Question 1 of 9: Equipment Selection for Gentle Handling of Shear-Sensitive Fluids

Question 1: Equipment Selection for Gentle Handling of Shear-Sensitive Fluids (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.

Given. Three shear-sensitive fluid types — (a) Bingham plastic (a rigid yield stress τ₀ must be exceeded before any flow occurs; behaves as a rigid solid below it), (b) pseudoplastic (shear-thinning; apparent viscosity falls reversibly and instantaneously as shear rate rises), and (c) thixotropic (time-dependent shear-thinning; internal structure breaks down progressively under continued shear and rebuilds only slowly at rest) — and twelve candidate pieces of tank/piping/pumping hardware (i)–(xii) for a tank-to-filler transfer line.

Find. For each hardware item, whether it is desirable for gentle handling of each of the three fluid types, and why.

Approach. Rank every item against the single governing principle for shear-sensitive product: minimize the magnitude of shear stress imposed AND the time/number of disturbance events the product sees, because a thixotropic fluid is damaged by cumulative shear history while a Bingham fluid is chiefly damaged by unnecessary excursions above τ₀.

(i) A cone bottom lets the product drain by gravity to a single low point with no stagnant corners, so no scraping or agitation is ever needed to move the last of the batch — the gentlest possible outcome for all three fluids. A slightly sloped flat bottom always leaves a residual film that must be mechanically encouraged to drain, adding an avoidable shear event. This matters most for the thixotropic fluid, because product left standing in a stagnant corner will gel further at rest and then need extra shear to remobilize when the tank is finally emptied.

(ii) A centre-line auger imposes a continuous, high-intensity local shear field at every point of every batch, which is precisely what gentle handling avoids — free drainage by gravity (helped by the cone bottom of (i)) is preferred whenever the fluid will flow on its own. For the Bingham fluid the auger is only marginally justifiable, and only in the corners a cone bottom cannot fully drain, since some mechanical assist may be needed once the local stress falls below τ₀ and flow stops; it should never be used routinely. For the pseudoplastic and, especially, the thixotropic fluid the auger is undesirable outright: it adds continuous unnecessary shear, and for the thixotropic fluid it also erases the very structure the process is trying to preserve, since that structure only rebuilds slowly once the auger stops.

(iii) A slow-moving swept wall keeps the tank wall clear of product build-up (which would otherwise skin over, dry, or — for the thixotropic fluid — gel in place) without imposing a large shear rate, because the wiper only needs to move at the rate the wall would otherwise foul. It is clearly desirable for the Bingham fluid (breaks up the stagnant near-wall plug that a yield-stress fluid otherwise leaves behind) and for the thixotropic fluid (prevents wall-set material from having to be re-sheared into the bulk later); for the pseudoplastic fluid it is a mild positive since fouling is less of a structural concern there.

(iv) Wall shear rate for a given volumetric flow scales inversely with the cube of the tube radius (γ̇ ∝ Q/R³ for laminar flow), so a modest increase in tubing diameter is a large, free reduction in peak shear rate for the same throughput — unambiguously desirable for all three fluids.

(v) A long-radius sweep elbow changes flow direction gradually; a standard (short-radius, near mitred) elbow imposes an abrupt local acceleration and a secondary (Dean) vortex, both of which spike the local shear rate at the fitting. Sweep elbows are desirable for all three fluids.

(vi) A centrifugal pump develops head by imparting a very high local shear rate to the fluid at the impeller tip and in the volute, and it also has poor efficiency (and can cavitate or recirculate) on a viscous or yield-stress fluid at low flow — undesirable for all three. It is worst for the thixotropic fluid, because the intense, brief impeller shear collapses the structure essentially irreversibly on the process timescale (the fluid will not have rebuilt its structure again before reaching the filler).

(vii) Gravity flow imposes no mechanical shear beyond what the pipe wall itself contributes at the (low) flow rate a gravity head can sustain, making it the gentlest transport mode of all — desirable for all three fluids. *For the Bingham fluid the available head must simply be checked against τ₀: if the static head cannot generate a wall shear stress exceeding the yield stress, gravity alone will not start the flow and a gentle assist (e.g. a larger head, or the swept wall of (iii)) is needed.

(viii) A rotary lobe (positive-displacement) pump moves fluid in discrete pockets with comparatively low internal shear and near-linear flow-vs-speed behaviour regardless of viscosity, which is exactly why lobe pumps are the standard choice for viscous, shear-sensitive food and process fluids — desirable for all three.

(ix) A large pump inlet keeps the suction-side velocity (and therefore suction-side shear and the risk of air entrainment, which can itself disrupt a delicate structure) low — desirable for all three.

(x) Every metre of pipe is additional wall-shear exposure time; minimizing pipe length between tank and filler minimizes both the total shear the product accumulates and its residence time under shear. This is desirable for all three fluids and doubly important for the thixotropic fluid, whose structure loss is a function of both the magnitude and the duration of shearing.

(xi) Every control valve is a local flow restriction with an accompanying shear/turbulence spike (and, if a valve is used to throttle rather than simply isolate, a continuous one) — minimizing the valve count is desirable for all three fluids.

(xii) Every change in elevation requires the product to accelerate or decelerate through the associated fittings and, on a real layout, usually adds pipe length and fittings as well — minimizing elevation changes keeps the layout simple and is desirable for all three fluids.