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) Surface and interfacial tension. Surface tension \(\sigma\) is the energy per unit area (equivalently, the contractile force per unit length) associated with the boundary between a liquid food and a gas (usually air), arising because molecules at the surface have fewer like neighbours than molecules in the bulk and are therefore in a higher-energy state that the liquid minimizes by contracting its surface area. Interfacial tension is the same concept applied to the boundary between two immiscible liquid (or liquid-solid) phases — for example, oil and water in a salad dressing or oil and a food solid — and is numerically smaller than the corresponding surface tension against air whenever the second phase itself has some affinity for the first, since that affinity partially offsets the imbalance in intermolecular forces at the interface.
(b) Work of cohesion, work of adhesion, and spreading coefficient. The work of cohesion \(W_c\) is the reversible work needed to pull a column of a single liquid apart, creating two new surfaces of that liquid against its own vapour, \(W_c = 2\sigma_1\). The work of adhesion \(W_a\) is the reversible work needed to separate a unit area of interface between two different phases (1 and 2) into two separate surfaces (each now against vapour), given by the Dupré equation \(W_a = \sigma_1+\sigma_2-\sigma_{12}\), where \(\sigma_{12}\) is the interfacial tension between the two phases. The spreading coefficient \(S\) of liquid 2 over liquid (or solid) 1 is the difference between the work of adhesion and the work of cohesion of the spreading liquid, $$S = W_a - W_{c,2} = \sigma_1 - \sigma_2 - \sigma_{12},$$ and its sign predicts behaviour directly: \(S>0\) means liquid 2 spreads spontaneously over liquid 1 (adhesion to the substrate is strong enough to overcome the spreading liquid's own cohesion), while \(S<0\) means it beads up instead (e.g. why an oily film can either spread across or bead on the surface of an aqueous food, depending on the relative tensions).
(c) Effect of temperature on surface tension. Surface tension decreases almost linearly with increasing temperature for essentially all liquid foods, because higher thermal energy increases molecular spacing and disorder at the surface, weakening the net inward cohesive pull that gives rise to surface tension; \(\sigma\to 0\) as the liquid approaches its critical temperature (where the distinction between liquid and vapour phases disappears). This is why warm liquid foods (e.g. heated fats, warmed dairy products) wet surfaces and foam more readily than the same product cold.
(d) Du Noüy ring (capillary pull) method. A thin platinum-iridium ring of precisely known circumference is lowered until just wetted by the liquid food surface, then slowly withdrawn while the vertical pulling force is continuously measured (traditionally by a torsion-wire balance, hence "surface tension balance"). As the ring rises, it drags a thin film of liquid upward with it, and the measured pulling force climbs to a maximum just before the film ruptures and detaches from the ring; at that maximum, the upward pull is balanced by the surface tension acting around both the inner and outer circumference of the film being lifted, $$F_{\max} = 2\sigma\left(2\pi R\right) \;\Rightarrow\; \sigma = \frac{F_{\max}}{4\pi R},$$ where \(R\) is the ring radius and the factor of 2 accounts for the film's two surfaces (inner and outer). A geometric (Harkins–Jordan) correction factor is normally applied to this ideal result to account for the non-vertical film shape and the finite wire diameter at detachment; the method is popular for liquid foods because it needs only a small sample, is fast, and (unlike the capillary-rise method) does not require the liquid to wet a narrow tube cleanly.
