Analysis of Vapor Pressure Rise and Reduced Pressure Filtration Fluid Movement Inside the Flask During Siphon Brewing

Changes in Glass Transition Temperature $(T_g)$ and Roasting Dynamics by Processing Method

Coffee roasting is a complex engineering process that extends beyond simple heat transfer, involving the interaction between the biochemical composition and physical structure of green coffee beans. Specifically, the initial differences in chemical components within the bean due to Natural and Washed processing act as key variables that dictate thermodynamic behavior throughout the roasting process. This article provides an in-depth analysis of how compositional changes based on processing affect the glass transition temperature $(T_g)$ and thermal energy balance of green coffee beans.

1. Glass Transition Temperature $(T_g)$ and the Gordon-Taylor Equation

The polymer matrix of green coffee (primarily cellulose and hemicellulose) utilizes moisture as a plasticizer to transition from a glassy state to a rubbery state. The $T_g$ at this stage can be modeled using the Gordon-Taylor equation.

$ T_g = \frac{w_s T_{gs} + k w_w T_{gw}}{w_s + k w_w} $

Here, $w_s$ and $w_w$ represent the mass fractions of the bean solids and water, respectively. In Natural processed coffee, sugars from the mucilage penetrate the cell walls, increasing hydrophilicity, which effectively lowers the $T_g$ during the early stages of roasting through interaction with water. Consequently, Natural processed beans undergo a faster transition to the rubbery state compared to Washed beans, accelerating plastic deformation of the cell walls early in the roast, which directly impacts the entrapment and diffusion rate of aromatic compounds within the cells.

2. Physical Governing Equations of Heat Transfer

Within a roasting drum, green coffee beans undergo a complex heat transfer process involving convection, conduction, and radiation. Each mechanism is governed by the following physical laws:

• Conduction: $q_{cond} = -k A abla T$ (Energy transfer occurring during contact with the drum surface)
• Convection: $q_{conv} = h A (T_g - T_s)$ (Dependent on the convective heat transfer coefficient $h$ between hot air and the bean surface)
• Radiation: $q_{rad} = \epsilon \sigma A (T_{surr}^4 - T_s^4)$ (Radiative energy from the heated inner walls of the drum)

Washed beans have the hydrophilic pectin layer removed from the surface, resulting in different heat absorption characteristics for initial convection and radiation compared to Natural beans. The high sugar content in Natural beans can cause surface stickiness, which minutely alters the conduction efficiency with the inner drum wall.

3. Transient Thermal Energy Balance and the Maillard Reaction

The key to determining the Rate of Rise (RoR) of the bean core temperature is the energy balance equation based on the first law of thermodynamics.

$ m C_p \frac{dT_s}{dt} = q_{cond} + q_{conv} + q_{rad} - Q_{evap} + Q_{rxn} $

In this equation, $Q_{evap} = \frac{dm_w}{dt} \Delta H_{vap}$ is the latent heat of vaporization, which is the primary cause of a sharp decline in RoR during the drying phase. Natural processed beans have more complex initial moisture absorption pathways, leading to irregular consumption patterns of latent heat of vaporization, which increases the difficulty of controlling RoR during the mid-roasting stage. Conversely, the Maillard reaction is accompanied by the reaction enthalpy $(Q_{rxn})$ of carbonyl compounds and amino acids. Natural beans maintain a high reaction rate constant due to abundant glucose, leading to more intense thermal decomposition $(Q_{rxn} > 0)$ near $200^{\circ} C$. These differences create a critical variance in the retention of volatile aroma compounds during the formation of the porous structure $(\epsilon \approx 0.3 \sim 0.5)$ after the first crack, serving as the thermodynamic foundation that determines the complexity of the final cup profile.

Variable	Natural	Washed
Glucose/Sucrose Ratio	High	Low
Initial $T_g$ (Moisture-based)	Low	Relatively High
$Q_{rxn}$ (Maillard contribution)	Very Strong	Constant
Physical Deformation	Easily Plastic Deformed	Primarily Brittle