Q.1 Which term best describes the movement of solutes from a region of high concentration to a region of low concentration in a bioreactor?
Convection
Diffusion
Dispersion
Osmosis
Explanation - Diffusion is the passive transport driven by concentration gradients, a key mechanism for mass transfer in bioprocesses.
Correct answer is: Diffusion
Q.2 In the context of transport phenomena, the Reynolds number is used to predict:
Heat transfer coefficient
Chemical reaction rate
Flow regime (laminar or turbulent)
Solute solubility
Explanation - Reynolds number (Re) compares inertial to viscous forces and indicates whether flow is laminar (Re < 2100) or turbulent (Re > 4000).
Correct answer is: Flow regime (laminar or turbulent)
Q.3 For a cylindrical packed‑bed reactor, which dimensionless group characterizes axial dispersion?
Schmidt number (Sc)
Péclet number (Pe)
Damköhler number (Da)
Nusselt number (Nu)
Explanation - Pe = uL/D_axial; a high Péclet number indicates low axial dispersion relative to convective transport.
Correct answer is: Péclet number (Pe)
Q.4 Which of the following equations represents the steady‑state mass balance for a non‑reactive solute in a tubular bioreactor with axial dispersion?
D d²C/dx² – u dC/dx = 0
ρ Cp dT/dt = k a (T_s – T)
∂C/∂t + u ∂C/∂x = D ∂²C/∂x²
r = k C^n
Explanation - For steady state (∂C/∂t = 0) and no reaction, the balance reduces to D d²C/dx² – u dC/dx = 0.
Correct answer is: D d²C/dx² – u dC/dx = 0
Q.5 In a well‑mixed bioreactor, the volumetric mass transfer coefficient (k_La) is most directly related to:
Bubble size and gas holdup
Viscosity of the liquid phase
Temperature of the reactor
Catalyst surface area
Explanation - k_La = k_L × a; a (interfacial area) depends on bubble size and gas holdup, while k_L depends on liquid properties.
Correct answer is: Bubble size and gas holdup
Q.6 Which transport mechanism dominates when a solute moves through a membrane due to a pressure gradient?
Diffusion
Convection
Osmosis
Electrophoresis
Explanation - Pressure‑driven flow (convective transport) pushes the fluid and any dissolved solutes through the membrane pores.
Correct answer is: Convection
Q.7 The Sherwood number (Sh) in a bioprocess is analogous to which dimensionless group in heat transfer?
Reynolds number (Re)
Prandtl number (Pr)
Nusselt number (Nu)
Péclet number (Pe)
Explanation - Sh = k L/D (mass transfer) is analogous to Nu = h L/k (heat transfer); both relate convective to diffusive transport.
Correct answer is: Nusselt number (Nu)
Q.8 In a plug‑flow bioreactor, the residence time distribution (RTD) function is:
Delta function (Dirac delta)
Exponential decay
Gaussian distribution
Uniform distribution
Explanation - Ideal plug flow has zero dispersion, giving an RTD of a Dirac delta at the mean residence time.
Correct answer is: Delta function (Dirac delta)
Q.9 Which term in the energy balance for a stirred‑tank reactor accounts for heat generated by microbial metabolism?
Q_in
Q_out
∑ΔH_rxn
U A ΔT
Explanation - The sum of reaction enthalpies (∑ΔH_rxn) captures heat released or absorbed by biochemical reactions.
Correct answer is: ∑ΔH_rxn
Q.10 The effective diffusion coefficient in a porous scaffold is reduced compared to free solution mainly due to:
Higher temperature
Increased viscosity
Tortuosity and porosity
Catalytic activity
Explanation - Pathway complexity (tortuosity) and reduced cross‑sectional area (porosity) lower the effective diffusion coefficient.
Correct answer is: Tortuosity and porosity
Q.11 When scaling up a bioreactor, which dimensionless group is most useful to preserve mixing characteristics?
Froude number (Fr)
Damköhler number (Da)
Péclet number (Pe)
Biot number (Bi)
Explanation - Fr = ω² D/g relates impeller speed to gravitational forces, helping maintain similar mixing patterns during scale‑up.
Correct answer is: Froude number (Fr)
Q.12 In a membrane bioreactor, the term "critical flux" refers to:
Maximum feed flow rate before fouling accelerates
Flux at which osmotic pressure equals trans‑membrane pressure
Flux that yields 100% substrate conversion
Flux at which temperature rise is observed
Explanation - Critical flux is the threshold permeate flux above which fouling rates increase sharply.
Correct answer is: Maximum feed flow rate before fouling accelerates
Q.13 The Biot number (Bi) in heat transfer is defined as:
h L/k
k L/h
ρ c L²/α
u L/ν
Explanation - Bi = (convective heat transfer coefficient × characteristic length) / thermal conductivity; indicates internal vs external resistance.
Correct answer is: h L/k
Q.14 For a first‑order enzymatic reaction occurring in a well‑mixed reactor, the Damköhler number (Da) is given by:
k V/Q
k τ
k L²/D
Re Sc
Explanation - Da = reaction rate × residence time (τ = V/Q) for first‑order kinetics; compares reaction to flow time scales.
Correct answer is: k τ
Q.15 Which of the following best describes axial dispersion in a tubular reactor?
Radial mixing due to turbulence
Longitudinal spreading of solute caused by velocity variations
Diffusion across the reactor wall
Heat loss to the surroundings
Explanation - Axial dispersion accounts for deviations from ideal plug flow due to velocity profile non‑uniformity and diffusion.
Correct answer is: Longitudinal spreading of solute caused by velocity variations
Q.16 The effective thermal conductivity of a porous biocatalyst bed can be estimated by:
k_eff = k_s ε + k_g (1‑ε)
k_eff = k_s (1‑ε) + k_g ε
k_eff = (k_s + k_g)/2
k_eff = k_s k_g/(k_s + k_g)
Explanation - Weighted average based on solid (k_s) and gas (k_g) fractions; ε is porosity.
Correct answer is: k_eff = k_s (1‑ε) + k_g ε
Q.17 In the context of mass transfer, the term "interfacial area" (a) is most commonly expressed in units of:
m²/m³
kg/m³
W/m²·K
mol/L·s
Explanation - Interfacial area per unit volume (a) quantifies the surface available for mass transfer, typically m² of interface per m³ of reactor volume.
Correct answer is: m²/m³
Q.18 If a bioprocess is operated under conditions where the Schmidt number (Sc) is very high, this indicates:
Dominant heat transfer over mass transfer
Low momentum diffusivity relative to mass diffusivity
High momentum diffusivity relative to mass diffusivity
Low viscosity of the fluid
Explanation - Sc = ν/D; a high Sc means kinematic viscosity (ν) is much larger than mass diffusivity (D).
Correct answer is: Low momentum diffusivity relative to mass diffusivity
Q.19 Which of the following statements about the Thiele modulus (Φ) is true for a porous catalyst pellet?
Φ < 1 indicates reaction‑limited regime
Φ > 1 indicates diffusion‑limited regime
Φ = 0 corresponds to no reaction
All of the above
Explanation - Φ compares reaction rate to internal diffusion; Φ < 1 reaction limited, Φ > 1 diffusion limited, Φ = 0 means no reaction.
Correct answer is: All of the above
Q.20 In a continuous stirred‑tank reactor (CSTR) with first‑order kinetics, the steady‑state concentration is given by:
C = C₀ exp(‑kτ)
C = C₀/(1 + kτ)
C = C₀ (1 – e^(‑kτ))
C = C₀ kτ
Explanation - For a CSTR, C_out = C_in/(1 + kτ) where τ = V/Q is the residence time.
Correct answer is: C = C₀/(1 + kτ)
Q.21 Which phenomenon primarily causes fouling in a membrane bioreactor during long‑term operation?
Thermal expansion
Biofilm formation
Viscous heating
Acoustic cavitation
Explanation - Microbial growth on membrane surfaces creates a biofilm that increases resistance to flow.
Correct answer is: Biofilm formation
Q.22 The term "Peclet number" in heat transfer (Pe_h) is defined as:
Re Pr
u L/α
k L/ρ c_p
h L/k
Explanation - Pe_h = (convective transport)/(conductive transport) = u L/α, where α is thermal diffusivity.
Correct answer is: u L/α
Q.23 When analyzing a batch bioreactor, the term “specific growth rate (μ)” is defined as:
dX/dt
1/X · dX/dt
dS/dt
k · C
Explanation - μ = (1/X)·(dX/dt) describes the relative rate of biomass increase.
Correct answer is: 1/X · dX/dt
Q.24 In a laminar flow through a circular tube, the velocity profile is:
Uniform across the cross‑section
Parabolic
Flat‑topped
Sinusoidal
Explanation - Laminar flow in a pipe follows Hagen–Poiseuille law, giving a parabolic velocity distribution.
Correct answer is: Parabolic
Q.25 The term "mass transfer coefficient (k_L)" has units of:
m/s
W/m²·K
mol/(L·s)
kg/(m³·s)
Explanation - k_L relates flux (mol/(m²·s)) to concentration difference (mol/m³), resulting in units of velocity (m/s).
Correct answer is: m/s
Q.26 In a gas‑liquid bioreactor, the volumetric oxygen transfer rate (OTR) is expressed as:
OTR = k_La (C* – C)
OTR = U A ΔT
OTR = Q ΔP
OTR = k V
Explanation - OTR = k_La times the driving force (saturation concentration minus actual dissolved oxygen).
Correct answer is: OTR = k_La (C* – C)
Q.27 Which of the following is NOT a typical source of heat generation in a bioprocess?
Microbial metabolic activity
Frictional heating due to stirring
Solar radiation
Exothermic chemical reactions
Explanation - Bioprocesses are usually conducted in controlled indoor environments; solar radiation is not a standard heat source.
Correct answer is: Solar radiation
Q.28 The term "tortuosity" (τ) in porous media refers to:
Ratio of pore diameter to particle size
Effective path length divided by straight path length
Porosity multiplied by permeability
Diffusivity ratio of gas to liquid
Explanation - Tortuosity quantifies how convoluted the pathways are compared with a straight line, affecting diffusion and flow.
Correct answer is: Effective path length divided by straight path length
Q.29 In a stirred‑tank bioreactor, increasing the impeller diameter while keeping speed constant will:
Increase Reynolds number
Decrease shear stress
Reduce mixing time
All of the above
Explanation - Larger impeller diameter raises Re (∝ D²), increases shear, and shortens mixing time due to larger swept volume.
Correct answer is: All of the above
Q.30 The effective diffusivity (D_eff) in a biopolymer gel is typically lower than the bulk diffusivity (D_bulk) because of:
Higher temperature in the gel
Increased solvent viscosity
Reduced free volume and tortuosity
Catalytic activity of the polymer
Explanation - Gel structure restricts molecular movement, lowering D_eff relative to D_bulk.
Correct answer is: Reduced free volume and tortuosity
Q.31 Which of the following best describes the role of the Nernst–Planck equation in bioprocess transport phenomena?
Describes heat conduction
Relates ionic flux to concentration, electric field, and pressure gradients
Predicts gas‑liquid mass transfer
Calculates viscosity of polymer solutions
Explanation - The Nernst–Planck equation accounts for diffusion, migration, and convection of charged species.
Correct answer is: Relates ionic flux to concentration, electric field, and pressure gradients
Q.32 For a first‑order reaction occurring in a porous pellet, the effectiveness factor (η) is given by:
η = 1/Φ tanh Φ
η = Φ/ sinh Φ
η = tanh Φ / Φ
η = Φ² / (1 + Φ²)
Explanation - Effectiveness factor for spherical geometry with first‑order kinetics is η = tanh Φ / Φ.
Correct answer is: η = tanh Φ / Φ
Q.33 When the Peclet number (Pe) is much greater than 1 in a tubular reactor, the dominant transport mechanism is:
Diffusion
Convection
Dispersion
Radiation
Explanation - Pe = u L/D; a high Pe means convective transport far outweighs diffusive spreading.
Correct answer is: Convection
Q.34 In a bioprocess, the term "heat of reaction" (ΔH_rxn) is negative for:
Endothermic reactions
Exothermic reactions
Isothermal processes
Adiabatic processes
Explanation - Exothermic reactions release heat, giving a negative ΔH_rxn in the energy balance.
Correct answer is: Exothermic reactions
Q.35 The term "mass transfer resistance" in a liquid‑film model is inversely proportional to:
Film thickness
Diffusivity
Concentration gradient
Viscosity
Explanation - Higher diffusivity reduces resistance; resistance ∝ film thickness / (D · area).
Correct answer is: Diffusivity
Q.36 In a continuous bioreactor, the residence time distribution (RTD) function E(t) is obtained by:
Differentiating the cumulative distribution F(t)
Integrating the concentration curve
Measuring temperature rise
Counting cells
Explanation - E(t) = dF(t)/dt; it describes the probability density of fluid element residence times.
Correct answer is: Differentiating the cumulative distribution F(t)
Q.37 Which of the following is a primary advantage of using a packed‑bed reactor for immobilized enzymes?
Higher shear stress
Better temperature control
Higher volumetric productivity due to increased surface area
Simpler downstream separation
Explanation - Immobilized enzymes on packing material provide large interfacial area, boosting reaction rates per reactor volume.
Correct answer is: Higher volumetric productivity due to increased surface area
Q.38 The dimensionless group that compares reaction rate to diffusion rate inside a catalyst pellet is:
Damköhler number (Da)
Thiele modulus (Φ)
Péclet number (Pe)
Biot number (Bi)
Explanation - Φ = (reaction rate × characteristic length²/D)¹ᐟ²; it contrasts internal diffusion with reaction.
Correct answer is: Thiele modulus (Φ)
Q.39 In the energy balance of a jacketed bioreactor, the term U A ΔT represents:
Heat generated by microbes
Heat removed or added through the jacket
Viscous dissipation
Mass transfer of oxygen
Explanation - U A ΔT is the overall heat transfer rate across the jacket wall, where U is overall coefficient and ΔT is temperature difference.
Correct answer is: Heat removed or added through the jacket
Q.40 Which transport phenomenon is most directly described by Fourier’s law?
Mass diffusion
Momentum convection
Heat conduction
Electrical conduction
Explanation - Fourier’s law states that heat flux is proportional to the temperature gradient.
Correct answer is: Heat conduction
Q.41 For a first‑order reaction in a plug‑flow reactor, the conversion X is given by:
X = 1 – exp(‑kτ)
X = kτ / (1 + kτ)
X = exp(‑kτ)
X = kτ
Explanation - Plug‑flow residence time τ = V/Q; conversion for first‑order kinetics follows X = 1 – e^(‑kτ).
Correct answer is: X = 1 – exp(‑kτ)
Q.42 In a bioreactor, the term "mixing time" is defined as:
Time required to reach thermal equilibrium
Time for a tracer to disperse uniformly within a specified tolerance
Time for substrate to be completely consumed
Time for cells to double
Explanation - Mixing time is measured by injecting a tracer and recording when concentration homogenizes within a set % of the final value.
Correct answer is: Time for a tracer to disperse uniformly within a specified tolerance
Q.43 The effective viscosity of a cell suspension often follows the Einstein relation for low solid fractions. Which expression represents this relation?
μ_eff = μ_0 (1 + 2.5 φ)
μ_eff = μ_0 (1 + φ)
μ_eff = μ_0 / (1 – φ)
μ_eff = μ_0 e^{φ}
Explanation - Einstein’s equation for dilute suspensions: μ_eff = μ_0 (1 + 2.5 φ), where φ is the volume fraction of particles.
Correct answer is: μ_eff = μ_0 (1 + 2.5 φ)
Q.44 Which dimensionless group is most useful to assess the relative importance of heat generation versus heat removal in an exothermic bioreactor?
Biot number (Bi)
Damköhler number (Da)
Péclet number (Pe)
Thiele modulus (Φ)
Explanation - Bi = (heat transfer resistance inside)/(outside); high Bi indicates internal heat generation dominates.
Correct answer is: Biot number (Bi)
Q.45 In a gas‑liquid membrane contactor, the mass transfer driving force is:
Pressure difference across the membrane
Partial pressure difference of the gas component
Temperature gradient
Electrical potential difference
Explanation - Gas transfer across a membrane is driven by the difference in partial pressures of the transferring species.
Correct answer is: Partial pressure difference of the gas component
Q.46 A bioreactor operated at a constant temperature of 37 °C and pH 7.0 is considered:
Isothermal and isobaric
Isothermal and isoelectric
Isobaric and isoelectric
Adiabatic and isobaric
Explanation - Constant temperature implies isothermal; unless pressure is varied, the system is also isobaric.
Correct answer is: Isothermal and isobaric
Q.47 The term "dead‑zone" in a stirred‑tank reactor refers to:
Region of high shear
Area near the impeller where mixing is most intense
Region with very low velocity where mixing is poor
Zone where temperature is highest
Explanation - Dead zones are low‑flow regions (e.g., near the tank walls) that may lead to poor mass and heat transfer.
Correct answer is: Region with very low velocity where mixing is poor
Q.48 Which of the following equations describes the relationship between shear stress (τ) and shear rate (γ̇) for a Newtonian fluid?
τ = μ γ̇
τ = K γ̇^n
τ = η γ̇^2
τ = μ γ̇ + λ γ̈
Explanation - Newtonian fluids have a linear relationship between shear stress and shear rate with viscosity μ as proportionality constant.
Correct answer is: τ = μ γ̇
Q.49 In a bioprocess, the term "specific heat capacity" (c_p) is defined as:
Heat required to raise the temperature of 1 kg of material by 1 K
Heat required to raise the temperature of 1 mol of material by 1 K
Heat generated per unit time
Heat removed per unit area
Explanation - Specific heat capacity is the amount of heat needed per unit mass to raise temperature by one Kelvin.
Correct answer is: Heat required to raise the temperature of 1 kg of material by 1 K
Q.50 The effective thermal diffusivity (α_eff) in a bioprocessing vessel is calculated as:
α_eff = k_eff / (ρ c_p)
α_eff = ρ c_p / k_eff
α_eff = k_eff · ρ c_p
α_eff = k_eff – ρ c_p
Explanation - Thermal diffusivity α = thermal conductivity / (density × specific heat).
Correct answer is: α_eff = k_eff / (ρ c_p)
Q.51 For a first‑order degradation of a substrate in a CSTR, the steady‑state substrate concentration is:
C = C₀ e^(‑kτ)
C = C₀/(1 + kτ)
C = C₀ (1 – e^(‑kτ))
C = C₀ kτ
Explanation - Same expression as biomass; for first‑order loss, outlet concentration equals inlet divided by (1 + kτ).
Correct answer is: C = C₀/(1 + kτ)
Q.52 The term "mass transfer coefficient" (k_La) is often increased by:
Increasing temperature only
Increasing agitation speed and gas flow rate
Reducing reactor volume
Adding inert salts
Explanation - Higher agitation improves liquid‑side mass transfer; higher gas flow raises interfacial area, both raising k_La.
Correct answer is: Increasing agitation speed and gas flow rate
Q.53 In transport phenomena, the term "dispersion coefficient" (D_disp) is used to describe:
Molecular diffusion only
Effective spreading due to velocity variations and diffusion
Heat transfer through a wall
Electrical resistance in a solution
Explanation - Dispersion combines molecular diffusion with macroscopic mixing caused by non‑uniform velocity fields.
Correct answer is: Effective spreading due to velocity variations and diffusion
Q.54 Which of the following statements about the Nusselt number (Nu) is correct?
Nu = h L/k and indicates the ratio of convective to conductive heat transfer
Nu = Re Pr and indicates the ratio of inertial to viscous forces
Nu = k L/h and indicates the ratio of conduction to convection
Nu = D L/k and is used for mass transfer
Explanation - Nu compares convective heat transfer (h) to conductive (k) over a characteristic length L.
Correct answer is: Nu = h L/k and indicates the ratio of convective to conductive heat transfer
Q.55 The term "heat of vaporization" is relevant in which bioprocess operation?
Fermentation broth cooling
Membrane filtration
Lyophilization (freeze‑drying)
Aeration of the reactor
Explanation - During freeze‑drying, water is sublimated; heat of vaporization (or sublimation) is the energy required for phase change.
Correct answer is: Lyophilization (freeze‑drying)
Q.56 When scaling up a bioreactor, maintaining the same power per unit volume (P/V) primarily preserves:
Oxygen transfer rate
Shear environment
Temperature profile
pH stability
Explanation - P/V is directly linked to the energy dissipated as shear; keeping it constant maintains similar shear stresses.
Correct answer is: Shear environment
Q.57 In the context of transport in porous catalysts, the term "Knudsen diffusion" becomes dominant when:
Pore diameter is much larger than molecular mean free path
Pore diameter is comparable to or smaller than molecular mean free path
Temperature is very low
Viscosity is high
Explanation - Knudsen diffusion occurs when molecule‑wall collisions dominate over molecule‑molecule collisions.
Correct answer is: Pore diameter is comparable to or smaller than molecular mean free path
Q.58 The term "heat transfer area" (A) in a jacketed bioreactor refers to:
Surface area of the impeller
Internal volume of the reactor
Total area of the jacket wall that contacts the process fluid
Cross‑sectional area of the inlet pipe
Explanation - A is the area through which heat is exchanged between the reactor contents and the jacket fluid.
Correct answer is: Total area of the jacket wall that contacts the process fluid
Q.59 The mass balance for a component A undergoing first‑order decay in a batch reactor is:
dC_A/dt = –k C_A
dC_A/dt = k C_A
dC_A/dt = –k
dC_A/dt = k
Explanation - First‑order decay: rate of change proportional to concentration with negative sign.
Correct answer is: dC_A/dt = –k C_A
Q.60 In a gas‑liquid bioreactor, the volumetric mass transfer coefficient k_La is typically increased by:
Reducing gas flow rate
Increasing bubble size
Increasing agitation speed
Lowering temperature
Explanation - Higher agitation breaks bubbles into smaller sizes, increases interfacial area, and improves liquid‑side mass transfer, raising k_La.
Correct answer is: Increasing agitation speed
Q.61 The term "specific power input" (P/V) in a stirred tank is expressed in:
W m⁻³
J kg⁻¹
W kg⁻¹
kW L⁻¹
Explanation - P/V denotes power per unit reactor volume, commonly reported as watts per cubic meter.
Correct answer is: W m⁻³
Q.62 Which dimensionless number indicates the ratio of heat generated by reaction to heat removed by convection in a reactor?
Damköhler number (Da)
Biot number (Bi)
Péclet number (Pe)
Thiele modulus (Φ)
Explanation - Da = (reaction rate)/(convective mass/heat transport rate); high Da indicates reaction dominates.
Correct answer is: Damköhler number (Da)
Q.63 In a laminar flow regime, the shear stress at the wall of a circular pipe is proportional to:
Flow rate squared
Velocity gradient at the wall
Pressure drop across the pipe
Fluid density
Explanation - Wall shear stress τ_w = μ (du/dr) at the wall; depends on the velocity gradient.
Correct answer is: Velocity gradient at the wall
Q.64 The term "mass transfer resistance" in a two‑film model for a gas‑liquid interface is the sum of:
Liquid film resistance + gas film resistance
Diffusion coefficient + viscosity
Temperature gradient + concentration gradient
Interfacial tension + surface area
Explanation - Total resistance = 1/k_L + 1/k_G; each term corresponds to a film on either side of the interface.
Correct answer is: Liquid film resistance + gas film resistance
Q.65 Which of the following best describes the role of the Reynolds number (Re) in scaling up bioreactors?
Ensures same temperature profile
Maintains similar flow regime (laminar/turbulent)
Controls pH stability
Sets the oxygen solubility
Explanation - Keeping Re constant during scale‑up helps preserve the character of the flow field.
Correct answer is: Maintains similar flow regime (laminar/turbulent)
Q.66 For a reaction occurring in a porous bead, the effectiveness factor η approaches 1 when:
Thiele modulus Φ ≫ 1
Thiele modulus Φ ≪ 1
Damköhler number Da ≫ 1
Péclet number Pe ≪ 1
Explanation - Low Φ indicates reaction is much slower than internal diffusion, so the whole pellet is effectively utilized (η ≈ 1).
Correct answer is: Thiele modulus Φ ≪ 1
Q.67 In a CSTR, the residence time distribution (RTD) is:
A Dirac delta function
An exponential decay
A Gaussian curve
Uniform distribution
Explanation - CSTR has a residence time probability density E(t) = (1/τ) exp(‑t/τ).
Correct answer is: An exponential decay
Q.68 Which factor does NOT directly affect the volumetric mass transfer coefficient (k_La) in an aerobic bioreactor?
Impeller speed
Gas sparger design
Temperature of the broth
pH of the medium
Explanation - k_La is primarily governed by physical factors (agitation, gas flow, temperature); pH influences biology but not k_La directly.
Correct answer is: pH of the medium
Q.69 In a packed‑bed reactor, the pressure drop per unit length is described by the Ergun equation. Which term in the Ergun equation accounts for viscous (laminar) flow contribution?
Term proportional to (1–ε)²/ε³ · μ u/D_p²
Term proportional to (1–ε) · ρ u²/D_p
Term proportional to ε · k_La
Term proportional to u³
Explanation - The first term of the Ergun equation represents viscous (laminar) losses; the second term represents inertial (turbulent) losses.
Correct answer is: Term proportional to (1–ε)²/ε³ · μ u/D_p²
Q.70 For a first‑order reaction in a tubular reactor with axial dispersion, the governing differential equation is:
D d²C/dx² – u dC/dx – k C = 0
u dC/dx + k C = 0
dC/dt = D d²C/dx² – k C
dC/dx = –k C/u
Explanation - Steady‑state mass balance with axial dispersion and first‑order reaction includes diffusion term, convection term, and reaction term.
Correct answer is: D d²C/dx² – u dC/dx – k C = 0
Q.71 The term "heat of formation" is used to describe:
Heat released or absorbed when a compound is formed from its elements
Heat generated during microbial metabolism
Heat lost due to convection
Heat required for phase change
Explanation - Standard enthalpy of formation refers to the enthalpy change when one mole of a compound forms from its constituent elements in their standard states.
Correct answer is: Heat released or absorbed when a compound is formed from its elements
Q.72 In a gas‑liquid membrane separator, which phenomenon primarily determines the selectivity of the membrane?
Pore size distribution
Membrane thickness
Surface charge of the membrane
Temperature of the feed
Explanation - Selectivity is often controlled by the size exclusion effect; pore size determines which molecules can pass.
Correct answer is: Pore size distribution
Q.73 When the Sherwood number (Sh) is high, this indicates:
Dominant diffusion resistance
Dominant convective mass transfer
Low interfacial area
High viscosity
Explanation - Sh = k_L L/D; a high value means the convective mass transfer coefficient k_L is large relative to diffusion.
Correct answer is: Dominant convective mass transfer
Q.74 In a bioprocess, the term "critical shear rate" is important because:
It defines the rate at which heat is generated
It marks the threshold above which cells may become damaged
It determines the solubility of gases
It controls the pH of the medium
Explanation - Excessive shear can lyse delicate cells; the critical shear rate is the maximum safe operating value.
Correct answer is: It marks the threshold above which cells may become damaged
Q.75 The relationship between the mass transfer coefficient (k_L) and the diffusion coefficient (D) for a stagnant film of thickness δ is:
k_L = D / δ
k_L = δ / D
k_L = D · δ
k_L = D² / δ
Explanation - For a planar film, k_L = D/δ, reflecting that a thinner film or higher diffusivity increases mass transfer.
Correct answer is: k_L = D / δ
Q.76 The term "heat of mixing" is relevant to which bioprocess step?
Fermentation
Centrifugation
Mixing of feed streams before inoculation
Sterilization
Explanation - When two liquids of different temperatures are mixed, heat of mixing can either release or absorb heat, affecting temperature control.
Correct answer is: Mixing of feed streams before inoculation
Q.77 Which of the following best describes the term "interfacial tension" in a gas‑liquid bioreactor?
Force per unit length acting at the gas‑liquid interface
Viscosity of the liquid phase
Diffusivity of oxygen in water
Temperature difference across the interface
Explanation - Interfacial tension is the energy required to increase the surface area of the interface, influencing bubble formation.
Correct answer is: Force per unit length acting at the gas‑liquid interface
Q.78 The term "mass transfer driving force" for a solute diffusing through a membrane is:
ΔT (temperature difference)
ΔP (pressure difference)
ΔC (concentration difference)
ΔV (velocity difference)
Explanation - Diffusive mass transfer across a membrane is driven by concentration gradients.
Correct answer is: ΔC (concentration difference)
Q.79 In a bioprocess, the parameter "specific oxygen uptake rate" (q_O2) is defined as:
Oxygen consumption per unit reactor volume per time
Oxygen consumption per unit cell mass per time
Oxygen dissolved concentration in the medium
Oxygen transfer coefficient
Explanation - q_O2 = (rate of O₂ consumption)/(biomass concentration), a key kinetic parameter.
Correct answer is: Oxygen consumption per unit cell mass per time
Q.80 When the Schmidt number (Sc) is very low (Sc < 0.1) for a solute in water, which transport mechanism dominates?
Molecular diffusion
Momentum diffusion (viscous effects)
Thermal diffusion
Electrical migration
Explanation - Low Sc means ν ≪ D, so momentum diffuses much faster than mass; convection dominates over diffusion.
Correct answer is: Momentum diffusion (viscous effects)
Q.81 In a continuous bioreactor, the term "space–time" (τ) is defined as:
Reactor volume divided by volumetric flow rate
Reactor surface area divided by flow rate
Temperature difference across the reactor
Pressure drop per unit length
Explanation - Space–time τ = V/Q, representing the average residence time of fluid elements.
Correct answer is: Reactor volume divided by volumetric flow rate
Q.82 Which of the following is a common assumption in the derivation of the one‑dimensional axial dispersion model?
Radial concentration gradients are negligible
Flow is turbulent throughout the reactor
Reaction rate is zero
Temperature is constant
Explanation - The model assumes plug flow in the radial direction, focusing only on axial dispersion.
Correct answer is: Radial concentration gradients are negligible
Q.83 The term "mass transfer coefficient" (k_La) can be increased by decreasing which of the following?
Bubble size
Viscosity of the liquid
Interfacial area
Temperature
Explanation - Smaller bubbles increase interfacial area, leading to a higher k_La.
Correct answer is: Bubble size
Q.84 In a gas‑liquid membrane aeration system, the overall mass transfer resistance is minimized when:
Both gas and liquid film resistances are equal
Liquid film resistance dominates
Gas film resistance dominates
Membrane thickness is maximal
Explanation - When resistances are balanced, the total resistance is minimized, maximizing overall transfer rate.
Correct answer is: Both gas and liquid film resistances are equal
Q.85 For a first‑order reaction in a CSTR, the dimensionless Damköhler number (Da) equals:
k τ
Re Sc
Pe / Sc
Sh · Bi
Explanation - Da = reaction rate × residence time = k τ for first‑order kinetics in a CSTR.
Correct answer is: k τ
Q.86 In the context of heat transfer, the term "overall heat transfer coefficient" (U) combines:
Conduction and convection resistances in series
Only the convection resistance on the hot side
Only the conduction resistance through the wall
Radiation and convection on both sides
Explanation - U accounts for all heat transfer resistances (film convection on both sides and wall conduction) in series.
Correct answer is: Conduction and convection resistances in series
Q.87 Which dimensionless number is used to characterize the relative importance of buoyancy forces to inertial forces in a fluid flow?
Froude number (Fr)
Reynolds number (Re)
Péclet number (Pe)
Nusselt number (Nu)
Explanation - Fr = u²/(g L); low Fr indicates buoyancy dominates, high Fr indicates inertia dominates.
Correct answer is: Froude number (Fr)
Q.88 In a batch bioreactor, the rate of temperature change due to metabolic heat can be expressed as:
ρ c_p V (dT/dt) = Q_met – Q_out
k_La (C* – C) = dC/dt
τ (dX/dt) = μ X
Re = ρ u D/μ
Explanation - Energy balance: accumulation of thermal energy equals metabolic heat generation minus heat removed.
Correct answer is: ρ c_p V (dT/dt) = Q_met – Q_out
Q.89 The term "critical supersaturation ratio" in crystallization processes is important because it:
Determines the reactor pressure
Controls the rate of nucleation
Sets the temperature of the reactor
Defines the viscosity of the medium
Explanation - Supersaturation drives nucleation; exceeding the critical ratio leads to rapid crystal formation.
Correct answer is: Controls the rate of nucleation
Q.90 In a porous catalyst pellet, the effective diffusivity (D_eff) is related to the bulk diffusivity (D_bulk) by:
D_eff = ε/τ · D_bulk
D_eff = τ/ε · D_bulk
D_eff = ε · τ · D_bulk
D_eff = D_bulk / (ε · τ)
Explanation - Effective diffusivity accounts for porosity (ε) and tortuosity (τ): D_eff = ε D_bulk/τ.
Correct answer is: D_eff = ε/τ · D_bulk
Q.91 The term "heat of reaction" in a bioreactor is typically expressed in units of:
J kg⁻¹
W m⁻²
J mol⁻¹
W L⁻¹
Explanation - Heat of reaction (ΔH_rxn) is the enthalpy change per mole of substrate reacted.
Correct answer is: J mol⁻¹
Q.92 Which phenomenon primarily causes fouling in a membrane used for ultrafiltration of cell culture broth?
Crystallization of salts
Adsorption of proteins and cell debris
Thermal degradation of the membrane
Gas bubble formation
Explanation - Biomolecules and particles deposit on the membrane surface, reducing permeability.
Correct answer is: Adsorption of proteins and cell debris
Q.93 In a plug‑flow reactor, the axial dispersion number (D/(u L)) is a measure of:
Relative importance of diffusion to convection
Heat loss to the environment
Shear stress distribution
pH gradient along the reactor
Explanation - The dispersion number quantifies how much axial mixing occurs compared with ideal plug flow.
Correct answer is: Relative importance of diffusion to convection
Q.94 The term "mass transfer coefficient" (k_L) for a liquid film is inversely proportional to:
Film thickness
Diffusivity
Interfacial area
Temperature
Explanation - k_L = D/δ; increasing film thickness δ reduces k_L.
Correct answer is: Film thickness
Q.95 When scaling up a bioreactor based on constant volumetric power input (P/V), the impeller speed (N) must be changed according to:
N ∝ (P/V)¹ᐟ³
N ∝ (P/V)²ᐟ⁵
N ∝ (P/V)¹ᐟ²
N ∝ (P/V)⁰
Explanation - For geometrically similar tanks, P ∝ N³ D⁵; keeping P/V constant leads to N ∝ (P/V)¹ᐟ³.
Correct answer is: N ∝ (P/V)¹ᐟ³
Q.96 The dimensionless group that compares the rate of heat conduction within a solid to the rate of heat convection at its surface is:
Biot number (Bi)
Péclet number (Pe)
Damköhler number (Da)
Nusselt number (Nu)
Explanation - Bi = (h L)/k, indicating the relative importance of internal conduction versus external convection.
Correct answer is: Biot number (Bi)
Q.97 In a gas‑liquid membrane contactor, the term "overall mass transfer coefficient" (K) is calculated as:
1/K = 1/k_L + 1/k_G
K = k_L + k_G
K = k_L · k_G
K = k_L / k_G
Explanation - Overall resistance is the sum of liquid and gas film resistances; reciprocal gives K.
Correct answer is: 1/K = 1/k_L + 1/k_G
Q.98 Which parameter is most directly affected by increasing the temperature of a liquid in a bioprocess?
Viscosity decreases, increasing diffusivity
Interfacial tension increases
Density increases
Molar mass changes
Explanation - Higher temperature reduces viscosity, which generally raises diffusion coefficients (D ∝ T/μ).
Correct answer is: Viscosity decreases, increasing diffusivity
Q.99 In a continuous stirred‑tank bioreactor, the term "mixing time" is typically measured using:
Tracer injection and concentration monitoring
Thermocouple readings
pH probe fluctuations
Pressure drop measurements
Explanation - A pulse of a detectable tracer is added, and the time to achieve a specified uniformity defines mixing time.
Correct answer is: Tracer injection and concentration monitoring
Q.100 The term "Péclet number for mass transfer" (Pe_m) can be expressed as:
Pe_m = u L/D
Pe_m = Re Sc
Pe_m = k_La L/D
Pe_m = ρ u L/μ
Explanation - Pe_m compares convective transport (u L) to diffusive transport (D).
Correct answer is: Pe_m = u L/D
Q.101 Which of the following best describes the effect of increasing the porosity (ε) of a packed‑bed catalyst on the pressure drop?
Pressure drop increases
Pressure drop decreases
No effect on pressure drop
Pressure drop first increases then decreases
Explanation - Higher porosity provides larger flow channels, reducing frictional losses and pressure drop.
Correct answer is: Pressure drop decreases
Q.102 The term "mass transfer coefficient" (k_L) for a spherical particle can be estimated using the correlation:
Sh = 2 + 0.6 Re^{1/2} Sc^{1/3}
Nu = 2 + 0.6 Re^{1/2} Pr^{1/3}
Da = k L/D
Fr = N² D/g
Explanation - This empirical correlation gives Sherwood number for external mass transfer around a sphere.
Correct answer is: Sh = 2 + 0.6 Re^{1/2} Sc^{1/3}
Q.103 In the context of bioprocess heat removal, the term "cooling duty" refers to:
Amount of heat that must be removed per unit time
Power required to stir the reactor
Rate of oxygen transfer
Volume of coolant circulated
Explanation - Cooling duty is the heat load that the cooling system must reject to maintain set temperature.
Correct answer is: Amount of heat that must be removed per unit time
Q.104 The effective thermal conductivity of a composite bioprocess system (solid + liquid) can be approximated using:
Series model (harmonic mean)
Parallel model (arithmetic mean)
Geometric mean
Logarithmic mean
Explanation - When phases are arranged in parallel to heat flow, effective conductivity is the weighted arithmetic average.
Correct answer is: Parallel model (arithmetic mean)
Q.105 Which of the following is NOT a typical cause of temperature gradients in large‑scale bioreactors?
Insufficient mixing
Exothermic metabolic heat
Uniform cooling jacket temperature
Non‑uniform gas sparging
Explanation - A uniform jacket temperature would help minimize gradients; the other factors create non‑uniformities.
Correct answer is: Uniform cooling jacket temperature
Q.106 In the design of a membrane bioreactor, the term "trans‑membrane pressure" (TMP) is defined as:
Pressure difference between feed and permeate sides
Pressure drop across the reactor
Absolute pressure inside the reactor
Hydrostatic pressure due to liquid head
Explanation - TMP drives filtration; it is the net pressure forcing fluid through the membrane.
Correct answer is: Pressure difference between feed and permeate sides
Q.107 Which dimensionless group is used to assess the relative importance of chemical reaction rate to mass transfer rate inside a catalyst pellet?
Thiele modulus (Φ)
Reynolds number (Re)
Froude number (Fr)
Biot number (Bi)
Explanation - Φ compares reaction rate to internal diffusion; high Φ indicates diffusion limitation.
Correct answer is: Thiele modulus (Φ)
Q.108 The term "specific heat capacity" (c_p) of the reactor contents determines:
How much temperature rises for a given heat input
Viscosity of the broth
Solubility of gases
pH stability
Explanation - c_p relates added heat to temperature change (ΔT = Q/(m c_p)).
Correct answer is: How much temperature rises for a given heat input
Q.109 In a stirred‑tank bioreactor, the term "shear rate" (γ̇) is proportional to:
Impeller speed (N)
Reynolds number (Re)
Péclet number (Pe)
Biot number (Bi)
Explanation - Shear rate scales with impeller tip speed, which is proportional to N × D.
Correct answer is: Impeller speed (N)
Q.110 Which of the following statements about the Damköhler number (Da) is correct for a catalytic packed‑bed reactor?
Da > 1 indicates reaction limited regime
Da < 1 indicates diffusion limited regime
Da = 1 indicates perfect balance between reaction and diffusion
Da is independent of pellet size
Explanation - When Da ≈ 1, reaction and transport rates are comparable; Da > 1 implies reaction dominates, Da < 1 implies transport dominates.
Correct answer is: Da = 1 indicates perfect balance between reaction and diffusion
Q.111 In a bioprocess, the term "heat of solution" refers to:
Heat released or absorbed when a solute dissolves in a solvent
Heat generated by microbial metabolism
Heat required for phase change
Heat lost due to convection
Explanation - Heat of solution (enthalpy of solution) is the enthalpy change upon dissolution.
Correct answer is: Heat released or absorbed when a solute dissolves in a solvent
Q.112 The term "mass transfer resistance" in a porous catalyst pellet is inversely proportional to:
Effective diffusivity (D_eff)
Particle radius (R)
Porosity (ε)
Tortuosity (τ)
Explanation - Higher D_eff reduces resistance; resistance ∝ 1/D_eff for diffusion‑controlled transport.
Correct answer is: Effective diffusivity (D_eff)
Q.113 Which dimensionless number is most appropriate to evaluate the ratio of convective to diffusive transport of heat in a flowing fluid?
Péclet number (Pe)
Reynolds number (Re)
Schmidt number (Sc)
Froude number (Fr)
Explanation - Pe = u L/α compares convection to thermal diffusion.
Correct answer is: Péclet number (Pe)
Q.114 When the interfacial area (a) in a bioreactor is increased, the volumetric mass transfer coefficient (k_La) will:
Decrease
Increase
Remain unchanged
Become zero
Explanation - k_La = k_L · a; larger a raises the overall coefficient, enhancing mass transfer.
Correct answer is: Increase
Q.115 In transport phenomena, the term "boundary layer thickness" (δ) is defined as:
Distance over which velocity changes from zero at the wall to free‑stream value
Thickness of the reactor wall
Diameter of the impeller
Length of the reactor
Explanation - δ characterizes the region near a solid surface where gradients (velocity, concentration, temperature) are significant.
Correct answer is: Distance over which velocity changes from zero at the wall to free‑stream value
Q.116 The dimensionless group that relates the rate of heat generation to the rate of heat removal in a reactor is:
Damköhler number (Da)
Biot number (Bi)
Péclet number (Pe)
Thiele modulus (Φ)
Explanation - Bi compares internal conductive resistance to external convective resistance, indicating heat removal capability.
Correct answer is: Biot number (Bi)
Q.117 In a gas‑liquid membrane system, which term is most likely to limit overall mass transfer for a highly soluble gas?
Gas‑side film resistance
Liquid‑side film resistance
Membrane pore resistance
Diffusion in the bulk liquid
Explanation - For a highly soluble gas, the liquid film resistance dominates because the gas film resistance is minimal.
Correct answer is: Liquid‑side film resistance
Q.118 The term "heat of dilution" is important when:
Mixing a concentrated acid with water
Performing a fermentation
Operating a membrane filter
Measuring pH
Explanation - Heat of dilution is the enthalpy change when a solute (often an acid/base) is diluted, affecting temperature control.
Correct answer is: Mixing a concentrated acid with water
Q.119 In a continuous bioprocess, the term "steady‑state" implies that:
All variables change linearly with time
Concentrations, temperature, and flow rates are constant with time
The reactor is not operating
Only temperature is constant
Explanation - Steady‑state means the system variables are time‑invariant, despite continuous flow.
Correct answer is: Concentrations, temperature, and flow rates are constant with time
Q.120 Which of the following correlations is commonly used to estimate the pressure drop in a packed‑bed reactor?
Ergun equation
Arrhenius equation
Stokes law
Nernst equation
Explanation - Ergun equation combines viscous and inertial contributions to predict pressure drop in packed beds.
Correct answer is: Ergun equation