Limiting the Diffusion Rate of High-Molecular-We\\r\\right Bitter Phenolic Compounds during Low-Temperature Cold Brew Extraction

Analysis of complex heat transfer mechanisms and bean property changes in roasting drums

The coffee roasting process is a physicochemical process that combines complex multi-phase flow and thermodynamic changes. This study investigates in depth how conduction, convection, and radiation regulate internal heat penetration in beans within a drum roaster, and the impact of the resulting changes in glass transition temperature $(T_g)$ on the cellular structure of the beans. In the early stages of roasting, the bean maintains a rubbery state plasticized by its moisture content, which serves as the core physical foundation for heat penetration and structural change.

Governing equations for heat transfer and roasting energy balance

Thermal energy inside a drum roaster is transferred to the surface of green beans and gradually diffuses to the center. The three main paths of heat transfer can be modeled physically as follows:

• Conduction: Occurs through direct contact between the drum surface and bean particles, following Fourier's Law. $q_{cond} = -k A abla T$where$kis the thermal conductivity of the bean andA$ is the contact area.
• Convection: Energy transfer by hot air (blown gas), determined by Newton's Law of Cooling. $q_{conv} = h A (T_g - T_s)$ where $h$ is the convective heat transfer coefficient, which depends on flow velocity.
• Radiation: Energy emitted from the heated inner drum wall, following the Stefan-Boltzmann Law. $q_{rad} = \epsilon \sigma A (T_{surr}^4 - T_s^4)$

These heat sources are integrated into the transient energy balance equation that determines the Rate of Rise (RoR) at the bean center. The following is the total energy balance equation for the system.

$ m C_p \frac{dT_s}{dt} = q_{cond} + q_{conv} + q_{rad} - \dot{m}_w \Delta H_{vap} + Q_{rxn} $

In the above equation, the term $\dot{m}_w \Delta H_{vap}$ represents the latent heat of moisture vaporization, which is a key endothermic factor that suppresses the RoR during the drying phase. As moisture evaporates after the mid-roasting point, the magnitude of this term decreases, resulting in a sharp surge in the RoR.

Glass transition temperature $(T_g)$ and physical state changes of cell walls

The polymer matrix of green beans uses moisture as a plasticizer to regulate its glass transition temperature $(T_g)$. According to the Gordon-Taylor relationship, the $T_g$ of a polymer mixture is defined as follows:

$ T_g = \frac{w_1 T_{g1} + k w_2 T_{g2}}{w_1 + k w_2} $

where $w_1$ and $w_2$ are the mass fractions of coffee solids and moisture, respectively. Early in the roast, the high moisture content inside the bean lowers $T_g$, keeping the cell walls in a rubbery state. In this state, plastic deformation of the cell walls due to external pressure and vapor pressure occurs easily. However, as moisture is lost, $T_g$ rises sharply, and the system transitions into a glassy state around the first crack. At this point, the beans become brittle, and their porous structure $(\epsilon \approx 0.3 \sim 0.5)$ becomes fixed.

Experimental analysis data

Stage	Main Mechanism	Heat Transfer Governing Factor	Physical State
Drying	Moisture Evaporation	Convection $(q_{conv})$	Rubbery
Maillard	Flavor Precursor Formation	Radiation $(q_{rad})$	Transition Zone
Pyrolysis	$CO_2$ Release/Brittleness	Conduction $(q_{cond})$	Glassy

Overall, successful roasting depends on precisely controlling these thermodynamic equilibria and material science phase transition points. To manage the endothermic power of $Q_{evap}$, a roaster must maximize initial convective heat transfer and properly regulate radiation as $Q_{rxn}$ shifts to an exothermic reaction after the crack, thereby achieving uniform heat penetration to the center of the bean. The efficiency of heat penetration before the cell structure completely hardens into a glassy state is a critical physical factor that determines the final flavor and body of the coffee.