Question 2 of 9: Structured Fluids and Colloid Concentration Effects on Rheology

Question 2: Structured Fluids and Colloid Concentration Effects on Rheology (20 marks)

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.

Part (a) — the "rubber ball filled with liquid" analogy. This describes a structured (encapsulated or gel-networked) food fluid: a relatively rigid, elastic outer structure (the "rubber skin") enclosing a much less viscous true liquid. At low rate of strain, the applied stress is not yet large enough to rupture or substantially deform the elastic skin, so almost all of the imposed strain energy is stored and returned elastically by the skin itself rather than causing the enclosed liquid to actually flow. An observer measuring the bulk resistance to deformation at low strain rate therefore senses a very high apparent viscosity — not because the enclosed liquid is intrinsically viscous, but because the intact structure is resisting deformation elastically, the classic signature of a yield-type or strongly viscoelastic material. At high rate of strain, the stress exceeds the skin's elastic (or rupture) limit, the structure breaks down or flows plastically, and the enclosed low-viscosity liquid is free to flow through/around the ruptured structure; the measured apparent viscosity then drops toward the true, much lower viscosity of the interior liquid. In short: the liquid is sensed as high-viscosity at low strain rate, while the structure is still intact and dominates the response, and as low-viscosity at high strain rate, once the structure has broken and the enclosed liquid governs the flow.

Part (b)(i) — colloid concentration and yield stress. Yield stress τ₀ increases with increasing colloid (particle, protein or polymer) concentration, and the increase is not linear: below a critical concentration the dispersed units are too dilute to form a continuous, space-filling network and τ₀ ≈ 0 (the material simply flows, however slowly); once concentration exceeds that percolation threshold, particle– particle (or chain–chain) contacts form an interconnected network able to bear stress elastically until it breaks, and τ₀ rises steeply — typically fitted as τ₀ ∝ (C − C_crit)^m with m commonly in the range 2–4 for food colloidal suspensions. Physically, more particles per unit volume means more network junctions that must be simultaneously broken before bulk flow can start, so the stress required to do so rises rapidly with concentration once the network is continuous.

Part (b)(ii) — colloid concentration and the power-law index n. The flow behaviour index n decreases (the fluid becomes more strongly shear-thinning, moving further below n = 1) as colloid concentration increases. At low concentration the dispersed units are far enough apart that hydrodynamic interactions dominate and the suspension behaves close to Newtonian (n → 1). As concentration rises, the resting (low-shear) state contains progressively more particle–particle or chain entanglement/network structure to be disrupted; increasing shear rate progressively aligns, deforms, or breaks that structure, so the apparent viscosity falls faster with shear rate the more structure there was to begin with, i.e. n decreases (pseudoplasticity strengthens) with increasing concentration. The two trends are linked: both reflect the same underlying growth of an interconnected particle network with concentration — a stronger network raises the stress needed to start flow (τ₀ ↑) and gives more structure left to break down progressively once flowing (n ↓).