Q: Using pure oxygen instead of air in an aerated bioreactor generally increases oxygen transfer because which factor changes most directly in the mass-transfer driving force?

Introduction / Context: Oxygen transfer rate (OTR) in gas-sparged reactors is often expressed as OTR = kLa * (C* − C), where C* is the saturation DO concentration and C is the bulk DO. Replacing air with pure oxygen mainly affects the driving force term, not necessarily the hydrodynamic coefficient kLa. Given Data / Assumptions: Same mixer, gas rate adjusted to avoid flooding. Temperature and salinity unchanged. No intentional change in bubble size distribution beyond gas composition. Concept / Approach: At fixed pressure and temperature, C* is proportional to the oxygen mole fraction in the gas phase (Henry’s law). Pure oxygen has a much higher oxygen partial pressure than air (≈1.0 vs ≈0.21), so C* increases several-fold, boosting OTR. Bubble size and kLa may or may not change appreciably; the primary, guaranteed effect is the larger C* − C driving force. Step-by-Step Solution: Write OTR = kLa * (C* − C).Note that switching to pure O2 increases pO2, hence increases C*.Conclude OTR rises mainly due to larger driving force; kLa may remain similar. Verification / Alternative check: Measured DO rise curves and sulfite tests under identical hydrodynamics show OTR scaling with C*, consistent with Henry’s law and increased pO2. Why Other Options Are Wrong: Smaller bubbles are not automatic; gas composition alone does not guarantee it. kLa is a hydrodynamic parameter; it does not inherently increase with pure O2. Partial pressure is higher, not lower, with pure oxygen. Broth density change is negligible and irrelevant here. Common Pitfalls: Attributing OTR gains to kLa rather than to C*; overlooking safety, cost, and flammability considerations with pure O2. Final Answer: The saturation concentration of oxygen is higher.

Q: Scale-up design problem (Rushton turbine): A cylindrical bioreactor holds 100,000 L of liquid (100 m^3) and has an aspect ratio of 2:1 (liquid height to tank diameter). Estimate the appropriate impeller diameter for a Rushton turbine using the commo…

Introduction / Context: Estimating impeller diameter is a routine early step in bioreactor specification and scale-up. For Rushton turbines in baffled cylindrical tanks, a common heuristic is D_impeller ≈ 0.33 * D_tank. To use the rule, we must first infer the tank diameter from liquid volume and aspect ratio (height/diameter). Given Data / Assumptions: Liquid volume V = 100,000 L = 100 m^3. Aspect ratio AR = H / D_tank = 2 : 1, so H = 2 * D_tank. Cylindrical working volume: V = (π * D_tank^2 / 4) * H. Standard Rushton diameter rule: D_impeller ≈ D_tank / 3. Concept / Approach: Compute D_tank from the cylinder volume formula using AR = 2. Then apply the one-third rule to obtain the impeller diameter. Finally, map the numerical result to the closest option. Step-by-Step Solution: Write V = (π/4) * D_tank^2 * H. With H = 2 * D_tank, V = (π/4) * D_tank^2 * 2 * D_tank = (π/2) * D_tank^3.Solve for D_tank: D_tank = (2 * V / π)^(1/3).Insert V = 100 m^3: D_tank ≈ (200 / π)^(1/3) ≈ 3.99 m (approximately 4.0 m).Apply the rule: D_impeller ≈ D_tank / 3 ≈ 4.0 / 3 ≈ 1.33 m.Choose the closest option: 1.3 m. Verification / Alternative check: Check volume using D_tank = 4.0 m and H = 8.0 m: V_calc = π/4 * 4.0^2 * 8.0 ≈ 100.5 m^3 (close to 100 m^3; rounding explains the small difference). The rule-of-thumb then yields D_impeller ≈ 1.33 m, consistent with the selected answer. Why Other Options Are Wrong: 3.3 m and 5.3 m: these are closer to full tank diameter choices, not one-third. 7.3 m: exceeds the tank diameter implied by the volume. 0.6 m: far below typical one-third sizing; would under-mix. Common Pitfalls: Forgetting to convert litres to cubic metres; misinterpreting aspect ratio (height-to-diameter vs diameter-to-height); applying the one-third rule before computing D_tank. Final Answer: 1.3 m.

Question 1

Impeller taxonomy for mixing: which of the following is NOT classified as an axial-flow impeller in bioreactor applications?

Accepted Answer

Introduction / Context: Impeller choice controls flow pattern, shear, mixing time, and gas dispersion. Recognizing whether an impeller generates axial flow (top-to-bottom circulation) or radial flow (outward from the blade) is core knowledge for reactor design. Given Data / Assumptions: Standard, unshrouded impellers in baffled tanks. Marine/propeller and hydrofoils are designed for axial pumping. Rushton turbine is the canonical radial-flow, flat-blade disk turbine. Concept / Approach: Axial flow impellers (propellers, marine impellers, hydrofoils, pitched-blade turbines) pump fluid along the shaft axis, improving top-bottom circulation and often giving lower shear at comparable pumping. The Rushton turbine produces strong radial jets, high shear zones near the blade edges, and is preferred for gas dispersion in some regimes. Step-by-Step Solution: Identify each impeller’s characteristic flow.Propeller/marine/hydrofoil/45° pitched-blade → axial.Rushton turbine → radial; therefore not axial. Verification / Alternative check: Flow visualization and velocity profiles from particle image velocimetry confirm axial vs. radial patterns for these classes. Why Other Options Are Wrong: Propeller, marine, hydrofoil, and pitched-blade: all designed to pump axially in baffled tanks. Common Pitfalls: Equating “turbine” with axial; many turbines (Rushton) are radial unless pitched for axial flow. Final Answer: A Rushton turbine.

Question 2

Intermig impellers in aerobic bioprocessing: what features and flow direction characterize this impeller type and why are they useful for gas dispersion?

Accepted Answer

Introduction / Context: Intermig impellers are variants tailored for gas–liquid contacting in bioreactors. They combine axial pumping with features that enhance bubble dispersion and reduce coalescence, improving oxygen transfer at lower power inputs compared with some radial impellers. Given Data / Assumptions: Gas-sparged, baffled tank with typical submergence. Intermig blades include protrusions/extensions to interact with gas holdup. Aerobic organisms require effective O2 transfer and moderate shear. Concept / Approach: Axial pumping sweeps bubbles upward, promoting circulation and residence time. The fork-like or profiled extensions on Intermig blades promote bubble cutting and redistribution, leading to higher interfacial area without excessive shear. The upward-directed flow pattern complements aeration strategies that enter from below. Step-by-Step Solution: Classify Intermig as axial flow by geometry and pumping direction.Note upward jet orientation beneficial for bubble carry-over and breakup.Identify fork-shaped extensions as bubble-interaction features.Conclude that all listed statements are consistent with Intermig design. Verification / Alternative check: Vendor data and CFD/visual studies show Intermig patterns with enhanced gas dispersion and lower power per kLa than some radial turbines. Why Other Options Are Wrong: “None” and “purely radial” contradict established descriptions. Common Pitfalls: Assuming only Rushton turbines disperse gas effectively; modern axial designs often outperform at scale with lower energy. Final Answer: All of the above.

Question 3

Improving oxygen transfer in shake-flask culture: which practical adjustments are commonly used to increase oxygen availability and kLa?

Accepted Answer

Introduction / Context: Shake flasks are workhorses for screening and small-scale cultivation. Oxygen transfer depends on surface area, liquid film renewal, and mixing. This question gathers the standard interventions to raise oxygen transfer without changing vessel type. Given Data / Assumptions: Orbital shaker with adequate temperature control. Breathable closures (e.g., vented caps, foam plugs). Newtonian or mildly non-Newtonian broth typical of early cultures. Concept / Approach: Lower working volume increases headspace and liquid surface area, improving gas–liquid exchange and sloshing. Higher shaking speed and/or larger orbital diameter increase surface renewal and mixing intensity, boosting kLa. Baffles disrupt circular flow, create internal waves, and raise turbulence near the surface, all of which increase oxygen transfer. These methods are often combined to reach desired DO levels. Step-by-Step Solution: Reduce fill volume to 10–20% of total flask volume to increase headspace and surface area.Raise shaking speed within vessel limits to enhance mixing and film renewal.Use baffled flasks to induce turbulence and improve kLa.Verify DO via optical/Clark probes or growth performance. Verification / Alternative check: Empirical correlations show kLa rising with rpm and decreasing with working volume; baffles shift curves upward by increasing turbulence and surface disruption. Why Other Options Are Wrong: Tightly sealing the flask suppresses gas exchange and can cause oxygen limitation or pressure buildup. Common Pitfalls: Overfilling flasks; ignoring heat generation at high rpm; using non-vented caps that limit oxygen despite aggressive shaking. Final Answer: All of the above.

Question 4

Operational ranges: industrial paddle agitators typically turn at what rotational speeds, and how does that relate to their mixing duty?

Accepted Answer

Introduction / Context: Paddle agitators are classic low-to-moderate shear mixers used in many process industries for blending, heat transfer, and maintaining suspensions. Knowing typical speed ranges helps match impeller choice to process goals and motor sizing. Given Data / Assumptions: Large tanks (hundreds to thousands of litres or more). Newtonian or mildly viscous liquids; limited gas dispersion duty. Standard two- or four-blade paddles with baffles in the vessel. Concept / Approach: Paddle impellers are designed to create bulk circulation at relatively low speeds, minimizing shear while still renewing heat-transfer surfaces. Typical industrial operation falls in the tens to low hundreds of rpm, commonly between about 20 and 150 rpm depending on diameter, viscosity, and duty. Much higher speeds are characteristic of small-diameter high-shear devices, not large paddles. Step-by-Step Solution: Identify application: gentle to moderate mixing, not high-shear dispersion.Apply standard practice: choose rpm in the 20–150 range to balance power and shear.Conclude that 20–150 rpm is the representative industrial range for paddles. Verification / Alternative check: Manufacturer curves and scaling rules (tip speed = π * D * N) show that at 20–150 rpm with large D, tip speeds and Re are appropriate for typical paddle duties. Why Other Options Are Wrong: 150–300 rpm, 400–800 rpm, 1150 rpm: excessively high for large paddles; these imply high shear and power. 1–5 rpm: too low for effective circulation in most liquid tanks. Common Pitfalls: Confusing small-scale lab mixers (which may run at hundreds of rpm) with large industrial paddles where diameter is much larger. Final Answer: 20 and 150 rpm.

Question 5

Biosurfactants in fermentation: detergent-like substances produced by microbes during culture will typically cause which interfacial effects in an aerated bioreactor?

Accepted Answer

Introduction / Context: Many microbes secrete surface-active molecules (biosurfactants) such as rhamnolipids or proteins that alter gas–liquid interfacial properties. These changes can strongly influence foam formation, bubble size distributions, oxygen transfer, and antifoam requirements. Given Data / Assumptions: Aerated, agitated culture with measurable foam formation. Surface-active compounds present at concentrations near or above their critical micelle concentration. No antifoam initially added. Concept / Approach: Surfactants preferentially adsorb at interfaces, lowering surface tension. Lower surface tension and interfacial elasticity stabilize small bubbles and suppress coalescence, increasing gas holdup and often promoting foam stability. While this can improve interfacial area, it may reduce effective kLa if excessive foaming disrupts gas handling or causes flooding. Step-by-Step Solution: Recognize adsorption at the gas–liquid interface as the primary effect.Infer decreased surface tension from surfactant presence.Conclude reduced bubble coalescence and increased foam stability follow. Verification / Alternative check: Surface tension measurements (du Nouy ring, Wilhelmy plate) and bubble column tests show decreased σ and altered bubble size distribution in the presence of biosurfactants. Why Other Options Are Wrong: “None” contradicts well-documented surfactant behavior. Common Pitfalls: Assuming lower surface tension always increases kLa; excessive foaming can hinder mass transfer and operations. Final Answer: All of the above.

Question 6

Energy efficiency comparison: for the same target yield in aerobic cultures, which stirrer type typically requires the least energy input under comparable conditions?

Accepted Answer

Introduction / Context: Modern axial-flow impellers such as Intermig are engineered to improve gas dispersion and oxygen transfer at reduced power per unit volume compared with classic radial turbines. Selecting the most energy-efficient design can lower operating costs and heat loads while maintaining productivity. Given Data / Assumptions: Comparable tank sizes and aeration rates; same process yield objective. Operation below flooding; standard submergence and baffles. Yield constrained primarily by oxygen transfer and mixing quality. Concept / Approach: Intermig impellers provide strong axial pumping and enhanced bubble breakup with lower specific power than Rushton turbines for a given kLa. Compared with generic disk or unoptimized MIG variants, Intermig designs often achieve required transfer at reduced rpm and torque, improving energy efficiency while limiting shear damage to cells. Step-by-Step Solution: Rank impellers by typical power per kLa: axial Intermig < MIG/unoptimized disks < Rushton turbines.Relate lower power to improved pumping and bubble management.Select Intermig as requiring the least energy for the same yield objective. Verification / Alternative check: Vendor and literature kLa–power correlations routinely show axial designs outperform radial turbines for aerobic cultures with similar gas rates. Why Other Options Are Wrong: MIG/disc: typically higher power at same kLa compared with Intermig designs. Rushton turbine: effective disperser but usually higher power demand. Pitched-blade at 90° acts radial; energy-intensive for gas dispersion. Common Pitfalls: Assuming one impeller fits all; ignoring broth rheology and gas rate when comparing efficiency. Final Answer: Intermig.

Question 7

Using pure oxygen instead of air in an aerated bioreactor generally increases oxygen transfer because which factor changes most directly in the mass-transfer driving force?

Accepted Answer

Introduction / Context: Oxygen transfer rate (OTR) in gas-sparged reactors is often expressed as OTR = kLa * (C* − C), where C* is the saturation DO concentration and C is the bulk DO. Replacing air with pure oxygen mainly affects the driving force term, not necessarily the hydrodynamic coefficient kLa. Given Data / Assumptions: Same mixer, gas rate adjusted to avoid flooding. Temperature and salinity unchanged. No intentional change in bubble size distribution beyond gas composition. Concept / Approach: At fixed pressure and temperature, C* is proportional to the oxygen mole fraction in the gas phase (Henry’s law). Pure oxygen has a much higher oxygen partial pressure than air (≈1.0 vs ≈0.21), so C* increases several-fold, boosting OTR. Bubble size and kLa may or may not change appreciably; the primary, guaranteed effect is the larger C* − C driving force. Step-by-Step Solution: Write OTR = kLa * (C* − C).Note that switching to pure O2 increases pO2, hence increases C*.Conclude OTR rises mainly due to larger driving force; kLa may remain similar. Verification / Alternative check: Measured DO rise curves and sulfite tests under identical hydrodynamics show OTR scaling with C*, consistent with Henry’s law and increased pO2. Why Other Options Are Wrong: Smaller bubbles are not automatic; gas composition alone does not guarantee it. kLa is a hydrodynamic parameter; it does not inherently increase with pure O2. Partial pressure is higher, not lower, with pure oxygen. Broth density change is negligible and irrelevant here. Common Pitfalls: Attributing OTR gains to kLa rather than to C*; overlooking safety, cost, and flammability considerations with pure O2. Final Answer: The saturation concentration of oxygen is higher.

Question 8

Scale-up design problem (Rushton turbine): A cylindrical bioreactor holds 100,000 L of liquid (100 m^3) and has an aspect ratio of 2:1 (liquid height to tank diameter). Estimate the appropriate impeller diameter for a Rushton turbine using the commo…

Accepted Answer

Introduction / Context: Estimating impeller diameter is a routine early step in bioreactor specification and scale-up. For Rushton turbines in baffled cylindrical tanks, a common heuristic is D_impeller ≈ 0.33 * D_tank. To use the rule, we must first infer the tank diameter from liquid volume and aspect ratio (height/diameter). Given Data / Assumptions: Liquid volume V = 100,000 L = 100 m^3. Aspect ratio AR = H / D_tank = 2 : 1, so H = 2 * D_tank. Cylindrical working volume: V = (π * D_tank^2 / 4) * H. Standard Rushton diameter rule: D_impeller ≈ D_tank / 3. Concept / Approach: Compute D_tank from the cylinder volume formula using AR = 2. Then apply the one-third rule to obtain the impeller diameter. Finally, map the numerical result to the closest option. Step-by-Step Solution: Write V = (π/4) * D_tank^2 * H. With H = 2 * D_tank, V = (π/4) * D_tank^2 * 2 * D_tank = (π/2) * D_tank^3.Solve for D_tank: D_tank = (2 * V / π)^(1/3).Insert V = 100 m^3: D_tank ≈ (200 / π)^(1/3) ≈ 3.99 m (approximately 4.0 m).Apply the rule: D_impeller ≈ D_tank / 3 ≈ 4.0 / 3 ≈ 1.33 m.Choose the closest option: 1.3 m. Verification / Alternative check: Check volume using D_tank = 4.0 m and H = 8.0 m: V_calc = π/4 * 4.0^2 * 8.0 ≈ 100.5 m^3 (close to 100 m^3; rounding explains the small difference). The rule-of-thumb then yields D_impeller ≈ 1.33 m, consistent with the selected answer. Why Other Options Are Wrong: 3.3 m and 5.3 m: these are closer to full tank diameter choices, not one-third. 7.3 m: exceeds the tank diameter implied by the volume. 0.6 m: far below typical one-third sizing; would under-mix. Common Pitfalls: Forgetting to convert litres to cubic metres; misinterpreting aspect ratio (height-to-diameter vs diameter-to-height); applying the one-third rule before computing D_tank. Final Answer: 1.3 m.

Question 9

In bioreactor design and scale-up, what is correct regarding the use of off-centre impellers (i.e., impellers mounted with a deliberate offset from the vessel axis)?

Accepted Answer

Introduction / Context: Large bioreactors present mixing and gas–liquid dispersion challenges that are not as prominent in small lab vessels. One practical strategy is to mount the impeller off the vessel centreline. This question probes when off-centre impellers are appropriate and why they are often chosen during scale-up to industrial sizes (greater than 10 m^3). Given Data / Assumptions: Cylindrical, baffled or partly baffled vessels typical of fermentation service. Industrial volumes may exceed 10 m^3 with tall aspect ratios. Process objectives include good bulk mixing, gas dispersion, and reduced vortexing. Concept / Approach: Off-centre (eccentric) mounting disrupts swirl and large coherent vortices, improves top-to-bottom circulation, and can enhance gas dispersion when multiple impellers are impractical. At very large scales, perfect baffling and ideal shaft alignment are difficult; a deliberate offset can mitigate maldistribution and dead zones without excessive power demand. Step-by-Step Solution: Identify scale limitation: in very large tanks, classical centreline mounting may create swirl and poor gas dispersion despite baffles.Recognize benefit of eccentricity: an offset promotes asymmetric flow patterns that break swirl and improve contact.Relate to size threshold: practice commonly introduces off-centre mounting for volumes greater than 10 m^3 (and especially at even larger scales).Therefore, select the option allowing off-centre use at volumes > 10 m^3. Verification / Alternative check: Mixing audits and tracer tests in large tanks often show improved circulation times with slight eccentricity or tilted shafts, confirming the engineering rationale. Why Other Options Are Wrong: Any size reactor: not necessary in small, well-baffled vessels; centreline mounting suffices. Less than 10 m^3: contradicts typical practice; benefits are most pronounced at larger scales. Never off-centre: overly absolute and ignores proven designs. Banned by sanitary codes: no universal prohibition; cleanability depends on detailed design. Common Pitfalls: Confusing off-centre mounting with a lack of baffles; both can be used together if hygienic design and validation are maintained. Final Answer: Off-centre impellers can be used when volume is greater than 10 m^3

Question 10

In aerated, agitated bioreactors, “flooding” describes which operating condition with respect to gas–liquid dispersion by the impeller?

Accepted Answer

Introduction / Context: Gas–liquid mass transfer is critical in aerobic bioprocesses. A key failure mode is “flooding,” where the agitator no longer disperses gas properly. Recognizing flooding is essential for preventing oxygen limitation and for protecting equipment from unstable hydrodynamics. Given Data / Assumptions: Agitated, sparged vessel with a mechanical impeller. Gas flow rate and impeller speed determine dispersion quality. Operating viscosity and surface tension are in the typical aqueous range. Concept / Approach: Flooding occurs when the gas rate is too high (or impeller speed too low) for the impeller to break up and disperse bubbles. Gas then bypasses the impeller zone and rises as large pockets or channels, escaping without effective dispersion, which drastically reduces kLa and oxygen transfer. Step-by-Step Solution: Consider the force balance: insufficient tip speed relative to gas holdup causes bubble coalescence and loss of dispersion.Observe the symptom: gas “slips” through the tank with minimal breakup, often accompanied by torque fluctuations.Infer the consequence: oxygen transfer collapses despite continuing aeration and agitation.Hence, flooding is when air escapes without being distributed by the agitator. Verification / Alternative check: Power draw curves show a drop in effective power under gas load at flooding; visual inspection reveals large gas cavities and poor bubble dispersion. Why Other Options Are Wrong: Medium spills/foam volume > broth: these describe foaming, not flooding. Sparging stops: that is a different failure (gas supply interruption). None of the above: incorrect because a precise definition exists. Common Pitfalls: Confusing flooding with “loading” (incipient gas accumulation) or with external foaming; flooding specifically concerns failed dispersion at the impeller. Final Answer: The air escapes without being distributed by the agitator

Question 11

For aerated mixing vessels handling aqueous solutions, which empirical dependence best represents the liquid-film mass transfer coefficient kL on specific power input (Pm/V)?

Accepted Answer

Introduction / Context: The liquid-side mass transfer coefficient (kL) reflects the rate at which dissolved species cross the liquid film surrounding bubbles or particles. In stirred, aerated tanks with aqueous media, kL is often correlated with turbulence intensity, which in turn scales with specific power input (Pm/V). Given Data / Assumptions: Newtonian, low-to-moderate viscosity aqueous solutions. Standard Rushton or axial-flow impellers with typical aeration rates. kL considered separately from interfacial area a (thus not kLa). Concept / Approach: Classical surface-renewal and turbulence theories predict that film thickness decreases with increasing energy dissipation, giving a sublinear power-law dependence of kL on (Pm/V). Empirical studies commonly report an exponent near 0.33 in water-like liquids, while the overall kLa includes an additional dependence on gas flow that governs interfacial area (a). Step-by-Step Solution: Relate turbulence to film renewal frequency: higher (Pm/V) increases eddy activity and reduces film thickness.Adopt empirical power-law form: kL ∝ (Pm/V)^n.For aqueous systems, n ≈ 0.33 is widely observed.Therefore, select kL ∝ (Pm/V)^0.33. Verification / Alternative check: Log–log plots of measured kL against (Pm/V) yield slopes close to 1/3 in water and dilute broths; deviations occur at high viscosity or with non-Newtonian rheology. Why Other Options Are Wrong: Exponents 0.50 or 0.66: too strong for typical aqueous kL scaling (more typical for other regimes or parameters). Exponent 1.00: unrealistically strong sensitivity. Independence: contradicts turbulence-controlled film dynamics. Common Pitfalls: Confusing kL with kLa; the latter depends on both kL and interfacial area a, which also varies with gas flow rate and dispersion quality. Final Answer: kL ∝ (Pm/V)^0.33

Question 12

During a fermentation run, the measured dissolved oxygen concentration in the broth decreases from the saturation level (about 7 ppm) to 1 ppm. What conclusion is most appropriate?

Accepted Answer

Introduction / Context: Dissolved oxygen (DO) is a primary constraint in aerobic fermentations. When DO drops substantially below the saturation concentration C*, oxygen transfer cannot keep up with cellular demand, leading to oxygen limitation and altered metabolism (e.g., overflow products, reduced productivities). Given Data / Assumptions: Initial DO ≈ saturation (about 7 ppm for the given conditions). DO subsequently measured at ≈ 1 ppm. Temperature, pressure, and salinity are assumed roughly constant during the observation. Concept / Approach: Oxygen transfer rate OTR = kLa * (C* − CL). When CL (the bulk DO) is far below C*, the driving force is large, yet if CL remains low, the cellular oxygen uptake rate OUR is meeting or exceeding the maximum OTR, signalling oxygen limitation on the culture side. Consequently, growth and production are constrained by O2 availability. Step-by-Step Solution: Recognize that CL << C* implies oxygen is being consumed faster than it is supplied.Link to physiology: aerobic pathways slow; cells may switch to overflow or stress responses.Conclude that growth is oxygen limited under these conditions.Plan corrective actions: increase kLa (agitation, aeration, pure O2) or reduce OUR (feed control). Verification / Alternative check: Step tests increasing agitation or aeration that restore DO confirm oxygen transfer limitation; off-gas analysis (O2, CO2) corroborates high OUR. Why Other Options Are Wrong: Not oxygen limited: contradicts the definition of limitation when CL is well below C*. Experimental error: possible but not the most reasonable default without evidence. No conclusion: the conclusion of limitation is standard when DO is stably low. Lower oxygen means higher growth: opposite to aerobic physiology. Common Pitfalls: Confusing a transient dip with sustained limitation; ensure the DO drop persists despite reasonable control actions before concluding chronic limitation. Final Answer: Microbial growth is oxygen limited since the oxygen concentration is lower than the saturation concentration

Question 13

A fermentation system has KLa = 3 s^-1 and C* = 5 ppm O2. If the bulk liquid contains no dissolved oxygen (CL = 0), what is the oxygen transfer rate (OTR)?

Accepted Answer

Introduction / Context: In aerated bioreactors, the oxygen transfer rate (OTR) quantifies how fast oxygen crosses from bubbles into the broth. The classic expression OTR = KLa * (C* − CL) connects mass transfer capability (KLa) and driving force (C* − CL). This problem is a direct substitution exercise often used in design and troubleshooting. Given Data / Assumptions: KLa = 3 s^-1 (liquid-phase volumetric mass transfer coefficient). C* = 5 ppm O2 (assume ppm ≈ mg·L^-1 for dilute aqueous solutions). CL = 0 mg·L^-1 (bulk liquid fully depleted of O2). Concept / Approach: Use OTR = KLa * (C* − CL). With CL = 0, the driving force is maximized and equals C*. Multiply KLa by C* to obtain the volumetric transfer rate in mg·L^-1·s^-1. Step-by-Step Solution: Identify driving force: C* − CL = 5 − 0 = 5 mg·L^-1.Compute OTR: OTR = 3 s^-1 * 5 mg·L^-1 = 15 mg·L^-1·s^-1.Report with appropriate units.Hence, OTR = 15 mg·L^-1·s^-1. Verification / Alternative check: If CL were half-saturated (2.5 mg·L^-1), OTR would be 3 * (5 − 2.5) = 7.5 mg·L^-1·s^-1, confirming linearity with driving force. Why Other Options Are Wrong: Zero: only true if C* = CL, not when CL = 0. 10 or 5 mg·L^-1·s^-1: result from incorrect arithmetic or using KLa or C* alone. 3 mg·L^-1·s^-1: equal to KLa, not OTR. Common Pitfalls: Confusing kL with KLa, or forgetting that ppm ≈ mg·L^-1 for dilute aqueous media at standard conditions. Final Answer: 15 mg·L^-1·s^-1

Question 14

To minimize impeller damage in aerated, agitated fermenters (e.g., erosion, cavitation, and mechanical stress), which design choice is most suitable?

Accepted Answer

Introduction / Context: Impeller damage can arise from gas cavity formation (gas holdup under blades), abrasive particulates, excessive shear, or cyclic mechanical loading. Choosing an appropriate impeller style helps manage hydrodynamic stresses and prolongs equipment life while maintaining adequate mixing and mass transfer. Given Data / Assumptions: Fermenters operate with gas sparging and mechanical agitation. Service may include shear-sensitive broths or solids. Design seeks to reduce damaging loads without sacrificing performance. Concept / Approach: Intermig impellers are engineered axial-flow devices with folded blades and cutouts that promote gentle circulation, better gas dispersion at lower shear near the blades, and reduced susceptibility to gas cavities that can cause vibration and erosion. Compared with classic radial-flow (e.g., Rushton) or generic axial-flow propellers, Intermig designs specifically target gas–liquid dispersion while mitigating damaging conditions around the blade edges. Step-by-Step Solution: Identify damage mechanisms: cavitation, erosion, and cyclic torque spikes during gassed operation.Match to impeller choice: Intermig geometry reduces localized shear and stabilizes gassed power draw.Conclude that Intermig impellers best minimize damage among the listed options.Select “Using Intermig impellers.” Verification / Alternative check: Plant experience reports smoother torque traces and lower blade wear with Intermig or similar hydrofoil designs in gassed service compared to flat-blade turbines. Why Other Options Are Wrong: Special axial-flow: helpful, but Intermig is the purpose-designed solution named in the options. Radial-flow: higher shear at blade tips; more prone to erosion under gassing. All of the above: overly broad; radial-flow contradicts the objective. Unbaffled vessels: increases swirl and reduces dispersion; can worsen loads. Common Pitfalls: Assuming any axial-flow impeller suffices; subtle geometric features matter for durability in gassed operation. Final Answer: Using Intermig impellers

Question 15

In aerobic microbial cultures, why are radial-flow impellers (e.g., Rushton turbines) commonly employed?

Accepted Answer

Introduction / Context: Choosing the right impeller for aerobic fermentation is central to achieving adequate oxygen transfer. Radial-flow impellers such as the Rushton turbine are classics in bioprocessing because they generate intense local turbulence and strong gas dispersion, raising interfacial area and kLa under many conditions. Given Data / Assumptions: Aerated, baffled vessel with mechanical agitation. Objective is maximizing oxygen transfer and mixing. Media viscosity is moderate. Concept / Approach: Radial-flow turbines discharge flow laterally into baffles, creating high energy dissipation zones. The resulting shear breaks bubbles into smaller sizes, increasing interfacial area and improving dispersion uniformity, which typically elevates kLa compared to gentle, low-shear devices. Step-by-Step Solution: Identify hydrodynamic signature: strong radial jets and high shear near blades.Connect to mass transfer: smaller bubbles and vigorous circulation raise kLa.Conclude that the purpose is high-shear, turbulence-driven dispersion.Choose the statement reflecting this function. Verification / Alternative check: kLa correlations often show higher exponents on power input for Rushton turbines versus some axial designs in particular regimes, corroborating their dispersion strength. Why Other Options Are Wrong: Energy-efficient low turbulence/low shear: describes axial hydrofoils, not radial turbines. Maximize bubble size: the opposite; they reduce bubble size. Eliminate baffles: baffles are still recommended to prevent swirl. Common Pitfalls: Assuming high shear is always beneficial; for shear-sensitive cells, axial-flow alternatives may be preferable. Final Answer: They provide high-shear, highly turbulent mixing that enhances gas dispersion

Question 16

A fermentation system has KLa = 3 s^-1 and C* = 5 ppm O2. If the bulk liquid is already saturated (CL = C*), what is the oxygen transfer rate (OTR)?

Accepted Answer

Introduction / Context: Oxygen transfer from bubbles into liquid is driven by the concentration difference between saturation (C*) and bulk dissolved oxygen (CL). When CL equals C*, there is no driving force, and the net transfer stops regardless of the KLa magnitude. This scenario frequently occurs at low cell densities or during idle gassing. Given Data / Assumptions: KLa = 3 s^-1 (system capacity). C* = 5 mg·L^-1; CL = C* = 5 mg·L^-1. Assume steady conditions with no rapid transients. Concept / Approach: Use OTR = KLa * (C* − CL). If CL = C*, the term in parentheses is zero; therefore, OTR is zero. Oxygen may still circulate between phases, but net transfer into the bulk does not occur until CL drops below C* due to cellular consumption. Step-by-Step Solution: Compute driving force: C* − CL = 5 − 5 = 0.Multiply by KLa: OTR = 3 * 0 = 0 mg·L^-1·s^-1.Interpretation: the system is supply-capable but demand-limited.Conclusion: OTR = 0 until cells consume oxygen. Verification / Alternative check: As soon as OUR > 0 lowers CL below C*, the same KLa will yield OTR = KLa * ΔC to match OUR at steady state. Why Other Options Are Wrong: 3, 5, or 15 mg·L^-1·s^-1: confuse KLa or C* with OTR; ignore ΔC = 0. 0.2 mg·L^-1·s^-1: arbitrary nonzero value without basis. Common Pitfalls: Assuming large KLa always means high OTR; without driving force, capacity is unused. Final Answer: Zero

Question 17

If the impeller speed is set too low in an aerated stirred tank, bubbles may accumulate and coalesce beneath the impeller. What is this condition called?

Accepted Answer

Introduction / Context: Correct impeller speed is vital for keeping bubbles dispersed. At too low a speed for a given gas rate, gas accumulates beneath the blades and forms a cavity that rotates with the impeller. This phenomenon is known as a flooded impeller and compromises oxygen transfer and mixing uniformity. Given Data / Assumptions: Aerated, baffled stirred tank with mechanical agitation. Gas flow rate is held while impeller speed is reduced. Liquid properties are water-like. Concept / Approach: When flooding occurs, the impeller loses “bite” on the liquid because gas occupies the blade region. The effective power draw falls, and bubble breakup is poor. The cure is to increase impeller speed, reduce gas rate, or change to an impeller less prone to flooding at the operating gas load. Step-by-Step Solution: Observe symptom: stable gas cavity and reduced torque.Link cause: insufficient tip speed for the imposed gas rate.Apply remedy: raise N, reduce Qg, or use a gassing-efficient impeller (e.g., Intermig or hydrofoil).Name the condition: flooded impeller. Verification / Alternative check: Torque and power measurements show a dip in gassed power when flooding initiates; visual inspection confirms coalesced gas under blades. Why Other Options Are Wrong: Coalesced impeller/river/dry: nonstandard terms. Choked: used in other contexts, not standard for this hydrodynamic state. Common Pitfalls: Confusing flooding with complete loss of aeration; gas still enters but is not effectively dispersed. Final Answer: Flooded impeller

Question 18

A reactor has a total (geometric) volume of 50,000 L and a headspace of 10,000 L. What is the working liquid volume inside the reactor?

Accepted Answer

Introduction / Context: Specifying a reactor requires distinguishing between total geometric volume, headspace for gas handling and foam, and working (liquid) volume. Accurate working volume is essential for calculating residence times, specific power input (P/V), and mass transfer coefficients such as KLa. Given Data / Assumptions: Total volume = 50,000 L. Headspace volume = 10,000 L (gas space above liquid). No internal fixtures significantly displacing volume (assumed negligible for this calculation). Concept / Approach: Working liquid volume equals total volume minus headspace. This simple subtraction is standard unless additional displacements (coils, internals) are specified. The resulting working volume is used in all volumetric performance metrics during operation. Step-by-Step Solution: Compute: V_liquid = V_total − V_headspace.Substitute numbers: 50,000 L − 10,000 L = 40,000 L.State the result clearly in litres.Thus, the working liquid volume is 40,000 L. Verification / Alternative check: If the process requires 20% headspace in a 50,000 L tank, 0.2 * 50,000 = 10,000 L, confirming the same calculation. Why Other Options Are Wrong: 10,000 or 20,000 or 30,000 L: incorrect subtraction or arbitrary fractions. 50,000 L: ignores headspace volume. Common Pitfalls: Confusing nominal vessel size with working volume; always confirm fill level and headspace policy for foaming systems. Final Answer: 40,000 L

Question 19

In agitation engineering, what is the correct expression for the impeller Reynolds number (Rei) in a stirred tank, using Di for impeller diameter, N for rotational speed, ρ for fluid density, and μ for fluid viscosity?

Accepted Answer

Introduction / Context: The impeller Reynolds number (Rei) is a dimensionless group that indicates the flow regime in a mechanically agitated vessel. It guides decisions on mixing scale-up, power draw correlations, gas dispersion, and mass transfer. This question tests recognition of the standard Rei formula expressed with commonly used variables in bioreactor design. Given Data / Assumptions: Stirred tank with an impeller of diameter Di rotating at speed N (revolutions per second or per minute converted to s^-1). Fluid of density ρ and dynamic viscosity μ (Newtonian assumption). No baffles or impeller-specific correction factors are included in Rei itself. Concept / Approach: Rei compares inertial to viscous forces. In stirred tanks, the characteristic velocity scale is N * Di and the characteristic length scale is Di. Thus Rei = (ρ * N * Di^2) / μ. This form parallels the pipe Reynolds number but replaces the mean velocity with a tip-speed scale and the diameter with the impeller diameter. Step-by-Step Solution: Choose velocity scale: U ~ N * Di.Form Reynolds number: Re = ρ * U * L / μ.Use L = Di and U = N * Di ⇒ Re = ρ * (N * Di) * Di / μ.Hence Rei = ρ * N * Di^2 / μ. Verification / Alternative check: Dimensional analysis confirms Rei is dimensionless: [ρ]=M L^-3, [N]=T^-1, [Di^2]=L^2, [μ]=M L^-1 T^-1; multiplying and dividing gives M L^-3 * T^-1 * L^2 / (M L^-1 T^-1) = 1. Why Other Options Are Wrong: Di * V * ρ / μ: introduces an undefined V; not the standard impeller scaling.Di^2 * V * ρ / μ: again uses V rather than N; incorrect for Rei.Di * N * ρ / μ: missing one factor of Di; wrong scaling. Common Pitfalls: Using rpm without converting to s^-1, mixing tip speed (π * Di * N) with Rei formula, or substituting tank diameter T for Di. Final Answer: Di^2 * N * ρ / μ

Question 20

In mixer selection for bioprocessing, what is the key advantage of axial-flow impellers (e.g., pitched-blade, marine) over radial-flow impellers (e.g., Rushton) under otherwise similar conditions?

Accepted Answer

Introduction / Context: Choosing between axial- and radial-flow impellers is central to designing bioreactors for microbes, animal cells, and plant cells. Axial-flow devices generate top-to-bottom circulation with comparatively lower shear, which is often critical for shear-sensitive cultures and flocculent or filamentous morphologies. Given Data / Assumptions: Similar tank geometry and power input ranges. Typical bioprocess media with suspended cells or microcarriers. Goal is to compare characteristic hydraulic effects, not project-specific costs. Concept / Approach: Radial impellers expel fluid laterally, creating strong shear near the blade tips and baffles—useful for gas dispersion but harsher to cells. Axial impellers push flow parallel to the shaft, producing bulk circulation with lower local energy dissipation rates. This supports oxygen transfer and mixing while limiting shear damage for sensitive cultures. Step-by-Step Solution: Identify design objective: maintain mixing and oxygen transfer with minimal shear.Axial impellers → lower shear profile, smoother flow field.Radial impellers → higher shear, suitable for intense gas dispersion tasks.Therefore, the defining advantage for bioprocesses is low shear with axial-flow impellers. Verification / Alternative check: Reported specific power dissipation maps show lower peak ε (W kg^-1) around axial impellers at equal bulk power inputs, correlating with improved viability in mammalian cell cultures. Why Other Options Are Wrong: Better solids lift in all cases: suspension depends on clearance, tank aspect ratio, and power number; not universally true.High shear conditions: characteristic of radial designs, not axial.Cheaper to build: cost depends on vendor and scale; not a general physical advantage. Common Pitfalls: Assuming a single impeller can serve all purposes; ignoring that axial designs can be combined with spargers/baffles to tune kLa while preserving lower shear. Final Answer: Provide low shear conditions that are gentler for shear-sensitive cells

Agitation and Aeration Questions