
Wadell's (true) sphericity is the ratio of the surface area of a sphere having the same volume as the particle to the actual surface area of the particle. It is the most rigorous but needs both volume and surface area.
Curray's sphericity, used widely for projected images, is d_i / d_c: the diameter of the largest circle that can be inscribed in the projected outline divided by the diameter of the smallest circle that circumscribes it.
The working definition in Mohsenin's textbook and in most agricultural engineering courses is the ratio of the geometric mean diameter to the major diameter: Φ = (L W T)^(1/3) / L. It follows from Wadell's idea by taking the volume as that of a triaxial ellipsoid and comparing the equal-volume sphere's diameter with the longest dimension. For a wheat kernel with L = 6.2 mm, W = 3.1 mm and T = 2.8 mm, D_g = 3.78 mm and Φ = 0.61. Some texts instead report (W/L) or use the arithmetic mean diameter in the numerator; these give different numbers for the same kernel, which is why a question must state its formula.
Sphericity matters in practice: low-sphericity seeds slide rather than roll, which affects metering on inclined plates and separation on spiral and inclined-belt separators; it also enters drag-coefficient and terminal-velocity correlations and the relation between surface area and volume used in drying and heat-transfer models.
Roundness measures the sharpness of the corners of a particle, which is different from its overall resemblance to a sphere. A cube has sharp corners and low roundness yet fairly high sphericity; a rounded elongated grain has high roundness but low sphericity. Curray's roundness is the ratio of the largest projected area of the object in its natural rest position, A_p, to the area of the smallest circle that circumscribes that projection, A_c. Wadell's roundness, borrowed from sedimentology, is the average radius of curvature of the corners divided by the radius of the maximum inscribed circle, Σr / (N R), for N corners.
Fruits and vegetables are also classified against charted standards: the outline of a sample is compared with a chart of named shapes such as round, oblate (flattened at the stem and blossom ends), oblong, conic, ovate, obovate, elliptic, truncate, ribbed and lopsided. Image analysis now gives quantitative descriptors directly from the outline.
Size and shape increase with moisture content for most grains and seeds as they swell; the dependence is often close to linear over the handling range, and the coefficients differ by crop and variety. A sorter set up for dry seed may therefore pass or reject differently when the seed is damp.
The volume of a regularly shaped item can be calculated from its dimensions: a sphere πD³/6, a triaxial ellipsoid πLWT/6, a prolate spheroid (rotated about its long axis) 4πab²/3 and an oblate spheroid 4πa²b/3, where a and b are the semi-axes along and across the axis of rotation.
For large items such as fruits and tubers, the platform-scale (water displacement) method is standard. A container of water sits on a scale; the item is pushed fully under the surface with a thin rod so that it does not touch the container, and the increase in scale reading equals the mass of water displaced. Volume = increase in reading / density of water. If the item is instead weighed in air and then suspended in water, the loss of weight equals the weight of displaced water, and specific gravity = weight in air / (weight in air - weight in water), multiplied by the specific gravity of water at the test temperature.
Small kernels absorb water, so displacement uses a liquid that is not absorbed readily, such as toluene, which has low surface tension and fills surface irregularities; its density must be corrected for temperature. Gas (air or helium) pycnometers avoid wetting altogether. They work on Boyle's law: a gas at known pressure in a reference chamber is expanded into a chamber holding the sample, and the drop in pressure gives the gas-free volume of the sample.
Several densities are defined, and the vocabulary is not uniform between texts. True (solid, substance) density is the mass divided by the volume of the solid material excluding all pores. Particle or kernel density is mass divided by the volume of an individual kernel including its internal closed pores; this is what toluene displacement measures and what most agricultural texts call 'true density' of grain. Bulk density is the mass of a bulk of material divided by the total volume it occupies, including the voids between kernels. For grain, ρ_b is measured by pouring from a standard height into a container of known volume, striking off the top without compacting, and weighing.
Bulk density depends on how the container is filled. Pouring from greater height, spreading the stream, or vibrating the container increases bulk density, and grain in a tall bin is compacted under its own weight so the mass stored can exceed volume × poured bulk density. Moisture affects bulk density in two directions at once: kernels swell, and friction between kernels changes. For many cereals bulk density falls as moisture rises over the storage range, but the direction and size of the change differ by crop, so it must be measured or taken from a crop-specific equation.
Test weight is a trade expression of bulk density, reported as kilograms per hectolitre (kg/hL) or pounds per bushel, measured with a standard filling apparatus defined by each country's grain standard. 1 kg/hL equals 10 kg/m³.
Bulk density is the design input for bin capacity, truck and wagon loading, the throughput of conveyors and elevators (mass flow = volumetric capacity × bulk density) and the load on bin walls and floors.
Porosity is the fraction of the total volume of a bulk that is occupied by air (voids). With the bulk density ρ_b and the kernel (true) density ρ_t, porosity ε = 1 - ρ_b / ρ_t, usually expressed as a percentage. The ratio of void volume to solid volume, the void ratio e = ε / (1 - ε), is used in soil mechanics and occasionally in grain mechanics. The kernel volume fraction, 1 - ε, is the packing fraction. For comparison, a random loose packing of equal smooth spheres has a porosity of roughly 0.4; grain bulks commonly fall in the range from about 35 to 55 percent, depending on crop, variety, moisture, foreign matter and filling method.
Porosity can also be measured directly with an air-comparison pycnometer. Two chambers of equal volume are connected by a valve. Chamber 1 is pressurised to gauge pressure P1 while chamber 2, filled with grain, is at atmospheric pressure. When the valve is opened, the pressure equalises at gauge P2. Applying Boyle's law at constant temperature, the void volume V_v in the sample chamber satisfies P1 V = P2 (V + V_v) in gauge terms, so the porosity of the sample chamber is ε = V_v / V = (P1 - P2) / P2 when the two chambers have equal volume V.
Porosity of individual products (internal porosity) is defined in the same way with true solid density and apparent density of the piece.
Air moves through a grain bulk in the voids, so porosity together with kernel size and shape controls the resistance of the bulk to airflow. The pressure drop per unit depth rises more than proportionally with airflow rate and is higher for small kernels (sorghum, millets, rapeseed) than for large ones (maize, soybean) at the same airflow. ASABE publishes airflow-resistance data and an equation of the Shedd form, ΔP / L = a Q² / ln(1 + b Q), with coefficients a and b for each crop, and the NCEES PE examination supplies that standard. A semi-theoretical alternative for packed beds is the Ergun equation, in which pressure drop depends on (1 - ε)² / ε³ for the viscous term and (1 - ε) / ε³ for the inertial term, so a small change in porosity has a large effect. Fines and broken kernels fill voids and concentrate under the spout where grain is poured, so the centre core of a bin resists airflow more and is the first place to spoil; coring (drawing out the centre) and spreaders are used to correct this.
Porosity also enters the heat capacity of the bulk, the effective thermal conductivity of stored grain, the volume of fumigant or controlled-atmosphere gas required per tonne, and the calculation of how much grain a bin of given volume holds once compaction is considered.
Friction between grain and a structural surface governs the slope of chutes and hopper walls, the loads on bin walls, and the behaviour of grain on conveyors and in augers. The coefficient of static friction μ_s is the ratio of the force needed to start sliding to the normal force. It is measured most simply on a tilting table: a bottomless frame filled with grain, or a few kernels glued together, rests on a test surface (galvanised steel, plywood, concrete, rubber, glass), and the surface is tilted slowly until the sample begins to slide. At that angle θ, μ_s = tan θ. The coefficient of kinetic (sliding) friction, lower than the static value, is measured with a pull test at constant speed. Internal friction, between grain and grain, is measured in a shear box or triaxial cell and expressed as an angle of internal friction.
The coefficient of friction of grains and seeds on most surfaces rises with moisture content, because the kernel surface softens and water films increase adhesion. Rougher surfaces such as plywood and concrete usually give higher coefficients than polished steel or glass, but the ranking and values depend on the crop, the surface finish and wear, so design data should be measured or taken from a standard for the specific pair.
The angle of repose is the angle between the horizontal and the free surface of a heap of granular material. The filling (static) angle of repose is formed when grain is poured onto a flat surface to form a cone; the emptying (dynamic) angle of repose is the slope of the surface left when grain drains out of an orifice in the floor of a box. With the cone method, if a cone of height h has base radius r, the angle is θ = arctan(h / r); with the box method, the angle is found from the height and horizontal distance of the remaining slope.
The angle of repose increases with moisture content, surface roughness, elongation and the content of chaff and fines, and decreases for round, smooth, dry kernels. It is used to design the slope of bin bottoms and chutes (a self-cleaning hopper floor must be steeper than the emptying angle of repose), to estimate the extra volume of the conical heap at the top of a flat bin or on a storage floor, and as a simple index of flowability.
In a tall bin, part of the weight of the grain is carried by friction on the walls, so the pressure does not keep rising linearly with depth as in a liquid. Janssen's analysis of a thin horizontal slice gives the lateral pressure at depth y as L = (ρ_b g R / μ') [1 - exp(-k μ' y / R)], where R is the hydraulic radius (cross-sectional area / perimeter, which is D/4 for a circular bin), μ' is the coefficient of friction of grain on the wall, and k is the ratio of lateral to vertical pressure. The vertical pressure is V = L / k. As depth increases the exponential term vanishes and the lateral pressure approaches the limit ρ_b g R / μ'. Engineers apply overpressure factors for emptying, because flow increases wall pressure, and design codes and the ASABE standard on bin loads specify the factors and the k value to use; these differ by code and country. The bulk density used should be the compacted value at the moisture content expected in storage.
When a particle moves relative to a fluid, the fluid exerts a drag force F_d = C_d A ρ_f V² / 2, where C_d is the drag coefficient, A the projected area normal to the flow, ρ_f the fluid density and V the relative velocity. A particle falling in still air accelerates until drag plus buoyancy equals its weight; that steady speed is the terminal velocity. Setting m g = ρ_f g V_p + C_d A ρ_f V_t² / 2 with V_p = m / ρ_p gives V_t = [2 m g (ρ_p - ρ_f) / (ρ_p ρ_f A C_d)]^(1/2). In an upward air stream of exactly V_t a particle hovers; this is how terminal velocity is measured in a vertical wind tunnel with a transparent test section, adjusting the air speed until the kernels float.
The drag coefficient depends on the particle Reynolds number Re = ρ_f V d / μ. In the Stokes (laminar) regime, roughly Re < 1, C_d = 24 / Re and the terminal velocity is V_t = g d² (ρ_p - ρ_f) / (18 μ); this applies to dust, spores, fine flour and spray-dried droplets. In the Newton regime, roughly 1000 < Re < 2 × 10⁵, C_d is nearly constant at about 0.44 for a sphere, and V_t grows with the square root of size. Grain kernels in air fall in or near the Newton regime. Real kernels are not spheres: they tumble, their orientation changes the projected area, and drag coefficients are reported against an equivalent diameter or measured directly. Sphericity enters correlations for non-spherical drag. Terminal velocity increases with kernel mass and moisture content.
Air separation exploits differences in terminal velocity. In a combine cleaning shoe or a winnower, the air speed is set above the terminal velocity of chaff, straw pieces, dust and light or shrivelled kernels and below that of sound grain, so the light fractions are blown out while the grain falls through the sieves. Where the terminal velocity distributions of the two fractions overlap, perfect separation is impossible and the operator trades grain loss against cleanliness.
Pneumatic conveying requires air velocity well above the terminal velocity of the material so that it is carried in suspension; dilute-phase systems commonly run at a conveying velocity of the order of one and a half to several times the terminal velocity, the margin being set by the design method used, bends and the risk of settling (saltation).
Hydrodynamic properties govern the handling of fruits and vegetables in water. Flumes carry potatoes, tomatoes and apples gently; the produce must be denser than, or close in density to, the water for the intended behaviour. Flotation in water or salt and sugar solutions separates by density: immature, hollow or insect-damaged items that are less dense float. The drag in water is far larger than in air at the same speed because water is about 800 times denser, which is why falling into water cushions impact in hydro-handling and why the Reynolds number for a given speed differs greatly from that in air.
Mechanical properties describe how a biological material deforms and fails under load. In a uniaxial compression test a sample is loaded between flat plates or by a probe on a universal testing machine at a set deformation rate, and force and deformation are recorded. For a cylindrical specimen cut from tissue, stress is σ = F / A and engineering strain is ε = ΔL / L0, so the modulus of elasticity is the slope of the initial linear part of the stress-strain curve. For whole convex bodies such as fruits, seeds and tubers, the contact area grows with load, so stress is not uniform. Hertz contact theory then relates force to deformation (deformation grows with force to the power two-thirds for elastic contact between curved surfaces), and the ASABE standard for compression tests of food materials of convex shape gives the equations that convert force, deformation, radii of curvature and Poisson's ratio into an apparent modulus of elasticity.
On a force-deformation curve for fruit flesh or a seed, three features are named. The bioyield point is where deformation increases with no increase, or a decrease, in force; it marks the onset of cell rupture inside the tissue and is the practical limit for handling, because damage begins there even if the skin is unbroken. The rupture point is where the material fails macroscopically and force drops sharply. The area under the curve to rupture is the energy absorbed, a measure of toughness. Firmness is commonly measured by the maximum force needed to push a cylindrical probe a fixed distance into peeled flesh, and is used to judge maturity and ripening; probe size, speed and depth are specified by the method and must be stated.
Biological materials are viscoelastic, so the measured modulus and failure force depend on loading rate. Faster loading generally gives a higher apparent modulus, because there is less time for viscous flow. Moisture content changes behaviour profoundly. Dry grain kernels are hard and brittle and fail by cracking; wetter kernels are softer and deform more before failure. Maize dried quickly at high temperature develops internal stress cracks, which later cause breakage in handling. Rice kernels fissure when they adsorb moisture rapidly after drying, which reduces head rice yield.
Fruit and vegetables are damaged mostly by impact and by compression in containers. In a drop test, the energy delivered on impact equals m g h, where m is mass and h is drop height. Bruise volume or bruise area increases with impact energy and depends on the firmness, temperature and turgor of the fruit and on the hardness of the surface struck. Padding, shorter drops, decelerators in bin fillers and soft water landings reduce damage.
A purely elastic solid stores energy and recovers fully; a purely viscous liquid dissipates energy and flows. Biological materials do both, and their behaviour is modelled with combinations of Hookean springs (σ = E ε) and Newtonian dashpots (σ = η dε/dt).
The Maxwell model is a spring and a dashpot in series. Under a sudden constant strain ε0, the stress relaxes exponentially: σ(t) = E ε0 exp(-t / λ), where λ = η / E is the relaxation time, the time for the stress to fall to 1/e, or about 36.8 percent, of its initial value. A Maxwell element alone cannot show creep recovery, and under constant stress it flows without limit. The generalised Maxwell model, several Maxwell elements in parallel, sometimes with a lone spring for the equilibrium modulus, fits the stress-relaxation curves of fruits, cheese, dough and gels; each element contributes an exponential term with its own relaxation time.
The Kelvin-Voigt model is a spring and a dashpot in parallel. Under a sudden constant stress σ0 it creeps towards the elastic strain: ε(t) = (σ0 / E) [1 - exp(-t / λ_r)], where λ_r = η / E is now called the retardation time, the time to reach 1 - 1/e, or about 63.2 percent, of the final strain. It does not show stress relaxation under constant strain.
The four-element Burgers model is a Maxwell element in series with a Kelvin-Voigt element. Under constant stress σ0 its creep strain is ε(t) = σ0 / E1 + σ0 t / η1 + (σ0 / E2) [1 - exp(-E2 t / η2)]: an instantaneous elastic strain from the free spring E1, a delayed elastic strain from the Kelvin element, and a steady viscous flow from the free dashpot η1. When the load is removed, the instantaneous and delayed parts recover but the flow does not, which leaves a permanent set. Creep tests of potatoes, apples, cheese and grain kernels are commonly fitted with this model, and the parameters describe how produce in the bottom of a deep container or pile deforms under the static load above it.
Two test modes are used. In a stress-relaxation test, a sample is deformed quickly to a fixed strain and the decaying force is recorded. In a creep test, a constant load is applied and the increasing deformation is recorded. For relaxation data, Peleg's linearised empirical model is widely used: F0 t / [F0 - F(t)] = k1 + k2 t, where F0 is the initial force. The reciprocal of k1 describes the initial rate of relaxation, and the reciprocal of k2 is the asymptotic fraction of the force that would relax; 1/k2 near 1 indicates a liquid-like material that relaxes almost completely, while a smaller value indicates a more solid, elastic material.
In dynamic (oscillatory) testing, a small sinusoidal strain is applied and the stress response measured. For a linear viscoelastic material the stress is sinusoidal with a phase lag δ. The storage modulus G' is the in-phase part, representing elastic energy stored; the loss modulus G'' is the out-of-phase part, representing energy dissipated. The loss tangent is tan δ = G'' / G'. A perfectly elastic solid has δ = 0; a Newtonian liquid has δ = 90 degrees. Gels have G' greater than G'' over a wide frequency range, while solutions of polymers show G'' greater than G' at low frequency.
The Deborah number De = λ / t_obs compares the material's relaxation time with the time scale of the process. When De is much larger than 1, the material behaves as a solid over that process; when it is much smaller than 1 it flows like a liquid. A cheese wheel stored for weeks slumps although it feels solid in the hand, and a dough that is elastic during rapid mixing flows during a long proof.
Rheology is the science of deformation and flow. For a fluid in simple shear, the shear stress τ is plotted against the shear rate γ̇ (velocity gradient, in s⁻¹) to give a flow curve. A Newtonian fluid has a straight flow curve through the origin, τ = μ γ̇, with a viscosity μ independent of shear rate and shear history; water, clarified juices, milk, vegetable oils and honey behave as Newtonian fluids over most processing conditions.
Non-Newtonian, time-independent fluids are described by models. The power-law (Ostwald-de Waele) model is τ = K γ̇ⁿ, where K is the consistency coefficient (Pa·sⁿ) and n the flow behaviour index. For n < 1 the fluid is shear-thinning (pseudoplastic): apparent viscosity η_a = τ / γ̇ = K γ̇^(n-1) falls as shear rate rises; most fruit and vegetable purées, concentrates and many sauces are shear-thinning. For n > 1 the fluid is shear-thickening (dilatant), as in concentrated starch suspensions. For n = 1 the power law reduces to Newton's law with K = μ.
Some materials need a minimum stress, the yield stress τ0, before they flow. The Bingham plastic model is τ = τ0 + μ_p γ̇ for τ > τ0. The Herschel-Bulkley model is τ = τ0 + K γ̇ⁿ and covers the most common food behaviour, shear-thinning with a yield stress, found in tomato ketchup, mayonnaise and many purées. The Casson model, τ^(1/2) = τ0^(1/2) + (η_c γ̇)^(1/2), is the classic model for molten chocolate. Time-dependent fluids change apparent viscosity with time of shearing at constant shear rate: thixotropic fluids thin with time and recover at rest (stirred yoghurt and many gels show this), while rheopectic fluids thicken, a rare behaviour in foods.
Viscometers impose a known flow and measure stress, or the reverse. In a capillary or tube viscometer, the pressure drop ΔP over length L and the flow rate Q give, for a Newtonian fluid, the Hagen-Poiseuille relation μ = π R⁴ ΔP / (8 L Q). The wall shear stress is τ_w = R ΔP / (2L) for any fluid, while the apparent wall shear rate 4Q / (π R³) is exact only for Newtonian fluids; for others it is corrected with the Rabinowitsch-Mooney equation, which uses the slope of log τ_w against log of the apparent shear rate.
Rotational instruments include concentric-cylinder (coaxial) viscometers, in which the fluid fills a narrow gap and the torque on one cylinder is measured; cone-and-plate geometries, which have the advantage that a small cone angle gives an almost uniform shear rate across the sample, γ̇ = ω / θ; and parallel-plate geometries, used for pastes and for dynamic tests. Single-spindle rotational viscometers that rotate a spindle in a large container are quick for quality control, but their shear rate is not well defined for non-Newtonian fluids, so readings are comparable only at the same spindle, speed and container.
The falling-ball viscometer uses Stokes' law: a sphere of radius r and density ρ_s falling at steady speed v through a Newtonian liquid of density ρ_f gives μ = 2 r² g (ρ_s - ρ_f) / (9 v), valid when the Reynolds number is small and wall effects are corrected.
Viscosity of liquids falls as temperature rises. The Arrhenius relation, η = A exp(E_a / R T), with T in kelvin and E_a an activation energy for flow, describes this for juices, oils and concentrates; for power-law fluids it is applied to K. Viscosity rises steeply with soluble-solids concentration, and concentration and temperature are often combined in one equation for juice concentrates and sugar syrups.
Rheological properties are the inputs for pipe and pump design and for heat-transfer and residence-time calculations in continuous processing. For laminar flow of a power-law fluid in a pipe, the velocity profile is flatter than the Newtonian parabola when n < 1, and the ratio of maximum to mean velocity is (3n + 1) / (n + 1), which equals 2 for a Newtonian fluid. The fastest particle therefore moves at less than twice the mean speed in a shear-thinning fluid but at more than twice in a shear-thickening fluid, which matters for the hold-tube length in aseptic processing, where safety is set by the fastest particle. The flow regime is judged with the generalised (Metzner-Reed) Reynolds number Re_MR = ρ D^n V^(2-n) / [K 8^(n-1) ((3n + 1) / 4n)^n], which reduces to ρ V D / μ when n = 1.
Specific heat c is the energy required to raise the temperature of unit mass by one kelvin, in kJ/kg·K. Because water has a far higher specific heat (about 4.18 kJ/kg·K) than the dry constituents of food (roughly 1.2 to 2.0 kJ/kg·K for carbohydrate, protein and fat, less for ash), the specific heat of a food is controlled mainly by its moisture content. Siebel's equations, derived from the idea that the dry solids contribute a fixed value and water its own value, are: above freezing, c = 0.837 + 3.349 X_w, and below freezing, c = 0.837 + 1.256 X_w, in kJ/kg·K with X_w the mass fraction of water (wet basis). A more general approach, the model of Choi and Okos, sums the specific heats of the components weighted by their mass fractions, c = Σ c_i X_i, with temperature-dependent equations for water, protein, fat, carbohydrate, fibre and ash.
Specific heat is measured by the method of mixtures: a sample at known temperature is dropped into water in an insulated calorimeter of known heat capacity, and the equilibrium temperature gives the specific heat from an energy balance, heat lost by sample = heat gained by water and calorimeter. Differential scanning calorimetry (DSC) measures heat flow into a small sample against a reference as temperature is scanned and gives specific heat, latent heats of melting and freezing, gelatinisation and denaturation. During freezing, latent heat is released over a range of temperatures because solutes depress the freezing point, so frozen-food calculations use enthalpy-temperature data rather than a single specific heat.
Thermal conductivity k (W/m·K) is the rate of heat conduction per unit area per unit temperature gradient (Fourier's law q = -k dT/dx). Water conducts heat at about 0.6 W/m·K, ice at about 2.2 W/m·K, roughly four times more, and air at about 0.025 W/m·K. As a result, conductivity of foods rises with moisture content, rises sharply on freezing, and falls with porosity. Grain in bulk is a poor conductor, around 0.1 to 0.2 W/m·K depending on crop and moisture, which is why hot spots in stored grain persist and why grain cooled by aeration stays cool for long periods.
Sweat's empirical equation for fruits and vegetables with moisture above about 60 percent wet basis is k = 0.148 + 0.493 X_w (W/m·K); for meats a similar equation is k = 0.08 + 0.52 X_w.
Measurement is by steady-state or transient methods. The guarded hot plate is steady-state: a known heat flux passes through a slab of known thickness and the temperature difference is measured; it is accurate but slow and unsuited to moist foods, in which moisture migrates. The line heat source (thermal conductivity probe) method is transient: a thin heated wire with a thermocouple is inserted into the sample and supplies heat at a constant rate Q per unit length; after initial effects, temperature rises linearly with the logarithm of time, and k = Q ln(t2 / t1) / [4π (T2 - T1)]. It is fast and widely used for grain, fruit and meat.
Thermal diffusivity α = k / (ρ c), in m²/s, measures how fast a temperature change spreads through a material: a high conductivity spreads heat quickly while a high heat capacity per unit volume, ρc, absorbs heat and slows the change. It is the property that appears in transient heat conduction (the heat equation ∂T/∂t = α ∇²T), and therefore in calculations of cooling time of fruit in hydrocoolers and forced-air coolers, heating time in retorts and blanchers and freezing time. Water has a thermal diffusivity of about 1.4 × 10⁻⁷ m²/s, and most moist foods lie close to it, roughly 1 to 2 × 10⁻⁷ m²/s; frozen foods have higher diffusivity because ice has higher conductivity and lower specific heat.
Diffusivity can be computed from measured k, ρ and c, or measured directly by recording the centre temperature of a sample of simple shape (cylinder, slab, sphere) subjected to a step change in surface temperature and matching the history with the analytical solution of the heat equation or with time-temperature charts. The Fourier number Fo = α t / L², with L a characteristic length, combines diffusivity with time and size: two products with the same Fo and Biot number reach the same dimensionless temperature, so doubling the size of a fruit roughly quadruples its cooling time when internal resistance dominates.
Dielectric properties describe how a material interacts with an alternating electric field. The relative complex permittivity is ε* = ε' - j ε''. The dielectric constant ε' measures the ability to store electrical energy; the dielectric loss factor ε'' measures the conversion of electrical energy to heat. Their ratio is the loss tangent, tan δ = ε'' / ε'. Water, being a polar molecule, has a high dielectric constant; dissolved salts add ionic conduction losses. Hence both ε' and ε'' rise with moisture content, and ε'' rises with salt content. Ionic conduction dominates losses at radio frequencies, and dipole rotation of water contributes strongly at microwave frequencies.
The power converted to heat per unit volume is P = 2π f ε0 ε'' E², where f is frequency, ε0 = 8.854 × 10⁻¹² F/m the permittivity of free space, and E the root-mean-square electric field strength. Heating rate therefore rises with frequency, loss factor and the square of field strength. Penetration depth, defined as the depth at which power falls to 1/e of its surface value, decreases as frequency and loss factor rise; for many moist foods it is of the order of a centimetre at 2450 MHz and several times larger at 915 MHz, and radio-frequency heating at 13.56, 27.12 or 40.68 MHz penetrates further still. The frequencies that may be used are allocated by national regulators: 2450 MHz is used worldwide, while the lower microwave band near 915 MHz differs between countries (896 MHz in the United Kingdom, for example).
Because ice has a much lower loss factor than liquid water, microwave thawing is prone to runaway heating: a thawed region absorbs more energy, heats faster and can cook while neighbouring regions remain frozen. Dielectric properties also explain uneven heating at edges and corners.
Electrical conductivity σ (S/m) measures the ability to carry current. For foods it depends on ionic content and moisture and rises with temperature, approximately linearly over processing ranges. In ohmic heating, an alternating current passes directly through the food and the power generated per unit volume is σ E² (or I² R for the whole sample); particles and liquid heat according to their own conductivities, so particles of lower conductivity than the carrier liquid lag behind, a central concern in ohmic process design.
Electrical properties are the basis of rapid grain moisture meters. Resistance-type meters measure the electrical resistance of grain compressed between electrodes; resistance falls steeply with moisture, and the reading must be corrected for temperature. Capacitance-type meters place a sample between electrodes in a measuring cell and measure capacitance, which depends on the dielectric constant and so on moisture and bulk density; a temperature and test-weight correction is applied. All rapid meters are calibrated against a reference oven method for each grain type and require periodic checking.
When light strikes produce, part is reflected from the surface (specular and diffuse reflectance), part is transmitted through the tissue and part is absorbed by pigments and water. Absorbance is A = log10(I0 / I); for clear solutions the Beer-Lambert law gives A = a b c, with a the absorptivity, b the path length and c the concentration, the basis of spectrophotometric analysis. Intact tissues scatter light strongly, so measurements on whole produce use reflectance or interactance geometries rather than simple transmission.
Colour is measured with tristimulus colorimeters or spectrophotometers and expressed in the CIE L*a*b* space: L* is lightness from 0 (black) to 100 (white), a* runs from green (negative) to red (positive) and b* from blue (negative) to yellow (positive). The chroma (saturation) is C* = (a*² + b*²)^(1/2), the hue angle is h = arctan(b* / a*) in degrees taken in the correct quadrant, and the total colour difference between two samples is ΔE = (ΔL*² + Δa*² + Δb*²)^(1/2).
Near-infrared (NIR) spectroscopy, using wavelengths roughly from 780 to 2500 nm, measures overtone and combination bands of O-H, C-H and N-H bonds and, after chemometric calibration, predicts moisture, protein, oil, starch and sugar content non-destructively; it is the basis of whole-grain analysers and of soluble-solids sorting of fruit on packing lines. Light transmission through eggs (candling) reveals cracks and blood spots; machine-vision sorters use reflectance at selected wavelengths to reject discoloured or diseased kernels and fruit; X-ray imaging reveals internal insect infestation and hollow heart.
Water activity a_w is the ratio of the partial vapour pressure of water in equilibrium with a material to the vapour pressure of pure water at the same temperature: a_w = p / p0. It ranges from 0 to 1. When a material is in equilibrium with the surrounding air, its water activity equals the equilibrium relative humidity expressed as a fraction, a_w = ERH / 100. Water activity, not moisture content, governs microbial growth, many chemical reactions and the direction in which moisture moves between components of a food or between grain and air. Two foods with the same moisture content can have very different water activities, which is why water activity is the variable used in shelf-life design.
For an ideal solution, Raoult's law gives a_w = x_w = n_w / (n_w + n_s), the mole fraction of water. One mole of sucrose in 1 kg of water (55.51 mol) gives a_w = 55.51 / 56.51 = 0.982. Real solutions deviate, and electrolytes lower a_w more than their formula moles suggest because they dissociate; empirical corrections such as Norrish's equation are used for concentrated sugar solutions.
Water activity is measured by equilibrating a sample in a small sealed chamber and measuring the humidity of the headspace, by chilled-mirror dew point sensors (the dew point of the headspace gives p), by capacitance or resistance humidity sensors, or gravimetrically by placing samples over saturated salt solutions that hold fixed relative humidities. At 25 °C, saturated lithium chloride gives about 0.11, magnesium chloride about 0.33, sodium chloride about 0.75 and potassium sulfate about 0.97; these values change slightly with temperature.
A moisture sorption isotherm is the curve of equilibrium moisture content (dry basis) against water activity at constant temperature. Most foods and grains give a sigmoid, type II isotherm. At low water activity, water is bound in a monolayer to polar sites; in the middle region it is held in multilayers; at high activity it is held by capillary condensation and in solution, and moisture content rises steeply. The adsorption isotherm (wetting a dry sample) and the desorption isotherm (drying a wet one) do not coincide: at the same water activity the desorption curve lies at higher moisture content. This hysteresis means that a dried product rewetting to a given humidity holds less water than the same product dried down to that humidity.
The Brunauer-Emmett-Teller (BET) equation, a_w / [(1 - a_w) M] = 1 / (M0 C) + [(C - 1) / (M0 C)] a_w, is linear in a_w and yields the monolayer moisture M0 from the slope and intercept; it fits only the low range, up to a water activity of roughly 0.4. The Guggenheim-Anderson-de Boer (GAB) equation, M = M0 C K a_w / [(1 - K a_w)(1 - K a_w + C K a_w)], adds a third constant and fits up to about 0.9; it is the model recommended by many food-engineering groups. For grains, ASABE publishes equilibrium-moisture relations, including the modified Henderson, modified Chung-Pfost, modified Halsey and modified Oswin equations, with constants for each crop; the original Henderson equation is 1 - a_w = exp(-c T M^n) with T absolute. Equilibrium moisture content at a given relative humidity falls as temperature rises, so warm air dries grain to a lower final moisture. The isosteric heat of sorption, from the Clausius-Clapeyron equation applied to isotherms at two temperatures, is the extra energy over the latent heat of free water needed to remove bound water; it rises as moisture content falls, which is why the last few points of moisture are the most costly to remove.
The food stability map relates reaction rates to water activity. Microbial growth stops below defined limits: as a general guide from the food microbiology literature, most spoilage bacteria need a water activity above about 0.90 to 0.91, most yeasts above about 0.88, most moulds above about 0.80, Staphylococcus aureus can grow aerobically down to about 0.86, xerophilic moulds and osmophilic yeasts down to about 0.60 to 0.61, and no microorganism grows below about 0.6. Individual strains, pH, temperature and preservatives shift these limits. Regulation uses water activity too: in the United States, a low-acid canned food is one with a pH above 4.6 and a water activity above 0.85; other countries define their categories in their own rules.
Chemical changes have their own patterns. Lipid oxidation is fastest at very low water activity, slowest near the monolayer moisture, and rises again at intermediate activity. Non-enzymatic (Maillard) browning peaks at intermediate water activity, roughly 0.6 to 0.8, where reactants are mobile but not diluted.
For stored grain, the equilibrium relative humidity of the intergranular air governs mould growth and insect activity. A safe storage moisture is commonly the moisture content in equilibrium with about 65 to 70 percent relative humidity at the storage temperature; the corresponding moisture differs by crop (oilseeds, with less water-binding starch and protein, are safe at a lower moisture content than cereals) and by climate, and national grading and storage guidelines give their own values. Moisture migrates through a bin by natural convection when one region is warmer than another, and condenses where warm moist air meets cold grain, which is why aeration aims to keep the whole mass at a uniform low temperature.
A B.Tech student uses this subject in the laboratory and in design assignments: measuring L, W and T of a hundred kernels and computing geometric mean diameter and sphericity, finding bulk and kernel density and porosity, timing a tilting table and a wind tunnel, fitting a power-law model to viscometer data and a GAB curve to sorption data. The habit to build is writing the moisture content and method next to every number and stating which formula variant was used, because examiners and supervisors check exactly that. These measurements feed later courses: grain drying, storage, size reduction, unit operations and food engineering all start from them.
An engineer five years into post-harvest or food-plant work uses properties to make sizing decisions: bin capacity from compacted bulk density, aeration fan selection from airflow resistance at the expected depth, cleaner air speed from terminal velocity of grain and trash, hopper angles from friction and angle of repose, pump and pipe sizing for purées from power-law constants at process temperature, and cooling or blanching time from thermal diffusivity. When a new crop or variety arrives, the practical decision is whether published values are good enough or whether a quick measurement is needed; the second is usually cheaper than a mis-sized machine.
A senior engineer with twenty-five years of practice uses properties to settle disputes and to write specifications. Is the bin wall failure due to overpressure on emptying, wrongly assumed bulk density or a change of crop? Is the claim of grain shrinkage computed on the correct moisture basis? Does a proposed microwave or radio-frequency process heat the product uniformly given its loss factor and penetration depth? Is the sorption isotherm of a new snack consistent with the claimed shelf life in a given film? Senior staff also decide which properties a quality laboratory should measure routinely and which instrument calibrations are traceable to reference methods.
A researcher with long experience works where the textbook models end: anisotropic and heterogeneous tissues, properties that change during processing (shrinkage, glass transition, phase change), multiscale models linking cell structure to bulk behaviour, and the discrete element method, which needs particle shape, friction and contact stiffness to simulate grain flow in bins and machines. The research questions include calibrating discrete-element parameters against angle of repose and shear tests, linking dielectric spectra to composition for non-destructive sensing, and developing hyperspectral and acoustic methods for internal quality. Rigorous reporting of moisture, temperature and method, and honest uncertainty estimates, remain the core of credible work.
This manual gives definitions, methods and equations but no tables of property values for specific crops, because published values vary widely with variety, moisture, temperature and method; use the cited handbooks and ASABE data for design values. Discrete element method calibration, glass-transition theory and the state diagram, acoustic and hyperspectral sensing, and the full Hertz equations of the ASABE compression standard are introduced only briefly. Standard numbers and bin-load overpressure factors change between editions and countries; check the current edition. Dielectric frequency allocations are set by national regulators and are given only as examples.
Original practice questions written to the syllabus and pattern of the exams named in each question's examTags. They are not past papers and do not reproduce any board's questions. Every numerical answer was computed by script; constants described as illustrative are for practice only.
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