Q: Flow regime calculation: A liquid flows at 11,400 L·h^-1 through a 4 cm-ID pipe. The liquid has density 1 g·mL^-1 and dynamic viscosity 0.001 kg·m^-1·s^-1. Identify the flow regime using the Reynolds number.

Introduction: Determining the flow regime (laminar, transitional, turbulent) in process lines is fundamental for pressure drop, mixing, and mass-transfer correlations. The Reynolds number, Re = ρ * v * D / μ, is the standard criterion for Newtonian liquids in pipes. Given Data / Assumptions: Volumetric flow rate Q = 11,400 L·h^-1 = 11.4 m^3·h^-1. Pipe inner diameter D = 0.04 m. Density ρ = 1 g·mL^-1 = 1000 kg·m^-3. Dynamic viscosity μ = 0.001 kg·m^-1·s^-1. Newtonian behavior; smooth pipe; single-phase liquid. Concept / Approach: Compute average velocity v = Q / A, where A = π * D^2 / 4. Then calculate Reynolds number Re = ρ * v * D / μ. Use the conventional thresholds: Re 4000 (turbulent). Step-by-Step Solution: Convert flow rate: Q = 11.4 m^3·h^-1 = 11.4 / 3600 ≈ 0.003167 m^3·s^-1.Compute area: A = π * 0.04^2 / 4 ≈ 0.001257 m^2.Find velocity: v = Q / A ≈ 0.003167 / 0.001257 ≈ 2.52 m·s^-1.Compute Re: Re = 1000 * 2.52 * 0.04 / 0.001 ≈ 1.01 × 10^5.Classify regime: Re ≫ 4000 ⇒ turbulent. Verification / Alternative check: Even with modest roughness, a Reynolds number around 10^5 is strongly turbulent. Predictions of friction factor and pressure drop should therefore use turbulent correlations (e.g., Blasius for smooth pipes or Moody chart with appropriate relative roughness). Why Other Options Are Wrong: Laminar: requires Re < 2100; not satisfied. Transitional: 2100–4000; much lower than the computed Re. Any regime: data are sufficient; the regime is clearly turbulent. Common Pitfalls: Failing to convert units (L·h^-1 to m^3·s^-1) correctly. Using kinematic viscosity instead of dynamic viscosity without dividing by density. Final Answer: Turbulent regime

Question 1

In animal cell culture, which statements correctly describe how gas bubbles can damage delicate cells during aeration and mixing?

Accepted Answer

Introduction: Animal cells lack a rigid cell wall and are highly sensitive to hydrodynamic and interfacial stresses. Aeration is essential for oxygen supply, yet bubbles and foam can harm cells through several mechanical mechanisms. Understanding these mechanisms guides the selection of sparging strategies, impeller design, and protective additives. Given Data / Assumptions: Cells are shear-sensitive and adhere to interfaces. Aeration creates bubbles and potentially foam at the gas–liquid surface. Interfaces can concentrate cells and expose them to rupture forces upon bubble breakage. Concept / Approach: When bubbles rise and burst at the surface, the rapid retraction of the liquid film and the release of surface energy produce strong micro-eddies and capillary forces. Cells attached to bubble surfaces can experience membrane rupture. In foams, cells entrained between bubbles can be stretched or compressed as bubbles move and coalesce, creating mechanical damage. Step-by-Step Solution: Step 1: Identify bubble surface attachment as a risk factor for cell damage.Step 2: Recognize that bubble bursting at the gas–liquid interface releases localized energy that can disrupt membranes.Step 3: Account for foam dynamics, where cells are dragged and deformed by moving bubbles.Step 4: Conclude that both mechanisms in (a) and (b) are valid contributors to damage. Verification / Alternative check: Empirical studies report improved viability when bubble exposure is reduced via micro-spargers, membrane oxygenation, or by adding shear protectants that reduce interfacial adsorption of cells. Why Other Options Are Wrong: UV radiation release: Physically incorrect; bubble collapse does not emit ultraviolet radiation. Selective lysis of only dead cells: Bubble-related damage is not selective; viable cells are also at risk. Common Pitfalls: Assuming that only bulk shear damages cells while ignoring interfacial stresses, or believing that higher airflow always increases oxygen transfer without considering viability loss due to foam and bursting bubbles. Final Answer: Both (a) and (b)

Question 2

Considering basic rheology, classify water with respect to flow behavior under shear and explain the implication for mixing calculations in bioprocessing.

Accepted Answer

Introduction: Rheology describes how fluids deform and flow in response to applied shear. Correctly identifying the rheological class of a fluid simplifies mixing, pumping, and scale-up calculations. Water is frequently used as a calibration and reference fluid in bioprocess laboratories. Given Data / Assumptions: Water at moderate temperatures and pressures is considered an ideal simple fluid. Viscosity is independent of shear rate for Newtonian fluids. Non-Newtonian behaviors include shear thinning, shear thickening, and time-dependent effects. Concept / Approach: In a Newtonian fluid, shear stress τ is proportional to shear rate γ_dot via τ = μ * γ_dot, where μ is constant viscosity. Therefore, viscosity remains constant regardless of impeller speed or instantaneous shear rate, which simplifies power and Reynolds number calculations. Step-by-Step Solution: Step 1: Recall the Newtonian model with constant μ.Step 2: Recognize that water fits this model over a wide shear range.Step 3: Conclude that water's viscosity does not change with impeller speed, aiding predictable mixing behavior.Step 4: Use this property to compute Reynolds number and select impeller regimes without shear-dependent corrections. Verification / Alternative check: Viscometric measurements show water's viscosity is a function primarily of temperature, not shear rate, confirming Newtonian behavior for typical bioprocess conditions. Why Other Options Are Wrong: pseudoplastic: Shear-thinning; viscosity decreases with shear rate. dilatant: Shear-thickening; viscosity increases with shear rate. rheopectic: Time-dependent thickening under constant shear. thixotropic: Time-dependent thinning under constant shear. Common Pitfalls: Confusing temperature dependence (real for water) with shear dependence (not applicable for Newtonian classification) or assuming all biological media behave like water; many broths are non-Newtonian. Final Answer: newtonian fluid

Question 3

Which statement best defines a Newtonian fluid in terms of viscosity behavior during mixing or under varying shear rates?

Accepted Answer

Introduction: Classifying fluids by how their viscosity responds to shear is essential for designing agitation and transfer operations. Newtonian fluids exhibit the simplest behavior, which greatly simplifies engineering correlations and scale-up. Given Data / Assumptions: Viscosity is defined as the ratio of shear stress to shear rate. Mechanical agitation varies shear rate but should not alter viscosity for Newtonian fluids. Time dependence is characteristic of thixotropy or rheopexy, not Newtonian behavior. Concept / Approach: Newtonian fluids have constant viscosity μ such that τ = μ * γ_dot. Thus, regardless of impeller speed (which changes γ_dot), μ remains constant, barring temperature changes. Non-Newtonian behaviors involve shear-thinning, shear-thickening, or time-dependent structural changes in the fluid. Step-by-Step Solution: Step 1: Identify that Newtonian definition requires constant μ with respect to γ_dot.Step 2: Compare options; only the option stating constant viscosity independent of mixing conditions matches the definition.Step 3: Recognize that options implying changes with speed or time correspond to non-Newtonian categories.Step 4: Select the correct constant-viscosity statement. Verification / Alternative check: Standard references list water, dilute salt solutions, and light oils as Newtonian; their viscosity is a function of temperature and pressure, not shear rate or mixing time within typical ranges. Why Other Options Are Wrong: changes during mixing but returns after: Thixotropic behavior. increases with speed: Dilatant (shear-thickening). decreases with speed: Pseudoplastic (shear-thinning). depends only on time: Time dependence is non-Newtonian. Common Pitfalls: Confusing thermal effects with shear dependence; a rise in temperature can lower viscosity, but that is not a shear-rate effect. Final Answer: is constant regardless of the stirrer speed or mixing time

Question 4

Identify the correct behavior of a dilatant (shear-thickening) fluid when subjected to increasing impeller speed or shear rate in a mixing operation.

Accepted Answer

Introduction: Dilatant or shear-thickening fluids display an increase in apparent viscosity with rising shear rate. Recognizing this behavior is crucial to avoid overloading mixers and pumps and to prevent unexpected heat generation or poor mixing performance in formulations containing suspended solids or concentrated starch systems. Given Data / Assumptions: Dilatancy refers to viscosity increase with shear rate. Impeller speed is a practical proxy for shear rate in stirred tanks. Other non-Newtonian behaviors include shear thinning and time-dependent effects. Concept / Approach: As shear rate increases, particle networks or microstructures in dilatant fluids resist flow more strongly, raising viscosity. This is the opposite of pseudoplastic fluids, which show decreased viscosity with shear rate due to alignment or structure breakdown. Step-by-Step Solution: Step 1: Recall that dilatant = shear-thickening.Step 2: Translate higher impeller speed to higher shear rate at the fluid scale.Step 3: Conclude that apparent viscosity rises with speed for a dilatant fluid.Step 4: Select the option that states an increase in viscosity with increasing speed. Verification / Alternative check: Rheograms of shear-thickening suspensions show upward-curving stress–shear rate plots. In mixing trials, torque demand often increases disproportionately at higher speeds. Why Other Options Are Wrong: constant viscosity: Newtonian behavior, not dilatant. changes during mixing but returns: Thixotropy or rheopexy, time-dependent effects. decreases with speed: Pseudoplastic (shear-thinning). no dependence on shear rate: Contradicts shear-thickening definition. Common Pitfalls: Operating at high speeds with shear-thickening slurries can cause motor overloads; engineers should perform torque checks and consider lower speeds or different impellers. Final Answer: increases with increasing stirrer speed

Question 5

In animal cell bioreactors, which combination of strategies is most appropriate to minimize bubble-induced cell damage while maintaining adequate oxygen supply?

Accepted Answer

Introduction: Animal cells are sensitive to interfacial and shear stresses caused by gas sparging and bubble bursting. Process engineers must balance oxygen transfer with cell viability. Several complementary methods reduce harmful bubble exposure while sustaining oxygen supply. Given Data / Assumptions: Cells are shear-sensitive and negatively affected by bubble surfaces and bursting. Oxygen demand must be met to avoid hypoxia. Multiple engineering controls exist: additives, alternative oxygenation, and gentler aeration pathways. Concept / Approach: Shear protectants (e.g., Pluronic F-68) reduce cell adsorption to gas–liquid interfaces. Bubble-free oxygenation (e.g., membrane oxygenators, liquid-phase oxygen carriers) supplies oxygen without direct sparging. Headspace aeration lowers bubble residence and bursting at the surface compared to vigorous sparging, further restricting interfacial damage. Step-by-Step Solution: Step 1: Mitigate interfacial damage by adding surfactant-like protectants that cushion cells.Step 2: Replace or supplement sparging with bubble-free oxygenation to eliminate direct bubble contact.Step 3: Employ headspace aeration to provide gentler gas transfer with fewer bubbles and lower foam.Step 4: Combine these strategies for robust protection while meeting oxygen transfer targets. Verification / Alternative check: Case studies show improved viability and productivity when sparging intensity is reduced and protectants are added. Oxygen transfer can be maintained by increased membrane area or by using enriched oxygen streams in bubble-free systems. Why Other Options Are Wrong: addition of a shear protectorant: Helpful but not the only required measure. using a bubble free oxygen delivery system: Effective but often combined with other tactics for best results. headspace aeration: Useful but may not fully satisfy oxygen demand alone. increasing sparging rate and impeller speed simultaneously: Usually increases damage risk despite higher oxygen transfer. Common Pitfalls: Attempting to solve oxygen limitation solely by raising airflow or agitation, which can reduce viability; overlooking foam control and antifoam selection compatible with downstream purification. Final Answer: all of the above

Question 6

Rheology in bioprocessing: Which dissolved or dispersed compound, when added at comparable mass fraction to an aqueous solution, will cause the greatest increase in apparent viscosity under gentle mixing conditions?

Accepted Answer

Introduction: Viscosity changes in bioprocess media arise from the size, shape, and interactions of solutes. This question tests your understanding of how macromolecular architecture (elongated versus compact) controls hydrodynamic volume, entanglement, and thus the apparent viscosity of solutions relevant to fermentation, downstream processing, and formulation. Given Data / Assumptions: All candidates are added at comparable mass fractions to water. Temperature and ionic strength are typical laboratory values. No gelation or chemical crosslinking occurs; we consider purely physical thickening. Shear rates are in the gentle mixing range typical of bench reactors. Concept / Approach: Apparent viscosity rises strongly with solute molecular weight and with anisotropic, chain-like shapes that create large hydrodynamic volumes and inter-chain interactions. Long-chain proteins (e.g., serum albumin when partially unfolded or behaving as an extended coil) produce higher solution viscosity than compact globular proteins of similar mass because they occupy more volume and entangle more readily. Small molecules like glucose contribute negligibly, and adding more water obviously cannot raise viscosity. Step-by-Step Solution: Identify which option provides the largest hydrodynamic volume per molecule: elongated chains > globular proteins > small sugars > water.Relate chain conformation to viscosity: extended coils increase entanglement and resistance to flow.Compare contributions at equal mass fraction: macromolecular coils dominate over small solutes.Conclude that a long-chain, flexible protein such as albumin causes the greatest viscosity increase. Verification / Alternative check: Empirical correlations (e.g., intrinsic viscosity [η]) scale strongly with molecular weight and coil dimensions. Solutions of flexible biopolymers (proteins in unfolded/extended states, polysaccharides) are demonstrably more viscous than those of compact globular proteins at the same mass fraction, while monosaccharides barely change viscosity within practical ranges. Why Other Options Are Wrong: Glucose: very small; contributes little to viscosity at typical concentrations. Water: dilutes the solution; does not increase viscosity. A compact, globular protein: increases viscosity somewhat but less than a long, flexible chain at comparable mass fraction. Common Pitfalls: Assuming molecular weight alone determines viscosity; shape and flexibility are equally critical. Ignoring shear-rate dependence (shear thinning) which further accentuates differences for chain-like solutes. Final Answer: A long-chain, flexible protein such as serum albumin

Question 7

Non-Newtonian behavior: A fluid whose apparent viscosity decreases as stirrer speed increases and also decreases progressively with mixing time is best classified as which combination?

Accepted Answer

Introduction: Industrial broths and formulated media often deviate from Newtonian behavior. Correctly identifying shear-rate and time-dependent effects is essential for scale-up, mixing, and mass-transfer predictions. This item checks recognition of a fluid that thins with shear rate and also thins with time under constant shear. Given Data / Assumptions: Apparent viscosity decreases as stirrer speed (shear rate) increases. At a fixed speed, viscosity further drops over time and then recovers when resting. No plastic yield stress is mentioned. Concept / Approach: Shear-thinning behavior indicates pseudoplasticity: viscosity falls as shear rate rises. Time-dependent viscosity decrease at constant shear indicates thixotropy, a reversible structural breakdown under shear with time that recovers at rest. The combined description “pseudoplastic, thixotropic” accurately captures both rate and time dependencies. Step-by-Step Solution: Map rate dependence: viscosity ↓ with shear rate ⇒ pseudoplastic.Map time dependence: viscosity ↓ with time at constant shear ⇒ thixotropic.Combine classifications to obtain “pseudoplastic, thixotropic.”Exclude rheopectic and dilatant behaviors (opposites). Verification / Alternative check: Flow curves (apparent viscosity vs. shear rate) and hysteresis loops from up/down shear ramps show classic thixotropic loops for such fluids. Many cell broths and polymer solutions exhibit this profile. Why Other Options Are Wrong: Newtonian: viscosity is constant, independent of shear rate and time. Dilatant, rheopectic: both imply thickening (viscosity increases) with rate and time, opposite to the description. Dilatant, pseudoplastic: self-contradictory pairing (dilatant = shear-thickening; pseudoplastic = shear-thinning). Common Pitfalls: Confusing thixotropy (time-dependent thinning) with mere shear-thinning (rate-dependent only). Assuming all non-Newtonian fluids are thixotropic; many are not time-dependent. Final Answer: Pseudoplastic, thixotropic fluid

Question 8

Viscometry principle: What does a Brookfield rotational viscometer measure directly to infer the viscosity of a fluid at a set spindle speed?

Accepted Answer

Introduction: Rotational viscometers are widely used in biotechnology and formulation labs for quick viscosity checks. Understanding what the instrument actually measures helps interpret data correctly for Newtonian and non-Newtonian fluids. Given Data / Assumptions: Brookfield viscometer employs a spindle rotating in the sample. Speed is controlled; torque is sensed by a calibrated spring or transducer. Geometry constants are known for each spindle and container. Concept / Approach: The instrument directly measures torque at a specified angular velocity. From torque and geometry, one computes an apparent viscosity (for non-Newtonian fluids) or true viscosity (for Newtonian fluids) after converting torque to shear stress and relating speed to shear rate via the spindle constants. Step-by-Step Solution: Hold spindle speed constant using the viscometer motor control.Measure resisting torque transmitted through the spring/transducer.Convert torque to shear stress using geometry factors.Relate rotational speed to shear rate; compute viscosity = shear stress / shear rate. Verification / Alternative check: Calibration oils of known viscosity yield torques consistent with the instrument’s conversion charts, confirming that torque is the primary measured quantity and viscosity is derived. Why Other Options Are Wrong: Shear stress alone or shear rate alone: neither is directly measured independently; both are inferred from torque and speed with geometry constants. Both directly and independently: not correct for Brookfield devices; torque is direct, shear rate is derived. Common Pitfalls: Reporting “viscosity” without noting the shear rate, which is essential for non-Newtonian fluids. Using inappropriate spindle/volume combinations that invalidate geometry assumptions. Final Answer: The torque required to rotate the spindle (impeller) at a set speed

Question 9

Cell damage in sparged mammalian bioreactors: Which sources of shear are implicated in causing injury to sensitive animal cells during aerated culture?

Accepted Answer

Introduction: Mammalian and other shear-sensitive cells are vulnerable to hydrodynamic stresses in aerated bioreactors. Recognizing the multiple loci of damaging shear helps engineers select gentler gas transfer strategies (e.g., larger bubbles, perfusion with micro-spargers, or bubble-free aeration systems). Given Data / Assumptions: Aerated (sparged) culture with gas bubbles rising to the surface. Presence of free surface where bubbles burst and form foam. Cells are non-cell-wall organisms with delicate membranes. Concept / Approach: Injurious shear arises in three main regions: the turbulent bulk due to mixing and bubble wakes; the free surface where bubble rupture creates transient, high-strain microjets and capillary waves; and the foam layer where films thin and bubbles interact, creating localized shear between interfaces. All contribute to cell damage risk. Step-by-Step Solution: Identify bulk mixing as a source: eddies and bubble wakes impose fluctuating shear on cells.Identify surface rupture: bursting bubbles generate rapid film retraction and microjets.Identify foam shear: bubble–bubble interactions and film drainage strain cells trapped near the surface.Conclude that all listed sources can cause damage. Verification / Alternative check: Lowering gas flow, adding shear protectants (e.g., Pluronic F-68), using headspace overlay instead of vigorous sparging, or employing micro-porous spargers with controlled bubble size all reduce cell lysis, consistent with multiregion shear mechanisms. Why Other Options Are Wrong: Any single source alone underestimates the combined impact observed in practice. Common Pitfalls: Blaming only impeller shear while ignoring surface phenomena. Assuming antifoam always helps; it can alter kLa and may have mixed effects on cell health. Final Answer: All of the above

Question 10

Units and dimensions: What is the SI unit of dynamic viscosity (μ) used in bioprocess calculations?

Accepted Answer

Introduction: Keeping units straight is essential for Reynolds number, pressure drop, and mass-transfer calculations. Dynamic viscosity has a specific SI unit that also ties directly to the Pascal-second (Pa·s). Given Data / Assumptions: We focus on dynamic viscosity μ (not kinematic viscosity ν). SI base units are used consistently. Newton’s law of viscosity: shear stress τ = μ * (du/dy). Concept / Approach: Shear stress τ has units of Pascals (Pa = N·m^-2 = kg·m^-1·s^-2). Shear rate du/dy has units s^-1. Rearranging τ = μ * (du/dy) gives μ = τ / (du/dy), so μ has units (kg·m^-1·s^-2) / s^-1 = kg·m^-1·s^-1, which is identical to Pa·s. Step-by-Step Solution: Start with τ = μ * γ̇ (where γ̇ is shear rate).Use [τ] = Pa = kg·m^-1·s^-2.Use [γ̇] = s^-1.Compute [μ] = [τ]/[γ̇] = (kg·m^-1·s^-2)/(s^-1) = kg·m^-1·s^-1 = Pa·s. Verification / Alternative check: Common reference values: water at 20°C has μ ≈ 1.0×10^-3 kg·m^-1·s^-1 (1 mPa·s), consistent with Pa·s units. Why Other Options Are Wrong: kg·m^-2·s^-2 or kg·m^-3·s^-1 or kg·m^-1·s^-2: these correspond to other derived quantities (e.g., pressure, density flow terms, or stress), not dynamic viscosity. Common Pitfalls: Confusing dynamic viscosity μ with kinematic viscosity ν = μ/ρ, which has units m^2·s^-1. Dropping or misplacing exponents, leading to dimensional inconsistency in calculations. Final Answer: kg·m^-1·s^-1 (equivalent to Pa·s)

Question 11

Shear-thinning definition: In a pseudoplastic fluid relevant to fermentation broths, how does apparent viscosity change as stirrer speed (shear rate) increases?

Accepted Answer

Introduction: Many biological fluids, including cell suspensions and polymer-rich media, are pseudoplastic. Correctly identifying shear-thinning behavior informs agitator sizing, power draw, and oxygen transfer modeling. Given Data / Assumptions: Pseudoplasticity refers to rate dependence, not necessarily time dependence. Shear rate correlates with stirrer speed in a given geometry. No yield stress is described. Concept / Approach: Pseudoplastic (shear-thinning) fluids show a decrease in apparent viscosity as shear rate increases. Microstructure (entanglements, flocs) aligns or breaks down under shear, providing less resistance to flow. This is distinct from thixotropy (time-dependent) or dilatancy (shear-thickening). Step-by-Step Solution: Raise stirrer speed ⇒ higher shear rate in the vessel.Microstructure aligns/breaks ⇒ lower resistance to deformation.Observed effect ⇒ apparent viscosity decreases.Classify ⇒ pseudoplastic (shear-thinning). Verification / Alternative check: Flow curves (log viscosity vs. log shear rate) show a negative slope for pseudoplastic fluids; power-law fits exhibit flow index n < 1. Why Other Options Are Wrong: Constant viscosity: Newtonian behavior, not pseudoplastic. Purely time-dependent recovery: thixotropy; rate dependence is not implied. Increases with speed: dilatant (shear-thickening), opposite of pseudoplastic. Common Pitfalls: Conflating rate-dependent thinning with time-dependent thinning (thixotropy). Assuming one measurement at a single speed reveals full rheology; multiple shear rates are needed. Final Answer: Decreases with increasing stirrer speed (shear-thinning)

Question 12

Broth rheology and morphology: Assuming no extracellular gum secretion, which culture type typically gives the highest broth viscosity during fermentation?

Accepted Answer

Introduction: Microbial morphology directly impacts broth rheology. Understanding which morphologies create viscous, non-Newtonian behavior is crucial for choosing aeration and agitation strategies and for predicting mass-transfer limitations. Given Data / Assumptions: No secretion of exopolysaccharide gums (so viscosity arises from cells themselves). Comparing unicellular forms (bacteria, yeast) to filamentous forms. Considering pelletized versus dispersed mycelial growth. Concept / Approach: Dispersed filamentous mycelia form long, flexible networks that entangle and dramatically increase apparent viscosity and elasticity (pseudoplastic, thixotropic behaviors). Pelletized fungi present lower surface area for entanglement and can yield lower bulk viscosity. Unicellular bacteria and yeasts, being small and non-filamentous, typically lead to near-Newtonian or mildly shear-thinning broths of much lower viscosity. Step-by-Step Solution: Identify morphology: long, poorly branched hyphae create fiber networks.Relate structure to rheology: networks entangle, increasing resistance to flow.Contrast with pellets: compact aggregates reduce network formation in the bulk.Conclude: dispersed mycelia produce the highest viscosities among the listed options. Verification / Alternative check: Power-law indices (n) < 1 and high consistency coefficients (K) are frequently observed for mycelial broths, along with pronounced thixotropic loops, confirming strong viscosity elevation relative to unicellular cultures. Why Other Options Are Wrong: Bacteria and yeast: small, spherical/rod cells with limited entanglement; viscosities close to water at modest cell densities. Pelletized fungi: lower bulk entanglement; may increase apparent yield stress but generally less viscous than dispersed mycelia. Common Pitfalls: Assuming all filamentous growth increases viscosity equally; morphology (pellet vs. dispersed) matters greatly. Overlooking agitation effects that can shift morphology between pellets and mycelia. Final Answer: Filamentous fungi growing as long, poorly branched chains (dispersed mycelia)

Question 13

Time-dependent rheology: A fluid whose viscosity changes with stirrer speed or mixing time but then returns to the original value once mixing stops is best described as what?

Accepted Answer

Introduction: Beyond rate dependence, many process fluids exhibit time dependence. Distinguishing thixotropy from rheopexy and from viscoelasticity is key for predicting start-up, shutdown, and intermittent mixing behavior in reactors and pipelines. Given Data / Assumptions: Viscosity changes with speed or time during mixing. Viscosity returns to its original value after mixing ceases and the fluid is allowed to rest. No permanent structural change or chemical reaction occurs. Concept / Approach: Thixotropy describes time-dependent structural breakdown under shear and recovery at rest. Apparent viscosity decreases during sustained shear and rebuilds when shear is removed. This is distinct from rheopexy (viscosity increases with time at constant shear), viscoelasticity (time-dependent stress–strain response but not necessarily viscosity recovery behavior), and Newtonian behavior (no time or rate dependence). Step-by-Step Solution: Observe time-dependent viscosity decrease under shear ⇒ thixotropic signature.Cease mixing and note recovery to initial value ⇒ reversible microstructure rebuilds.Exclude rheopexy (time-dependent thickening) and purely elastic phenomena.Classify the fluid as thixotropic. Verification / Alternative check: Hysteresis loops on up/down shear ramps show area between curves for thixotropic fluids, and creep–recovery tests demonstrate structural rebuilding over time at rest. Why Other Options Are Wrong: Newtonian: viscosity is constant; no time or rate effects. Rheopectic: opposite time dependence (thickening under sustained shear). Viscoelastic: describes stress relaxation and elastic recoil but not necessarily the reversible viscosity drop/recovery described. Common Pitfalls: Confusing viscoelasticity with thixotropy; many thixotropic fluids are also viscoelastic, but the defining feature here is time-dependent thinning with recovery. Attributing irreversible changes to thixotropy; by definition it is reversible. Final Answer: Thixotropic (time-dependent thinning with recovery at rest)

Question 14

Flow regime calculation: A liquid flows at 11,400 L·h^-1 through a 4 cm-ID pipe. The liquid has density 1 g·mL^-1 and dynamic viscosity 0.001 kg·m^-1·s^-1. Identify the flow regime using the Reynolds number.

Accepted Answer

Introduction: Determining the flow regime (laminar, transitional, turbulent) in process lines is fundamental for pressure drop, mixing, and mass-transfer correlations. The Reynolds number, Re = ρ * v * D / μ, is the standard criterion for Newtonian liquids in pipes. Given Data / Assumptions: Volumetric flow rate Q = 11,400 L·h^-1 = 11.4 m^3·h^-1. Pipe inner diameter D = 0.04 m. Density ρ = 1 g·mL^-1 = 1000 kg·m^-3. Dynamic viscosity μ = 0.001 kg·m^-1·s^-1. Newtonian behavior; smooth pipe; single-phase liquid. Concept / Approach: Compute average velocity v = Q / A, where A = π * D^2 / 4. Then calculate Reynolds number Re = ρ * v * D / μ. Use the conventional thresholds: Re < 2100 (laminar), 2100–4000 (transitional), > 4000 (turbulent). Step-by-Step Solution: Convert flow rate: Q = 11.4 m^3·h^-1 = 11.4 / 3600 ≈ 0.003167 m^3·s^-1.Compute area: A = π * 0.04^2 / 4 ≈ 0.001257 m^2.Find velocity: v = Q / A ≈ 0.003167 / 0.001257 ≈ 2.52 m·s^-1.Compute Re: Re = 1000 * 2.52 * 0.04 / 0.001 ≈ 1.01 × 10^5.Classify regime: Re ≫ 4000 ⇒ turbulent. Verification / Alternative check: Even with modest roughness, a Reynolds number around 10^5 is strongly turbulent. Predictions of friction factor and pressure drop should therefore use turbulent correlations (e.g., Blasius for smooth pipes or Moody chart with appropriate relative roughness). Why Other Options Are Wrong: Laminar: requires Re < 2100; not satisfied. Transitional: 2100–4000; much lower than the computed Re. Any regime: data are sufficient; the regime is clearly turbulent. Common Pitfalls: Failing to convert units (L·h^-1 to m^3·s^-1) correctly. Using kinematic viscosity instead of dynamic viscosity without dividing by density. Final Answer: Turbulent regime

Question 15

Bubble-free aeration: What is typically required to supply oxygen without forming bubbles in sensitive cell cultures or protein formulations?

Accepted Answer

Introduction: Some cultures (e.g., mammalian cells) and biopharmaceutical processes are highly sensitive to bubble-induced shear and air–liquid interfaces. Bubble-free aeration delivers oxygen by diffusion through a membrane into the liquid, avoiding bubbles and reducing shear damage and foaming. Given Data / Assumptions: Goal is oxygen supply without sparging. Membrane contactors or silicone tubing are available. Carbon dioxide removal is handled by the same or a complementary route via partial pressure gradients. Concept / Approach: Gas-permeable materials (e.g., silicone, certain fluoropolymers) allow O2 to diffuse from a gas side to the liquid side driven by partial pressure differences. This enables O2 transfer and CO2 stripping without forming bubbles inside the culture, minimizing shear and interfacial stress. Step-by-Step Solution: Select an O2-permeable membrane (tubing or hollow-fiber contactor).Provide a controlled O2 partial pressure on the gas side.Allow diffusion across the membrane into the broth, raising dissolved O2.Optionally remove CO2 by maintaining a lower CO2 partial pressure on the gas side. Verification / Alternative check: Membrane-based oxygenation is widely used in perfusion bioreactors and small-scale culture devices, showing stable dissolved oxygen without foam formation and reduced cell damage relative to sparging at comparable oxygen transfer rates. Why Other Options Are Wrong: Replacing air with CO2: carbon dioxide does not supply oxygen; it displaces it. Adding oxygen as hydrogen peroxide: unsafe and chemically inappropriate; membranes do not function that way. Filling headspace with CO2: would lower oxygen availability and acidify the medium; counterproductive. Common Pitfalls: Underestimating membrane area required for target kLa; design must match oxygen demand. Ignoring fouling or wetting of membranes, which reduces performance over time. Final Answer: Silicone tubing or gas-permeable membranes to facilitate dissolved gas transfer without bubbles

Question 16

Fluid rheology — If the apparent viscosity of a fluid decreases with the length of time that it is being mixed (at roughly constant shear), what is this fluid behavior called?

Accepted Answer

Introduction: Engineers frequently encounter non-Newtonian fluids whose apparent viscosity depends on not only shear rate but also the duration of shearing. The question tests recognition of time-dependent thinning versus thickening behaviors and distinguishes these from purely shear-rate–dependent or elastic responses. Given Data / Assumptions: Mixing occurs at roughly constant shear conditions. The measured apparent viscosity decreases as mixing continues over time. No large temperature drift or composition change during the observation. Concept / Approach: Thixotropy is the phenomenon where viscosity decreases with time under constant shear, typically due to reversible breakdown of a microstructure (e.g., flocculated networks). Rheopexy is the opposite: viscosity increases with time under shear. Pseudoplastic or dilatant labels refer primarily to dependence on shear rate at a given moment, not on elapsed time at constant shear. Viscoelasticity refers to storage and loss moduli and elastic recoil, not inherently to time-thinning under constant conditions. Step-by-Step Solution: Identify time dependence: viscosity change is tied to mixing time at constant shear, indicating a structural breakdown process.Map to terminology: time-dependent thinning corresponds to thixotropy.Exclude alternatives: rheopexy would thicken; Newtonian viscosity would be constant; viscoelasticity is about elastic response; dilatancy is shear-thickening with rate, not time. Verification / Alternative check: Perform a three-interval thixotropy test on a rotational rheometer (low–high–low shear). A hysteresis loop in the flow curve (downward shift after high-shear interval) confirms thixotropy. Recovery with a rest period further corroborates a reversible structure breakdown–rebuild cycle. Why Other Options Are Wrong: Newtonian: viscosity independent of shear rate and time. Rheopectic: time-dependent thickening, opposite of the observation. Viscoelastic: describes elastic effects, not necessarily time-thinning. Dilatant: shear-thickening with increasing rate, not a time effect at constant shear. Common Pitfalls: Confusing pseudoplasticity (rate effect) with thixotropy (time effect); misattributing temperature drift to rheology; ignoring rest-time recovery behavior. Final Answer: Thixotropic (time-dependent thinning)

Question 17

Viscoelastic fluids — Which statement best characterizes the viscosity behavior of a viscoelastic fluid during and after mixing?

Accepted Answer

Introduction: Viscoelastic fluids exhibit both viscous flow and elastic response (they can store and dissipate energy). This question probes the qualitative behavior of such materials during and after imposed deformation in routine mixing operations common to bioprocessing and food engineering. Given Data / Assumptions: Small to moderate deformation rates typical of lab or pilot mixing. Temperature and composition approximately constant. Observation includes behavior during shear and upon cessation of shear. Concept / Approach: Viscoelasticity implies time-dependent stress relaxation and creep. Under shear, microstructure can align or partially break; after shear stops, elastic recovery and structural rebuild tend to return rheological properties toward the pre-shear state. This reversible character contrasts with purely time-dependent irreversible changes (e.g., chemical degradation). It also differs from strictly rate-dependent behavior that lacks elastic recoil. Step-by-Step Solution: Note the coexistence of viscous flow (permanent) and elastic recovery (reversible) in viscoelastic materials.Under sustained shear, the apparent viscosity may change due to alignment; upon stopping, partial recovery occurs.Therefore, a statement that acknowledges change during mixing and recovery after mixing captures viscoelastic behavior. Verification / Alternative check: Stress relaxation tests (step strain) show decaying stress, and creep–recovery tests show partial strain recovery, both signatures of viscoelasticity. Oscillatory rheology reveals storage modulus G' and loss modulus G' that define elastic and viscous contributions across frequency. Why Other Options Are Wrong: (a) Describes Newtonian fluids, not viscoelastic ones. (c) Always increasing with speed is dilatancy, not general viscoelasticity. (d) Always decreasing with speed is pseudoplasticity, not necessarily viscoelastic. (e) Elastic solids alone lack steady-flow viscosity; viscoelastic fluids have both G' and measurable apparent viscosity. Common Pitfalls: Equating viscoelasticity with any single rate trend; ignoring recoverable strain; assuming changes during mixing are irreversible chemical changes rather than physical microstructure effects. Final Answer: Viscosity may change during mixing but returns (partially or fully) toward its original state after mixing stops.

Question 18

Temperature dependence — Which statement correctly describes how viscosity changes with increasing temperature for liquids and gases?

Accepted Answer

Introduction: Understanding how viscosity varies with temperature is essential for pump sizing, mixing scale-up, and heat- and mass-transfer correlations. Liquids and gases exhibit opposing trends because their molecular transport mechanisms differ fundamentally. Given Data / Assumptions: Moderate pressure range where idealized trends apply. No phase change over the temperature span considered. Comparisons are qualitative (increase vs decrease). Concept / Approach: In liquids, viscosity is dominated by cohesive intermolecular forces; heating reduces these cohesive constraints, allowing molecules to slide past one another more easily, thus lowering viscosity. In gases, viscosity reflects momentum transfer by molecular motion; increasing temperature raises molecular speed and mean kinetic energy, increasing momentum exchange and, therefore, viscosity. Step-by-Step Solution: Identify liquid mechanism: stronger intermolecular attractions at low T impede flow; higher T weakens these restraints.Identify gas mechanism: higher T implies faster molecules and more frequent, energetic collisions that enhance momentum transport.Conclude opposite trends: liquids thin with heat; gases thicken modestly with heat. Verification / Alternative check: Empirical correlations (e.g., Andrade for liquids, Sutherland or Chapman–Enskog for gases) quantitatively capture these trends and are standard in transport property databases used by engineers. Why Other Options Are Wrong: (a) Both decreasing contradicts gas behavior. (b) Both increasing contradicts liquid behavior. (d) Claims gases decrease, which is opposite typical gas trends. (e) Temperature effects are often decisive in design and cannot be neglected. Common Pitfalls: Extrapolating gas trends to very high pressures where non-ideal effects intervene; conflating viscosity with density changes, which may move in different directions. Final Answer: Viscosity of gases increases with temperature, but viscosity of liquids decreases with temperature.

Question 19

Cell-culture additives — Pluronic F-68 protects mammalian cells from shear damage primarily because it is a non-ionic surface-active agent that does what?

Accepted Answer

Introduction: Pluronic F-68 (also called Poloxamer 188) is a widely used non-ionic surfactant in animal cell culture. The question examines why this additive reduces shear-related cell damage in aerated, agitated systems common to bioreactors and shake flasks. Given Data / Assumptions: Suspension cultures of shear-sensitive mammalian cells (e.g., CHO, hybridoma). Aeration and agitation produce bubbles and gas–liquid interfaces. Pluronic F-68 is present at typical concentrations (e.g., 0.05–1.0 g/L). Concept / Approach: Cell damage often occurs when cells attach to bubbles, are transported to the surface, and are ruptured upon bubble bursting due to high interfacial stress. A non-ionic surfactant adsorbs at interfaces, modifies surface tension, and forms protective layers that reduce cell–bubble adhesion and mitigate the violent stresses of bubble collapse. Although some antifoams break foams, Pluronic F-68 commonly stabilizes interfaces while protecting cells from interfacial trauma. Step-by-Step Solution: Recognize the key damage pathway: bubble attachment and rupture at the surface.Identify surfactant action: adsorption at interfaces reduces direct cell–interface contact and stress transmission.Pluronic F-68 therefore serves as a shear protectant primarily via interfacial effects, not as a nutrient or coagulant. Verification / Alternative check: Empirical studies show improved viability and titer upon F-68 addition under aerated conditions; microscopy reveals fewer cells associated with bubbles and higher post-aeration integrity compared with surfactant-free controls. Why Other Options Are Wrong: (b) F-68 is not a strong defoamer; many silicone-based antifoams are used for destabilizing foams. (c) It is not a vitamin source. (d) It does not coagulate cells; excessive aggregation would harm mass transfer. (e) It does not affect mechanical speed directly. Common Pitfalls: Assuming all surfactants are antifoams; overlooking that stabilizing interfaces can still protect cells by preventing harmful bubble–cell interactions. Final Answer: Stabilizes gas–liquid interfaces and foams, reducing cell–bubble adhesion and protecting cells during bubble rupture.

Question 20

Mixing regimes in stirred tanks — Which statement about flow regimes and the role of speed and baffles is most accurate?

Accepted Answer

Introduction: Flow regime identification is fundamental to predicting power draw, blending times, and mass/heat-transfer coefficients in agitated vessels. This question distinguishes correct statements about regime classification from common misconceptions about speed and baffles. Given Data / Assumptions: Cylindrical, baffled vessels with typical impellers. Reynolds number for mixing defined as Re = rho * N * D^2 / mu. Fluids may be Newtonian or non-Newtonian, but the concept of regime via Re remains instructive. Concept / Approach: Regimes are often categorized as laminar (Re ≲ 10), transitional (10 ≲ Re ≲ 10^4), and turbulent (Re ≳ 10^4) for Newtonian systems. Baffles help prevent vortex formation and promote radial/axial flow; they do not create laminar flow. Increasing speed raises Re, but turbulence is not guaranteed if viscosity or scale constraints keep Re low (e.g., very viscous polymer solutions, large D with low N limits, or non-Newtonian effects). Step-by-Step Solution: Assess statement (a): Regime classification by Re is standard practice — correct.Assess statement (b): Speed helps, but high viscosity or small impellers can keep Re low; thus, “always” is incorrect.Assess statement (c): Baffles reduce swirl and increase turbulence intensity for a given N; they do not make flow laminar.Since (a) is true and (b)/(c) are false, “all of the above” cannot be right. Verification / Alternative check: Correlations for power number vs Re show regime transitions; photographic flow visualization confirms that baffles suppress vortex yet enhance bulk turbulence at sufficient Re. Why Other Options Are Wrong: (b) Overgeneralizes; turbulence depends on Re, not speed alone. (c) Misstates baffle function; they encourage turbulent, not laminar, flow. (d) Cannot be right since (b) and (c) are wrong. (e) Cannot be right since (a) is correct. Common Pitfalls: Misusing speed as a surrogate for Re; assuming baffles “calm” flow into laminar; ignoring non-Newtonian effective viscosity shifts. Final Answer: Mixing in stirred tanks can be classified as laminar, transitional, or turbulent depending on Reynolds number.

Fluid Flow Questions