First-Principles Mathematical Derivation of Falling Film Evaporation
Falling film evaporators combine gravity-driven thin liquid film hydrodynamics with boiling free-surface heat transfer inside vertical cylindrical conduits.
1. Overall Mass & Evaporation Balances
Solids conservation dictates product flow $\dot{m}_{prod}$ and water removal $\dot{m}_{evap}$:
\dot{m}_{prod} = \dot{m}_{feed} \cdot \left( \frac{x_{in}}{x_{out}} \right)\n \dot{m}_{evap} = \dot{m}_{feed} - \dot{m}_{prod} = \dot{m}_{feed} \left(1 - \frac{x_{in}}{x_{out}}\right)
2. Wetting Rate & Chun-Seban Heat Transfer
Liquid mass flow per unit inside tube perimeter at the bottom of the tubes ($\Gamma_{bot}$) represents the critical wetting threshold:
\Gamma_{bot} = \frac{\dot{m}_{prod}}{\pi \cdot D_i \cdot N_{tubes}}\quad [kg/m\cdot s]\n Re_f = \frac{4 \cdot \Gamma}{\mu_L}
The inside boiling falling film coefficient $h_i$ follows the Chun & Seban model for wavy-laminar or turbulent films:
\text{Wavy-Laminar } (Re_f < 1600):\quad h_i = 0.822 \left( \frac{k_L^3 \rho_L^2 g}{\mu_L^2} \right)^{1/3} Re_f^{-0.22}\n \text{Turbulent } (Re_f \ge 1600):\quad h_i = 0.0038 \left( \frac{k_L^3 \rho_L^2 g}{\mu_L^2} \right)^{1/3} Re_f^{0.4} Pr_L^{0.65}
3. Overall Calandria Area & Tube Sizing
\Delta T_{eff} = T_{steam} - (T_{evap} + BPE)\n A_{total} = \frac{Q}{U \cdot \Delta T_{eff}}\implies N_{tubes} = \frac{A_{total}}{\pi \cdot D_o \cdot L}
5 Fatal Traps & Engineering Pitfalls in Falling Film Evaporator Design
1. Sub-Critical Wetting Rate Film Dry-Out & Severe Scaling
If liquid wetting rate at the tube bottom falls below $\Gamma_{min}$ ($< 0.10\,\text{kg/m}\cdot\text{s}$ for dairy or organics), surface tension tears the liquid film into narrow rivulets. The dry dry-out patches bake product instantly onto the hot tube wall, causing irreversible carbonized fouling and shutting down the plant.
2. Top Distribution Tray Ferrule Maldistribution
A mere 1 to 2 mm slope in the top liquid distributor tray starves peripheral tubes while over-flooding central tubes. Starved tubes experience immediate film rupture, while flooded tubes fail to evaporate properly, degrading overall capacity by 35%.
3. Boiling Point Elevation (BPE) Temperature Pinch
At high discharge concentrations (e.g. 50% caustic or 70° Brix sugar), Boiling Point Elevation increases boiling temperature by $5^\circ\text{C}$ to $15^\circ\text{C}$. Failing to subtract BPE from $(T_{steam} - T_{evap})$ can pinch effective $\Delta T$ to near zero, destroying evaporation capacity.
4. Co-Current Vapor Shear & Entrainment Carryover
In long tubes ($L > 10\,\text{m}$), downward co-current vapor accelerates to $> 30\,\text{m/s}$. Violent interfacial gas shear rips liquid droplets off the film and entrains them into the vapor duct, fouling vapor recompression fans (MVR) or contaminating condensate.
5. Non-Condensable Gas Blanketing in Vacuum Calandrias
Under vacuum operation, minute air leaks through flange gaskets introduce non-condensable gases into the steam shell. Air accumulates against outer tube surfaces, forming a stagnant gas blanket that drops steam condensing coefficients by up to 80% unless continuous vacuum venting is maintained.
Frequently Asked Questions: Falling Film Evaporator Design
What is a Falling Film Evaporator and why is it preferred for heat-sensitive liquids? +
A Falling Film Evaporator is a specialized vertical shell-and-tube heat exchanger in which process liquid enters the top distribution head and flows down the inside surfaces of vertical tubes as a thin, continuous falling film. Heating steam or vapor condenses on the outer tube shell. Because the liquid moves under gravity with high velocities, liquid holdup inside the tubes is minimal, yielding ultra-short residence times (typically 10 to 30 seconds). Furthermore, boiling occurs at the film free surface under vacuum without hydrostatic head boiling suppression, making it ideal for thermally sensitive foods, pharmaceuticals, dairy, fruit juices, and polymers.
What is the Minimum Wetting Rate (MWR) and why is film dry-out catastrophic? +
The Minimum Wetting Rate ($\Gamma_{min}$) is the minimum liquid mass flow rate per unit of internal tube perimeter required to maintain an unbroken, continuous liquid film over the entire tube length: $\Gamma = \frac{\dot{m}_{liquid}}{\pi D_i N_{tubes}}$ ($kg/m\cdot s$). If $\Gamma$ drops below $\Gamma_{min}$ (typically $0.08\text{--}0.15\,\text{kg/m}\cdot\text{s}$ for aqueous solutions), surface tension tears the thin film into narrow rivulets, exposing bare metal patches. On these dry-out patches, residual solids bake into an insoluble, carbonized scale, destroying heat transfer and requiring complete plant shutdown for chemical CIP acid cleaning.
How does the Chun & Seban correlation predict falling film evaporation coefficients? +
Chun & Seban (1971) established that falling film evaporation heat transfer depends on the film Reynolds number $Re_f = \frac{4 \Gamma}{\mu_L}$ and Prandtl number $Pr_L$. In the wavy-laminar regime ($30 < Re_f < 1600$), heat transfer is dominated by molecular conduction through the thinning wavy film: $h_i = 0.822 \left( \frac{k_L^3 \rho_L^2 g}{\mu_L^2} \right)^{1/3} Re_f^{-0.22}$. In the fully turbulent regime ($Re_f \ge 1600$), eddy diffusivity boosts turbulent heat transfer: $h_i = 0.0038 \left( \frac{k_L^3 \rho_L^2 g}{\mu_L^2} \right)^{1/3} Re_f^{0.4} Pr_L^{0.65}$.
What is Boiling Point Elevation (BPE) and how does it impact available delta T? +
As dissolved solute concentration increases during evaporation, the vapor pressure of the solution decreases, causing its boiling temperature to rise above that of pure water at the same vacuum pressure. This temperature rise is the Boiling Point Elevation ($BPE$). For example, 50% caustic soda (NaOH) exhibits a $BPE > 30^\circ\text{C}$. The effective temperature driving force is $\Delta T_{eff} = T_{steam} - (T_{evap} + BPE)$. Sizing without BPE leads to gross undersizing of heat transfer area.
Why is liquid distribution at the top tube sheet critical? +
Uniform liquid distribution across all calandria tubes is the single most critical mechanical factor in falling film evaporator reliability. Precision distribution devices—such as perforated spray trays with individual tube ferrules, notched distribution cups, or tangential swirl nozzles—are installed in every tube inlet. If the distribution tray is slightly out of level by even 1 to 2 mm, liquid shortcuts to one side of the vessel, starving the opposite quadrant of tubes and triggering immediate film breakdown and tube burnout.