Interphase Mass Transfer and Two-Film Theory

Scope: Equilibrium; film theory; overall coefficients; driving forces. Four lessons connect microscopic transport or process operating principles to practical calculations. Relevant laboratory models: 7, 8.

Central engineering ideas

Equilibrium does not imply absence of mass transfer everywhere in a contactor; it specifies the relation between concentrations immediately on the two sides of an interface. Gas and liquid bulk values can remain far from equilibrium. Two-film analysis imagines a resistance on each side, although the physical interface may be more dynamic and the film thickness is an effective rather than literal quantity.

When an overall coefficient is reported, write its driving-force basis alongside its units. A gas-film coefficient based on gas mole fraction cannot be numerically inserted as a coefficient based on partial pressure. The slope of the phase equilibrium line converts resistance between bases. For reactive absorption, a liquid-side enhancement factor is sometimes needed; this is not justified by data from physical absorption alone.

Four-lesson reading path

Lesson 1: Partition equilibria and driving-force conventions

A species partitions according to phase-equilibrium relations; using incompatible gas and liquid concentration bases produces meaningless overall coefficients. The working equation y_A^*=m x_A makes a limited, testable claim about the dependence of transfer on specified properties. A gas absorber operates near equilibrium at the rich-liquid end, leaving little transfer driving force. The validity check is especially important here: Use the local interfacial equilibrium, not the global bulk compositions. Before moving on, state in words what a higher driving force means physically, whether the response is proportional to area, and which temperature or composition must be used to obtain properties.

[Read Lesson 1](../lessons/unit-03-lesson-01.html).

Lesson 2: Two-film theory and interfacial states

In series-film descriptions, the same molar transfer rate crosses both films at steady state, while concentration drops depend on resistance. The working equation 1/K_G=1/k_G + m/k_L makes a limited, testable claim about the dependence of transfer on specified properties. A solvent with low liquid-side mixing gives poor absorption despite an effective gas-side contactor. The validity check is especially important here: Interfacial chemical reaction can fundamentally change the liquid-film model. Before moving on, state in words what a higher driving force means physically, whether the response is proportional to area, and which temperature or composition must be used to obtain properties.

[Read Lesson 2](../lessons/unit-03-lesson-02.html).

Lesson 3: Overall coefficients and controlling resistance

The resistance fraction determines where process improvements are effective. Changing a small resistance yields little improvement. The working equation f_L=(m/k_L)/(1/k_G+m/k_L) makes a limited, testable claim about the dependence of transfer on specified properties. Adding gas agitation to a system controlled by liquid film resistance makes limited difference. The validity check is especially important here: Coefficients reported for partial pressure and mole fraction cannot be interchanged without conversion. Before moving on, state in words what a higher driving force means physically, whether the response is proportional to area, and which temperature or composition must be used to obtain properties.

[Read Lesson 3](../lessons/unit-03-lesson-03.html).

Lesson 4: Interfacial area and contact equipment

Interfacial area varies with droplet, bubble, wetting and packing behavior; an observed volumetric coefficient conflates local transfer and available area. The working equation r_A=K_G a (y-y^*) makes a limited, testable claim about the dependence of transfer on specified properties. A packed bed flooding event increases liquid holdup but may reduce effective wetting and stable performance. The validity check is especially important here: Do not interpret laboratory kLa as pure diffusivity. Before moving on, state in words what a higher driving force means physically, whether the response is proportional to area, and which temperature or composition must be used to obtain properties.

[Read Lesson 4](../lessons/unit-03-lesson-04.html).

Analysis, synthesis and laboratory practice

First create a one-page property table: list fluid phase, bulk composition, surface or interface state, temperature, pressure, and the reference from which viscosity or diffusivity was obtained. Next sketch the principal control volume and write a component balance even when a transfer correlation is already known. Conservation closure should be computed using independent inventory data, not simply by substituting the computed flux back into the same equation.

Then use the simulation models to build a two-dimensional experiment: perform one sweep in the primary adjustable parameter and repeat at two distinct fixed values of a secondary parameter. Compare the resulting curves and explain whether the ranking changes. When model rankings do change, identify the competing effects. Where the equation predicts no change with a parameter that matters experimentally, the discrepancy is useful evidence of a missing mechanism rather than a reason to manipulate the fit.

For technical reporting, preserve the input CSV, baseline calculation, units and full list of assumptions. Include a short paragraph that distinguishes model sensitivity from actual process uncertainty, and identify one input that should be measured more precisely before design decisions. Link the interpretation to a measurable concentration, flow, pressure or inventory instead of treating the plotted output as a stand-alone achievement.

Suggested learning evidence: a control-volume sketch, two parameter sweeps, a worked balance, one falsification experiment and a paragraph about uncertainty.

Unit 3, Lesson 1: Partition equilibria and driving-force conventions

Unit: Interphase transfer. Core model: y_A^*=m x_A. Interactive laboratory: [Laboratory 07](../labs/lab-07.html).

What the phenomenon means

A species partitions according to phase-equilibrium relations; using incompatible gas and liquid concentration bases produces meaningless overall coefficients. The governing relationship is y_A^*=m x_A. In the calculation, every coefficient and concentration must be tied to a specific thermodynamic or hydraulic state. When a textbook draws a flux arrow, that arrow represents a signed rate through a stated area; it does not by itself prove that the assumed regime exists. The objective of the lesson is to connect the measurable laboratory signal to the correct transfer mechanism and to identify when one mechanism is no longer dominant.

Equilibrium does not imply absence of mass transfer everywhere in a contactor; it specifies the relation between concentrations immediately on the two sides of an interface. Gas and liquid bulk values can remain far from equilibrium. Two-film analysis imagines a resistance on each side, although the physical interface may be more dynamic and the film thickness is an effective rather than literal quantity.

A process example and a defensible workflow

A gas absorber operates near equilibrium at the rich-liquid end, leaving little transfer driving force. Start with a physical sketch showing control volumes, phase boundaries, sensor positions and the relevant flow rates. Identify the driving potential, compute a result on a consistent mole, mass, time and area basis, and translate the result into a quantity that a laboratory could measure. Confirm conservation independently. A predicted high flux is not automatically useful: it may require an unacceptable pressure, cause overheating, or imply an unrealistic solvent inventory. The preferred answer balances transfer rate with credible operating limits.

To check the engineering consequence, compute the predicted response at the nominal case, then repeat after increasing the principal resistance by 25%. For a truly inverse dependence on resistance, the answer should fall to 80% of its original value. If your result rises instead, revisit the boundary definitions and the sign convention. This is a sensitivity test, not a substitute for experimental validation.

Interpretation and validity

When an overall coefficient is reported, write its driving-force basis alongside its units. A gas-film coefficient based on gas mole fraction cannot be numerically inserted as a coefficient based on partial pressure. The slope of the phase equilibrium line converts resistance between bases. For reactive absorption, a liquid-side enhancement factor is sometimes needed; this is not justified by data from physical absorption alone.

Model assumptions should be tested against data rather than copied uncritically from a standard derivation. Vary one independent parameter at a time when possible; then vary a second parameter to reveal interaction. Report whether a discrepancy has the sign expected for fouling, film resistance, transient storage or a changed equilibrium. Use a simple residual plot instead of relying exclusively on R².

Failure mode to recognize: Use the local interfacial equilibrium, not the global bulk compositions. Document at least one observation that would falsify the current model. If a theoretical response is monotonic, ask what physical effect could make an observed curve flatten or reverse. The simulation provides a controlled numerical experiment; only measured property data and an appropriate scale-up study can establish real equipment performance.

Guided investigation

• Write each symbol and its SI units for y_A^*=m x_A. Distinguish a total rate from a flux and any concentration ratio from a dimensional concentration.
• Run the linked laboratory at its baseline settings and export the parameter-response curve. Identify a portion where the physical response is strongest.
• Predict the effect of raising the principal independent parameter by 10%, then compare the simulated value with your prediction. Explain any nonlinear response using the original equation.
• Identify a measurement that would estimate the most uncertain coefficient. Describe sensor position, replicate count and whether a control experiment is needed.

Questions for self-check

1. Which assumption permits the governing equation to be used here, and what real observation might contradict it?
2. If the primary driving-force measurement has a +5% systematic bias, what direction of bias would appear in the inferred coefficient?
3. Which is more useful for scaling this model: matching the total mass-transfer rate or matching the dimensionless groups, and why?

Unit 3, Lesson 2: Two-film theory and interfacial states

Unit: Interphase transfer. Core model: 1/K_G=1/k_G + m/k_L. Interactive laboratory: [Laboratory 07](../labs/lab-07.html).

What the phenomenon means

In series-film descriptions, the same molar transfer rate crosses both films at steady state, while concentration drops depend on resistance. The governing relationship is 1/K_G=1/k_G + m/k_L. In the calculation, every coefficient and concentration must be tied to a specific thermodynamic or hydraulic state. When a textbook draws a flux arrow, that arrow represents a signed rate through a stated area; it does not by itself prove that the assumed regime exists. The objective of the lesson is to connect the measurable laboratory signal to the correct transfer mechanism and to identify when one mechanism is no longer dominant.

Equilibrium does not imply absence of mass transfer everywhere in a contactor; it specifies the relation between concentrations immediately on the two sides of an interface. Gas and liquid bulk values can remain far from equilibrium. Two-film analysis imagines a resistance on each side, although the physical interface may be more dynamic and the film thickness is an effective rather than literal quantity.

A process example and a defensible workflow

A solvent with low liquid-side mixing gives poor absorption despite an effective gas-side contactor. Start with a physical sketch showing control volumes, phase boundaries, sensor positions and the relevant flow rates. Identify the driving potential, compute a result on a consistent mole, mass, time and area basis, and translate the result into a quantity that a laboratory could measure. Confirm conservation independently. A predicted high flux is not automatically useful: it may require an unacceptable pressure, cause overheating, or imply an unrealistic solvent inventory. The preferred answer balances transfer rate with credible operating limits.

An experiment should separately record an initial value, a late value and at least one intermediate point. Compare the rate inferred from each interval. Under a steady, linear, constant-property model the slopes should be similar after excluding instrument transients; a systematic change suggests the claimed steady regime was not reached or the physical properties are changing.

Interpretation and validity

When an overall coefficient is reported, write its driving-force basis alongside its units. A gas-film coefficient based on gas mole fraction cannot be numerically inserted as a coefficient based on partial pressure. The slope of the phase equilibrium line converts resistance between bases. For reactive absorption, a liquid-side enhancement factor is sometimes needed; this is not justified by data from physical absorption alone.

A reliable material balance begins by choosing a control surface and defining what passes through it. If the measured concentration belongs to the bulk while the governing law requires the interfacial value, the missing boundary condition must be solved or independently measured. Draw the transfer path before deciding which concentration difference is available. This small discipline prevents fitting a physically impossible flux to a convenient linear graph.

Failure mode to recognize: Interfacial chemical reaction can fundamentally change the liquid-film model. Document at least one observation that would falsify the current model. If a theoretical response is monotonic, ask what physical effect could make an observed curve flatten or reverse. The simulation provides a controlled numerical experiment; only measured property data and an appropriate scale-up study can establish real equipment performance.

Guided investigation

• Write each symbol and its SI units for 1/K_G=1/k_G + m/k_L. Distinguish a total rate from a flux and any concentration ratio from a dimensional concentration.
• Run the linked laboratory at its baseline settings and export the parameter-response curve. Identify a portion where the physical response is strongest.
• Predict the effect of raising the principal independent parameter by 10%, then compare the simulated value with your prediction. Explain any nonlinear response using the original equation.
• Identify a measurement that would estimate the most uncertain coefficient. Describe sensor position, replicate count and whether a control experiment is needed.

Questions for self-check

1. Which assumption permits the governing equation to be used here, and what real observation might contradict it?
2. If the primary driving-force measurement has a +5% systematic bias, what direction of bias would appear in the inferred coefficient?
3. Which is more useful for scaling this model: matching the total mass-transfer rate or matching the dimensionless groups, and why?

Unit 3, Lesson 3: Overall coefficients and controlling resistance

Unit: Interphase transfer. Core model: f_L=(m/k_L)/(1/k_G+m/k_L). Interactive laboratory: [Laboratory 07](../labs/lab-07.html).

What the phenomenon means

The resistance fraction determines where process improvements are effective. Changing a small resistance yields little improvement. The governing relationship is f_L=(m/k_L)/(1/k_G+m/k_L). In the calculation, every coefficient and concentration must be tied to a specific thermodynamic or hydraulic state. When a textbook draws a flux arrow, that arrow represents a signed rate through a stated area; it does not by itself prove that the assumed regime exists. The objective of the lesson is to connect the measurable laboratory signal to the correct transfer mechanism and to identify when one mechanism is no longer dominant.

Equilibrium does not imply absence of mass transfer everywhere in a contactor; it specifies the relation between concentrations immediately on the two sides of an interface. Gas and liquid bulk values can remain far from equilibrium. Two-film analysis imagines a resistance on each side, although the physical interface may be more dynamic and the film thickness is an effective rather than literal quantity.

A process example and a defensible workflow

Adding gas agitation to a system controlled by liquid film resistance makes limited difference. Start with a physical sketch showing control volumes, phase boundaries, sensor positions and the relevant flow rates. Identify the driving potential, compute a result on a consistent mole, mass, time and area basis, and translate the result into a quantity that a laboratory could measure. Confirm conservation independently. A predicted high flux is not automatically useful: it may require an unacceptable pressure, cause overheating, or imply an unrealistic solvent inventory. The preferred answer balances transfer rate with credible operating limits.

Before a design estimate becomes a purchasing specification, attach a measurement plan: the temperature and composition range, the reference for transport properties, the proposed independent validation case and an acceptable error tolerance. If the coefficient comes from a chart, record the relevant fluid regime, dimensionless groups and length definition so that another engineer can reproduce it.

Interpretation and validity

When an overall coefficient is reported, write its driving-force basis alongside its units. A gas-film coefficient based on gas mole fraction cannot be numerically inserted as a coefficient based on partial pressure. The slope of the phase equilibrium line converts resistance between bases. For reactive absorption, a liquid-side enhancement factor is sometimes needed; this is not justified by data from physical absorption alone.

Practical measurements have time constants. A concentration electrode or humidity sensor may respond more slowly than the process, causing a fitted diffusion time or mass-transfer coefficient to absorb instrument delay. Record probe location and sampling interval, and compare apparent rates in the first, middle and final periods of the experiment. If the response changes with stirring intensity, external transfer may be important.

Failure mode to recognize: Coefficients reported for partial pressure and mole fraction cannot be interchanged without conversion. Document at least one observation that would falsify the current model. If a theoretical response is monotonic, ask what physical effect could make an observed curve flatten or reverse. The simulation provides a controlled numerical experiment; only measured property data and an appropriate scale-up study can establish real equipment performance.

Guided investigation

• Write each symbol and its SI units for f_L=(m/k_L)/(1/k_G+m/k_L). Distinguish a total rate from a flux and any concentration ratio from a dimensional concentration.
• Run the linked laboratory at its baseline settings and export the parameter-response curve. Identify a portion where the physical response is strongest.
• Predict the effect of raising the principal independent parameter by 10%, then compare the simulated value with your prediction. Explain any nonlinear response using the original equation.
• Identify a measurement that would estimate the most uncertain coefficient. Describe sensor position, replicate count and whether a control experiment is needed.

Questions for self-check

1. Which assumption permits the governing equation to be used here, and what real observation might contradict it?
2. If the primary driving-force measurement has a +5% systematic bias, what direction of bias would appear in the inferred coefficient?
3. Which is more useful for scaling this model: matching the total mass-transfer rate or matching the dimensionless groups, and why?

Unit 3, Lesson 4: Interfacial area and contact equipment

Unit: Interphase transfer. Core model: r_A=K_G a (y-y^*). Interactive laboratory: [Laboratory 07](../labs/lab-07.html).

What the phenomenon means

Interfacial area varies with droplet, bubble, wetting and packing behavior; an observed volumetric coefficient conflates local transfer and available area. The governing relationship is r_A=K_G a (y-y^*). In the calculation, every coefficient and concentration must be tied to a specific thermodynamic or hydraulic state. When a textbook draws a flux arrow, that arrow represents a signed rate through a stated area; it does not by itself prove that the assumed regime exists. The objective of the lesson is to connect the measurable laboratory signal to the correct transfer mechanism and to identify when one mechanism is no longer dominant.

Equilibrium does not imply absence of mass transfer everywhere in a contactor; it specifies the relation between concentrations immediately on the two sides of an interface. Gas and liquid bulk values can remain far from equilibrium. Two-film analysis imagines a resistance on each side, although the physical interface may be more dynamic and the film thickness is an effective rather than literal quantity.

A process example and a defensible workflow

A packed bed flooding event increases liquid holdup but may reduce effective wetting and stable performance. Start with a physical sketch showing control volumes, phase boundaries, sensor positions and the relevant flow rates. Identify the driving potential, compute a result on a consistent mole, mass, time and area basis, and translate the result into a quantity that a laboratory could measure. Confirm conservation independently. A predicted high flux is not automatically useful: it may require an unacceptable pressure, cause overheating, or imply an unrealistic solvent inventory. The preferred answer balances transfer rate with credible operating limits.

Make a small mass-balance closure table with inflow, outflow, transfer rate and accumulation. Flux integrated over area must agree with the change in inventory after any time integration. When a calculation satisfies a local transfer law but violates total inventory, the likely issue is a basis conversion, interface area or hidden phase holdup.

Interpretation and validity

When an overall coefficient is reported, write its driving-force basis alongside its units. A gas-film coefficient based on gas mole fraction cannot be numerically inserted as a coefficient based on partial pressure. The slope of the phase equilibrium line converts resistance between bases. For reactive absorption, a liquid-side enhancement factor is sometimes needed; this is not justified by data from physical absorption alone.

A dimensionally plausible equation can still be wrong for the equipment. Confirm the area to which the flux refers, the concentration basis (mass, molar, dry or wet), and whether the flow is per total area or open pore area. In scaled equipment, area-to-volume ratio varies with size, so equal concentration gradients do not automatically imply equal total processing time.

Failure mode to recognize: Do not interpret laboratory kLa as pure diffusivity. Document at least one observation that would falsify the current model. If a theoretical response is monotonic, ask what physical effect could make an observed curve flatten or reverse. The simulation provides a controlled numerical experiment; only measured property data and an appropriate scale-up study can establish real equipment performance.

Guided investigation

• Write each symbol and its SI units for r_A=K_G a (y-y^*). Distinguish a total rate from a flux and any concentration ratio from a dimensional concentration.
• Run the linked laboratory at its baseline settings and export the parameter-response curve. Identify a portion where the physical response is strongest.
• Predict the effect of raising the principal independent parameter by 10%, then compare the simulated value with your prediction. Explain any nonlinear response using the original equation.
• Identify a measurement that would estimate the most uncertain coefficient. Describe sensor position, replicate count and whether a control experiment is needed.

Questions for self-check

1. Which assumption permits the governing equation to be used here, and what real observation might contradict it?
2. If the primary driving-force measurement has a +5% systematic bias, what direction of bias would appear in the inferred coefficient?
3. Which is more useful for scaling this model: matching the total mass-transfer rate or matching the dimensionless groups, and why?

Applied project — Unit 3: Interphase transfer

Engineering decision

Equilibrium does not imply absence of mass transfer everywhere in a contactor; it specifies the relation between concentrations immediately on the two sides of an interface. Gas and liquid bulk values can remain far from equilibrium. Two-film analysis imagines a resistance on each side, although the physical interface may be more dynamic and the film thickness is an effective rather than literal quantity.

Project brief: Design a small experimental method to compare two candidate operating conditions related to partition equilibria and driving-force conventions; two-film theory and interfacial states; overall coefficients and controlling resistance; interfacial area and contact equipment. The purpose is not to produce a procurement specification, but to identify which input most affects mass transfer and whether an economical operating change could plausibly meet the desired duty.

Data and deliverables

• Draw a process flow schematic showing flow paths, relevant interfacial area and material inventory.
• Specify the two parameter sets using the bounds in the interactive laboratories; preserve the original and modified CSV files.
• Derive the governing model and predict relative response without touching the controls. Then compare with calculated responses.
• Determine the physical property that would contribute most to uncertainty. Plan at least three replicate measurements at two operating points.
• Document material compatibility, potential exposure or emissions, hydraulic constraints and credible failure mechanisms.
• Write a one-page decision statement recommending either a pilot trial, a revised analytical model, or rejection of the proposed change.

Independent validation

When an overall coefficient is reported, write its driving-force basis alongside its units. A gas-film coefficient based on gas mole fraction cannot be numerically inserted as a coefficient based on partial pressure. The slope of the phase equilibrium line converts resistance between bases. For reactive absorption, a liquid-side enhancement factor is sometimes needed; this is not justified by data from physical absorption alone.

A strong answer explicitly separates a screening assumption from a measured process characteristic. If two mechanisms can lead to the same observed transfer rate, propose a controlled test that discriminates between them. Scale-up should retain the causal mechanism, not just the appearance of a laboratory curve.

Evaluation: method and assumptions 25%; balance closure and units 20%; experiment design 20%; quantitative interpretation 20%; candid limitations and safety 15%.

Laboratory 05: Laminar flat-plate Sherwood number

Relevant unit: Convective transfer. Governing relationship: Sh_L = 0.664 Re_L^0.5 Sc^(1/3).

Physical question

What happens to the predicted laminar flat-plate sherwood number when its principal adjustable parameter changes, and how does that sensitivity relate to the mechanism described in this unit? The baseline parameter values are synthetic teaching inputs, not measurements from a named plant. This experiment is designed to expose a mathematical trend and make its units visible before real property data are substituted.

Experimental setup and protocol

Average laminar flat-plate correlation; illustrative Re < 5×10⁵. List the assumptions on paper before changing inputs. Treat the first control as the independent variable; keep the remaining parameters fixed for the first sweep. Read the numerical output at the minimum, baseline and maximum setting, then export the 121-point curve. Repeat at a second value of the parameter most strongly coupled to the driving force. Use the on-screen schematic to identify the direction of transport and the conceptual location of the limiting resistance. It is not a scale drawing.

Parameters

• Air speed: default 1.2 m/s, adjustable range 0.1–8 m/s. Check the measurement source and correlation domain before substitution.
• Plate length: default 0.3 m, adjustable range 0.05–1.5 m. Check the measurement source and correlation domain before substitution.
• Kinematic viscosity: default 1.5e-05 m²/s, adjustable range 8e-06–3e-05 m²/s. Check the measurement source and correlation domain before substitution.
• Species diffusivity: default 1.4e-05 m²/s, adjustable range 5e-06–3e-05 m²/s. Check the measurement source and correlation domain before substitution.

Interpretation and model boundaries

Convective transfer coefficients connect a driving concentration difference to a net flux through a near-wall region. Their numerical value depends on length scale and boundary conditions; a coefficient measured around a sphere cannot be carried unchanged to a plate or pipe. The Schmidt number compares momentum and molecular species diffusivity, so using the same liquid viscosity at all temperatures can misstate transfer trends.

The response curve is a local sensitivity plot in which other controls remain fixed. It does not automatically represent a physical trajectory through a reactor or a separation column. A reported ''outside model validity'' result indicates a mathematical or physical constraint such as an inverted concentration difference, invalid pinch, an incompatible moisture ordering, or a correlation beyond its specified regime. The laboratory deliberately leaves these cases visible so they can be diagnosed instead of silently clipped.

Investigation questions

1. Calculate the baseline result independently using Sh_L = 0.664 Re_L^0.5 Sc^(1/3). Convert all parameter units first. What is the largest source of numerical uncertainty?
2. Explain the curvature or straightness of the sweep. Does doubling the first parameter double, halve, or otherwise change the response?
3. Which plausible operating effect is excluded by the model: property variation, pressure drop, fouling, chemical reaction, unsteady accumulation, or imperfect contact? Describe a test for that effect.
4. If a customer specification required the output to improve by 15%, identify two possible changes and discuss an operational cost or safety implication of each.

Use restriction: Educational sensitivity model; it is not a substitute for verified correlations, material data, equipment design standards or engineering sign-off.

Laboratory 06: Turbulent pipe coefficient

Relevant unit: Convective transfer. Governing relationship: Sh = 0.023 Re^0.83 Sc^(1/3); k=Sh D/d.

Physical question

What happens to the predicted turbulent pipe coefficient when its principal adjustable parameter changes, and how does that sensitivity relate to the mechanism described in this unit? The baseline parameter values are synthetic teaching inputs, not measurements from a named plant. This experiment is designed to expose a mathematical trend and make its units visible before real property data are substituted.

Experimental setup and protocol

Screening correlation for fully developed turbulent flow (Re > 10,000). List the assumptions on paper before changing inputs. Treat the first control as the independent variable; keep the remaining parameters fixed for the first sweep. Read the numerical output at the minimum, baseline and maximum setting, then export the 121-point curve. Repeat at a second value of the parameter most strongly coupled to the driving force. Use the on-screen schematic to identify the direction of transport and the conceptual location of the limiting resistance. It is not a scale drawing.

Parameters

• Mean speed: default 1.5 m/s, adjustable range 0.2–5 m/s. Check the measurement source and correlation domain before substitution.
• Pipe diameter: default 0.04 m, adjustable range 0.01–0.15 m. Check the measurement source and correlation domain before substitution.
• Kinematic viscosity: default 1e-06 m²/s, adjustable range 7e-07–2e-06 m²/s. Check the measurement source and correlation domain before substitution.
• Diffusivity: default 1e-09 m²/s, adjustable range 5e-10–5e-09 m²/s. Check the measurement source and correlation domain before substitution.

Interpretation and model boundaries

Convective transfer coefficients connect a driving concentration difference to a net flux through a near-wall region. Their numerical value depends on length scale and boundary conditions; a coefficient measured around a sphere cannot be carried unchanged to a plate or pipe. The Schmidt number compares momentum and molecular species diffusivity, so using the same liquid viscosity at all temperatures can misstate transfer trends.

The response curve is a local sensitivity plot in which other controls remain fixed. It does not automatically represent a physical trajectory through a reactor or a separation column. A reported ''outside model validity'' result indicates a mathematical or physical constraint such as an inverted concentration difference, invalid pinch, an incompatible moisture ordering, or a correlation beyond its specified regime. The laboratory deliberately leaves these cases visible so they can be diagnosed instead of silently clipped.

Investigation questions

1. Calculate the baseline result independently using Sh = 0.023 Re^0.83 Sc^(1/3); k=Sh D/d. Convert all parameter units first. What is the largest source of numerical uncertainty?
2. Explain the curvature or straightness of the sweep. Does doubling the first parameter double, halve, or otherwise change the response?
3. Which plausible operating effect is excluded by the model: property variation, pressure drop, fouling, chemical reaction, unsteady accumulation, or imperfect contact? Describe a test for that effect.
4. If a customer specification required the output to improve by 15%, identify two possible changes and discuss an operational cost or safety implication of each.

Use restriction: Educational sensitivity model; it is not a substitute for verified correlations, material data, equipment design standards or engineering sign-off.

Unit 3 assessment — Interphase transfer

The assessment distinguishes memorization, calculation, interpretation and model criticism. Use SI conversions explicitly, give dimensional units for computed transfer rates and justify equilibrium assumptions.

Problem 1: Partition equilibria and driving-force conventions

A gas absorber operates near equilibrium at the rich-liquid end, leaving little transfer driving force. Write a component balance and model the transfer using y_A^*=m x_A. Repeat the result after a 20% change in the dominant physical coefficient, if the chosen model is linear in that coefficient. Explain what physically changes when the input varies, specify one observation that would invalidate the equation, and identify the minimum additional measurement required to calculate an engineering uncertainty interval.

Instructor guidance: A complete response identifies units and basis, draws the interfacial or control-volume boundary, makes the rate/flux distinction, and explains why a favorable model result may still be infeasible. The reported model limitation should include: Use the local interfacial equilibrium, not the global bulk compositions.

Problem 2: Two-film theory and interfacial states

A solvent with low liquid-side mixing gives poor absorption despite an effective gas-side contactor. Write a component balance and model the transfer using 1/K_G=1/k_G + m/k_L. Repeat the result after a 20% change in the dominant physical coefficient, if the chosen model is linear in that coefficient. Explain what physically changes when the input varies, specify one observation that would invalidate the equation, and identify the minimum additional measurement required to calculate an engineering uncertainty interval.

Instructor guidance: A complete response identifies units and basis, draws the interfacial or control-volume boundary, makes the rate/flux distinction, and explains why a favorable model result may still be infeasible. The reported model limitation should include: Interfacial chemical reaction can fundamentally change the liquid-film model.

Problem 3: Overall coefficients and controlling resistance

Adding gas agitation to a system controlled by liquid film resistance makes limited difference. Write a component balance and model the transfer using f_L=(m/k_L)/(1/k_G+m/k_L). Repeat the result after a 20% change in the dominant physical coefficient, if the chosen model is linear in that coefficient. Explain what physically changes when the input varies, specify one observation that would invalidate the equation, and identify the minimum additional measurement required to calculate an engineering uncertainty interval.

Instructor guidance: A complete response identifies units and basis, draws the interfacial or control-volume boundary, makes the rate/flux distinction, and explains why a favorable model result may still be infeasible. The reported model limitation should include: Coefficients reported for partial pressure and mole fraction cannot be interchanged without conversion.

Problem 4: Interfacial area and contact equipment

A packed bed flooding event increases liquid holdup but may reduce effective wetting and stable performance. Write a component balance and model the transfer using r_A=K_G a (y-y^*). Repeat the result after a 20% change in the dominant physical coefficient, if the chosen model is linear in that coefficient. Explain what physically changes when the input varies, specify one observation that would invalidate the equation, and identify the minimum additional measurement required to calculate an engineering uncertainty interval.

Instructor guidance: A complete response identifies units and basis, draws the interfacial or control-volume boundary, makes the rate/flux distinction, and explains why a favorable model result may still be infeasible. The reported model limitation should include: Do not interpret laboratory kLa as pure diffusivity.

Problem 5: Laboratory analysis

Select Laboratory 07 from the unit and export a sensitivity CSV. Report the largest and smallest finite result, calculate a percentage sensitivity at the baseline using two nearby points, and explain whether you expect the same sensitivity when the temperature or composition changes. Give at least two plausible sources of nonrepeatability in a physical test.

Rubric (100 points): physical model and assumptions 25; calculations and dimensional checks 25; clear diagrams and evidence 15; data interpretation 20; limitations and safety 15. Numbers produced by the simulation are not independent evidence that its selected correlation applies to a real installation.