Mass transfer Study Guide

📖 Core Concepts Mass Transfer – net movement of mass from one location (stream, phase, component) to another. Driving Force – usually a chemical potential gradient; species flow from high to low chemical potential. Transport Mechanisms – Diffusive: molecular motion down concentration/chemical‑potential gradients. Convective: bulk fluid motion carrying species. Uniform Chemical Potential – in a single phase this means uniform concentration; in a multiphase system it means the species is mostly in its preferred phase. Typical Operations – distillation, absorption, stripping, liquid‑liquid extraction, adsorption, membrane filtration. Analogy – Momentum (Newton), heat (Fourier), and mass (Fick) transfer share linear forms at low Reynolds numbers. --- 📌 Must Remember Mass‑transfer coefficient (k) quantifies the rate: \( \text{rate} = k \, A \, \Delta C \). Key dimensionless numbers (used in correlations): Reynolds (Re) – inertia vs. viscous forces. Peclet (Pe) – convection vs. diffusion (\(Pe = Re \, Sc\)). Schmidt (Sc) – momentum diffusivity vs. mass diffusivity (\(Sc = \nu/D\)). Sherwood (Sh) – convective mass transfer vs. pure diffusion (\(Sh = k L / D\)). Maximum theoretical extent occurs when chemical potential is uniform throughout the system. Low‑Re analogy: \(J = -D \nabla C\) (mass) ↔ \(q = -kt \nabla T\) (heat) ↔ \(\tau = -\mu \nabla u\) (momentum). --- 🔄 Key Processes Distillation (vapour‑liquid) Vapor rises → mass transfer of volatile component to vapour phase. Condenser returns non‑volatile components. Absorption (gas‑liquid) Gas contacts liquid → soluble species transfer into liquid. Driving force: \( \Delta \mu = \mu{gas} - \mu{liquid} \). Stripping (liquid‑gas) Liquid fed with volatile component → component stripped into gas stream. Liquid‑Liquid Extraction Two immiscible liquids contacted; solute partitions based on preference (distribution coefficient). Adsorption (solid‑fluid) Contaminant molecules adhere to solid surface (e.g., activated carbon). --- 🔍 Key Comparisons Diffusion vs. Convection Diffusion: driven solely by concentration/chemical‑potential gradients; slow, dominant at low Re. Convection: bulk flow adds transport; dominates at high Re. Distillation vs. Stripping Distillation: removes low‑volatility components from vapour; product is liquid. Stripping: removes high‑volatility components from liquid; product is gas. Low‑Re Analogy vs. High‑Re Reality Low Re: linear governing equations → direct analogy among momentum, heat, mass. High Re: Navier–Stokes non‑linearity breaks analogy; correlations become empirical. --- ⚠️ Common Misunderstandings “Mass transfer always needs a membrane.” – Wrong; diffusion and convection occur without membranes (e.g., absorption). “Higher Reynolds always means faster mass transfer.” – Not always; turbulence enhances mixing, but mass‑transfer coefficient also depends on diffusivity (Sc). “Uniform concentration = no driving force.” – Only true in a single phase; in multiphase systems a species can still have a driving force if it prefers one phase. --- 🧠 Mental Models / Intuition “Chemical potential hill” – Imagine species rolling downhill from high to low chemical potential; the steeper the hill, the faster the flow. “Traffic analogy for ReSc” – Low traffic (low Re) → cars (molecules) move slowly, diffusion dominates. Heavy traffic (high Re) → cars pushed by flow, convection dominates. “Sherwood number as a “boost” factor – Sh > 1 means convection is giving a boost over pure diffusion. --- 🚩 Exceptions & Edge Cases High‑Re flow with strong temperature gradients – heat–mass coupling can invalidate simple Fick’s law; need combined heat‑mass analysis. Multiphase systems with preferential solubility – Uniform chemical potential may correspond to most of the species in the preferred phase, not complete mixing. Non‑Newtonian fluids – Standard Re‑based correlations may be inaccurate; use empirical data. --- 📍 When to Use Which Use Sherwood correlations (e.g., \(Sh = 2 + 0.6 Re^{1/2} Sc^{1/3}\)) for external flow over a sphere or tube when geometry matches the empirical basis. Apply Fick’s law for internal diffusion in stagnant or low‑Re layers. Choose absorption when the target component is more soluble in the liquid phase; choose stripping when the component is more volatile in the gas phase. Select liquid‑liquid extraction if the solute has a strong distribution coefficient between two immiscible liquids. --- 👀 Patterns to Recognize “High Sc, low Re → diffusion‑limited” – expect low Sherwood numbers, mass transfer controlled by diffusivity. “Presence of a membrane → primarily diffusive resistance” – focus on permeability and concentration gradient. “Uniform temperature but varying composition → mass‑transfer‑only problem – ignore heat‑mass coupling. “Reynolds > 10,000 → turbulence regime – use turbulent correlations (e.g., empirical Sh–Re–Sc). --- 🗂️ Exam Traps Distractor: “Mass transfer coefficient always increases with Reynolds number.” Why tempting: Higher Re → more mixing. Why wrong: Coefficient also depends on Sc; for very high Sc the increase may be modest. Distractor: “Maximum conversion occurs when concentration is uniform across phases.” Why tempting: Uniformity sounds like equilibrium. Why wrong: In multiphase systems the preferred phase may hold most of the solute; uniform concentration isn’t the target. Distractor: “Sherwood number is dimensionless concentration.” Why tempting: All dimensionless groups involve concentration. Why wrong: Sh = \(kL/D\); it compares convective to diffusive mass transfer, not a concentration value. ---