22-Agric-A6 Physical Properties of Biological Materials and Food Products · May 2016
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. 04-Agric-A6 Physical Properties of Biological Materials and Food Products, National Exams May 2016 — a three-hour closed-book exam (approved calculator permitted; one aid sheet, both sides). Nine questions are set and candidates answer any five, each worth 20 marks, for a 100-mark paper. All nine are worked here so the set is a complete study resource.
Reference texts. M.A. Rao, S.S.H. Rizvi, A.K. Datta and J. Ahmed, Engineering Properties of Foods, 4th ed. (rheology of fluid and semisolid foods, particle size, surface/interfacial properties); N.N. Mohsenin, Physical Properties of Plant and Animal Materials, 2nd ed. (thermal properties, calorimetry, texture and rheological testing); R.P. Singh and D.R. Heldman, Introduction to Food Engineering, 5th ed. (thermal-property measurement, freezing-point depression, particle size); J.F. Steffe, Rheological Methods in Food Process Engineering, 2nd ed. (viscometry, viscoelasticity, the Kelvin-Voigt model, time-dependent flow behaviour); R.L. Earle, Unit Operations in Food Processing, 2nd ed. (particle-size averages, specific surface from sieve data).
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
(a) Viscosity recovery after rapid agitation. Immediately after intense agitation stops and the fluid is left under a very low ("structure-probing") shear, its apparent viscosity is at a local minimum because internal structure — entangled polymer/protein networks, weak flocs, or associated micelles — has just been broken down. What happens next separates two classes of material. A thixotropic fluid recovers: with the disruptive shear removed, Brownian motion and weak physical bonds progressively rebuild the network, and apparent viscosity climbs back up over seconds to hours, typically approaching its rested value along a decaying-rate (roughly exponential) curve, as sketched below. A fluid whose structure breakdown is irreversible (sometimes called rheodestructive, or said to exhibit permanent "shear thinning" rather than thixotropy) shows little or no recovery: bonds that were mechanically ruptured (e.g. covalent or strong secondary bonds, or particles that have been permanently comminuted) do not reform, so viscosity stays near its sheared-down value indefinitely.
(b) Rate of strain. Strain \(\epsilon\) is a dimensionless ratio of displacement to a reference length, so its rate, $$\frac{d\epsilon}{dt} = \frac{d}{dt}\!\left(\frac{\Delta x}{y}\right) = \frac{1}{y}\frac{d(\Delta x)}{dt} = \frac{v}{y},$$ has dimension \([T^{-1}]\) (reciprocal time). This is exactly the same dimension as the shear rate used in viscosity, \(\Delta v/\Delta y = [\text{L}\,\text{T}^{-1}]/[\text{L}] = [T^{-1}]\). The two are therefore dimensionally, and in fact physically, the same quantity: shear strain is a displacement gradient \(\gamma = \Delta x/\Delta y\), and its time derivative, \(\dot\gamma = d\gamma/dt = (\Delta v)/\Delta y\), is precisely the "rate of strain." This is why shear rate and rate of strain are used interchangeably in rheology — both measure how fast one fluid layer slides past its neighbour, normalized by the layer spacing.
(c) Rheological moduli. A modulus is a proportionality constant relating an applied stress to the resulting strain, \(M = \text{stress}/\text{strain}\), so all four share dimensions of stress (force/area) but differ in which stress and strain pair they relate.
