Boiling Drying Mechanism and Kinetics for Paste/Slurry Foods

Reference ID: MET-C8E7 | Process Engineering Reference Sheets Calculation Guide

Introduction & Context

Boiling drying is a critical unit operation in the food processing industry, specifically for the dehydration of high‑moisture pastes and slurries. This process involves spreading a thin film of material onto a heated surface, such as a drum or belt dryer, where heat is transferred to the product to induce rapid evaporation, a principle that is closely related to atomization and rapid drying for liquid‑to‑powder conversion. Accurate calculations are essential for process engineers to estimate the residence time required to achieve a target moisture content, size the drying equipment, and optimize energy consumption while preventing thermal degradation of heat‑sensitive food products.

Methodology & Formulas

The drying kinetics are modeled by dividing the process into two distinct phases: the sensible heating period and the constant-rate evaporation period. The following formulas define the physical behavior of the system:

1. Solids Mass Fraction (Wet Basis)

\[ w_{s} = \frac{1}{1 + X_{0}} \]

2. Dry Solid Mass

\[ M_{s} = \rho_{paste} \cdot A \cdot L \cdot w_{s} \]

3. Water Mass to be Removed

\[ \Delta m_{w} = M_{s} \cdot (X_{0} - X_{final}) \]

4. Heat Transfer Coefficient

The overall heat transfer coefficient is primarily governed by the conductive resistance of the thin film, and its value can be significantly enhanced by employing advanced equipment such as the rotating heated cylinder technology for liquid and paste foods. For a detailed discussion of this approach, see rotating heated cylinder technology for liquid and paste foods.

\[ U = \frac{k_{paste}}{L} \]

5. Heat Transfer Rate

\[ \dot{Q} = U \cdot A \cdot (T_{h} - T_{sat}) \]

6. Drying Time Calculations

The time required for the constant-rate evaporation period is derived from the latent heat of vaporization (\(\lambda\)):

\[ t_{const} = \frac{\Delta m_{w} \cdot \lambda}{\dot{Q}} \]

The time required for the sensible heating period (raising the paste from initial temperature \(T_{i}\) to saturation temperature \(T_{sat}\)) is:

\[ t_{heat} = \frac{M_{s} \cdot (c_{p,s} + X_{0} \cdot c_{p,w}) \cdot (T_{sat} - T_{i})}{\dot{Q}} \]

The total process time is the sum of the heating and constant-rate periods:

\[ t_{total} = t_{const} + t_{heat} \]

Parameter	Constraint/Threshold	Consequence
Film Thickness (L)	L ≤ 0.01 m	Exceeding 10 mm leads to bulk boiling and splashing; model becomes invalid.
Surface Temperature (T_h)	T_h ≤ 140 °C	Temperatures above this threshold increase the risk of material scorching.
Heat Transfer Coefficient (U)	100 ≤ U ≤ 500 W/(m² · K)	Values outside this range indicate non-standard drying conditions or measurement error.
Moisture Content	X₀ > X_final	Physical impossibility; initial moisture must exceed final moisture.

Boiling drying relies on the rapid phase change of internal moisture into vapor, driven by heat transfer that exceeds the latent heat of vaporization at the product interface. Unlike convective drying, which is often limited by external mass transfer resistance, boiling drying involves:

Internal pressure buildup caused by rapid vapor generation.
Formation of a porous structure due to vapor escape channels.
Enhanced moisture migration rates through capillary action and pressure-driven flow.

The drying kinetics for slurry foods are governed by the interaction between thermal conductivity and moisture diffusivity. Key parameters include:

The effective moisture diffusivity coefficient, which changes as the solid content increases.
The heat transfer coefficient at the heating surface.
The critical moisture content, representing the transition from the constant rate period to the falling rate period.
The rheological properties of the slurry, which dictate the thickness of the boundary layer.

Crust formation often occurs when the surface evaporation rate significantly outpaces the internal moisture migration rate. To prevent this, consider the following strategies:

Implement a staged temperature profile to maintain a lower surface temperature during the initial phase.
Utilize mechanical agitation or surface scraping to disrupt the formation of a dry skin.
Adjust the initial solid content of the slurry to optimize the viscosity and internal diffusion pathways.
Apply vacuum conditions to lower the boiling point, allowing for moisture removal at lower thermal gradients.

Worked Example: Batch Drying of Fruit Paste Under Vacuum

Scenario: A fruit paste slurry (initial moisture 80 % wet basis) is dried on a vacuum drum dryer. The chamber pressure is maintained at 0.2 bar, setting the saturation temperature to 60 °C. The heated drum surface is held at 120 °C. The paste is applied as a uniform film 2 mm thick over an area of 1 m². The initial temperature of the paste is 20 °C. The target final moisture content is 0.25 kg water per kg dry solids (20 % wet basis). Determine the total drying time required, assuming constant‑rate evaporation dominates.

Knowns (Input parameters):

Initial moisture content, \(X_0 = 4.0\) kg water/kg dry solids
Final moisture content, \(X_{final} = 0.25\) kg water/kg dry solids
Hot surface temperature, \(T_h = 120.0\) °C
Saturation temperature (at 0.2 bar), \(T_{sat} = 60.0\) °C
Initial paste temperature, \(T_i = 20.0\) °C
Film thickness, \(L = 0.002\) m
Heat transfer area, \(A = 1.0\) m²
Paste bulk density, \(\rho_{paste} = 1100.0\) kg/m³
Thermal conductivity of wet paste, \(k_{paste} = 0.6\) W/(m·K)
Latent heat of vaporization at 60 °C, \(\lambda = 2360.0\) kJ/kg
Specific heat of dry solids, \(c_{p,s} = 1.5\) kJ/(kg·K)
Specific heat of water, \(c_{p,w} = 4.18\) kJ/(kg·K)

Step-by-Step Calculation:

Compute solids mass fraction (wet basis): \(w_s = \frac{1}{1 + X_0} = \frac{1}{1 + 4.0} = 0.2\) (dimensionless).
Compute dry solid mass in the film: \(M_s = \rho_{paste} \cdot A \cdot L \cdot w_s = 1100.0 \cdot 1.0 \cdot 0.002 \cdot 0.2 = 0.44\) kg.
Compute mass of water to be removed during constant-rate period: \(\Delta m_w = M_s \cdot (X_0 - X_{final}) = 0.44 \cdot (4.0 - 0.25) = 1.65\) kg.
Compute heat required for evaporation: \(Q_{req} = \Delta m_w \cdot \lambda = 1.65 \cdot 2360.0 = 3894.0\) kJ.
Determine overall heat transfer coefficient (conductive limit through film): \(U = \frac{k_{paste}}{L} = \frac{0.6}{0.002} = 300.0\) W/(m²·K).
Compute heat transfer rate (constant during evaporation): \(\dot{Q} = U \cdot A \cdot (T_h - T_{sat}) = 300.0 \cdot 1.0 \cdot (120.0 - 60.0) = 18000.0\) W (J/s).
Compute constant-rate drying time (convert \(Q_{req}\) from kJ to J): \(t_{const} = \frac{Q_{req} \times 1000}{\dot{Q}} = \frac{3894.0 \times 1000}{18000.0} = 216.333\) s.
Compute sensible heating time (heating paste from \(T_i\) to \(T_{sat}\)): \(Q_{sens} = M_s \cdot (c_{p,s} + X_0 \cdot c_{p,w}) \cdot (T_{sat} - T_i) = 0.44 \cdot (1.5 + 4.0 \cdot 4.18) \cdot (60.0 - 20.0) = 320.672\) kJ. \(t_{heat} = \frac{Q_{sens} \times 1000}{\dot{Q}} = \frac{320.672 \times 1000}{18000.0} = 17.815\) s.
Total drying time (sum of contributions): \(t_{total} = t_{const} + t_{heat} = 216.333 + 17.815 = 234.148\) s.

Final Answer: The total drying time required to reduce the fruit paste from 80 % moisture to 20 % moisture under the given vacuum drying conditions is 234.148 s (approximately 3.9 min).

"Un projet n'est jamais trop grand s'il est bien conçu." — André Citroën

"La difficulté attire l'homme de caractère, car c'est en l'étreignant qu'il se réalise." — Charles de Gaulle

Boiling Drying Mechanism and Kinetics for Paste/Slurry Foods

Introduction & Context

Methodology & Formulas

Worked Example: Batch Drying of Fruit Paste Under Vacuum

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