Fluid Dynamics

Puck Physics and Tamping Mechanics for Espresso Channeling Prevention

Published: 2026-06-15 | Read Time: 4 min

1. Thermal Resistance of the Purine Ring Structure

It is commonly assumed that dark-roasted beans have most of their caffeine destroyed; however, in organic chemistry terms, the caffeine (C₈H₁₀N₄O₂) molecule is a highly stable nitrogen compound characterized by tightly interlocked carbon rings.

Caffeine possesses a purine derivative structure, where a pyrimidine ring and an imidazole ring are fused. This purine ring system is resonance-stabilized, resulting in very high molecular bond energy. Generally, even within the maximum operating temperature range of roasters (220–230°C), significant chemical bond cleavage or pyrolysis of caffeine molecules rarely occurs. This is due to the thermodynamic stability of the purine ring itself, which allows caffeine molecules to maintain their structural integrity even in the high-temperature environment of the roasting process.

2. High-Temperature Sublimation Reaction of Caffeine and Mass Change Effects

Caffeine exhibits sublimation characteristics, where it undergoes a phase transition directly from solid to gas at approximately 178°C under atmospheric pressure. This means that caffeine has a low triple point temperature and relatively high sublimation pressure, causing it to vaporize directly without passing through a liquid phase at standard atmospheric pressure. The sublimation process is an endothermic reaction $(\Delta H_{sub} > 0)$, and as temperature increases, the vapor pressure of caffeine increases exponentially according to the following Clausius-Clapeyron relation:

$\ln P = -\frac{\Delta H_{sub}}{R T} + B$

Where $P$ is the vapor pressure, $\Delta H_{sub}$ is the enthalpy of sublimation, $R$ is the ideal gas constant, $T$ is the absolute temperature, and $B$ is a constant. While some of the caffeine molecules vaporized during roasting are forced out through the exhaust line of the roaster, the amount lost is less than 10% of the total caffeine content in the beans. In reality, as roasting progresses, the weight loss (Loss on Drying, LoD) due to moisture $(\approx 10-12\%)$, carbon dioxide, and other volatile organic compounds reaches 15–20%, which is significantly greater than the mass loss of caffeine due to sublimation. Therefore, based on the same weight (e.g., 10g of roasted beans), the caffeine density of dark-roasted beans tends to be calculated as relatively higher than that of green beans. This is a relative concentration effect that occurs because the overall bean mass reduction rate is greater than the absolute reduction in total caffeine.

3. Glass Transition and Moisture-Plasticization Effects in Bean Structure

The physical changes in coffee beans are closely related to thermodynamic phase transitions. The amorphous polymer matrix, composed primarily of cellulose and hemicellulose in green beans, transitions from a glassy state to a rubbery state at a specific temperature. This transition temperature is known as the glass transition temperature $(T_g)$. Below $T_g$, beans are hard and exhibit brittleness, whereas above $T_g$, they become flexible and capable of plastic deformation.

Moisture acts as a powerful plasticizer for the bean's polymer matrix. For green beans with high moisture content $(w)$, $T_g$ decreases significantly according to the Gordon-Taylor relation. This relation can be expressed as follows:

$T_g = \frac{w_p T_{gp} + k w_w T_{gw}}{w_p + k w_w}$

Where $w_p$ is the mass fraction of the dry polymer, $T_{gp}$ is the glass transition temperature of the dry polymer, $w_w$ is the mass fraction of moisture, $T_{gw}$ is the glass transition temperature of water (or a reference temperature representing the plasticizing effect), and $k$ is an empirical constant. In the early stages of roasting, when the internal moisture content is high, $T_g$ is relatively low, facilitating the transition to a rubbery state even near room temperature, which promotes flexibility and plastic deformation of the cell walls. However, as moisture evaporates during roasting, $w_w$ decreases and $T_g$ rises sharply; after the first crack, the beans develop high brittleness and a porous structure $(\epsilon \approx 0.3 \sim 0.5)$. These structural changes have a profound impact on heat transfer characteristics, as well as the final density, strength, and extraction properties of the beans.

4. Heat Transfer Mechanisms During Coffee Roasting

The three main mechanisms for transferring energy into the coffee beans during the roasting process are conduction, convection, and radiation.

Conduction: Heat transfer through direct contact between the inner drum wall and the bean particles. It is described by Fourier’s law of heat conduction.

Where $q_{cond}$ is the conductive heat flux, $k$ is the thermal conductivity of the bean, $A$ is the heat transfer area, and abla T$ is the temperature gradient.

Convection: Heat transfer by fluid flow between the hot air (roasting gas) in the roaster and the bean surface. It follows Newton’s law of cooling.

Where $q_{conv}$ is the convective heat flux, $h$ is the convective heat transfer coefficient, $A$ is the heat transfer area, $T_{air}$ is the air temperature, and $T_s$ is the bean surface temperature.

Radiation: A mode of heat transfer where electromagnetic energy emitted by the heated inner drum wall is absorbed by the bean surface. It is explained by the Stefan-Boltzmann law.

Where $q_{rad}$ is the radiative heat flux, $\epsilon$ is the emissivity of the bean surface, $\sigma$ is the Stefan-Boltzmann constant, $A$ is the heat transfer area, $T_{surr}$ is the absolute temperature of the surrounding wall, and $T_s$ is the absolute temperature of the bean surface.

Convection and conduction are dominant in the early stages of roasting, but the proportion of radiative heat transfer gradually increases as the temperature rises. The balance of each heat transfer mode depends on the roaster design (e.g., drum type, airflow), batch size, and roasting profile.

5. Transient Energy Balance at the Bean Core

The Rate of Rise (RoR) at the core during coffee roasting is governed by the transient energy balance equation according to the first law of thermodynamics. Considering the heat energy flowing into the beans, the chemical reaction heat generated internally, and the endothermic effect of moisture evaporation, it can be defined as follows:

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

Each term is defined as follows:

$m$: Mass of the bean
$C_p$: Specific heat capacity of the bean
$\frac{dT_s}{dt}$: Rate of change in temperature of the bean surface or core (RoR)
$q_{cond}, q_{conv}, q_{rad}$: Heat fluxes due to conduction, convection, and radiation (see Section 4 above)
$Q_{evap}$: Heat absorbed by the latent heat of vaporization of moisture. As moisture inside the bean evaporates, it consumes heat, expressed as: $Q_{evap} = \frac{dm_w}{dt} \Delta H_{vap}$ where $\frac{dm_w}{dt}$ is the moisture evaporation rate and $\Delta H_{vap}$ is the latent heat of vaporization of water. During the drying phase of roasting, the massive endothermic heat of vaporization ($Q_{evap} > 0$, hence the negative sign in the energy balance equation) causes the RoR to stagnate or decline temporarily (RoR Plateau).
$Q_{rxn}$: Enthalpy of Maillard and pyrolysis reactions. The Maillard reaction in the early to middle stages of roasting is primarily endothermic $(Q_{rxn} < 0)$, but after the first crack, from around 200^{\circ}\text{C} onwards, pyrolysis reactions of cellulose, lignin, etc., shift to exothermic$(Q_{rxn} > 0)$. This exothermic reaction, combined with a decrease in the moisture evaporation rate, is a primary cause of the sharp rise in RoR.

This energy balance analysis provides the scientific basis for roasters to effectively control the RoR, particularly in managing the RoR slowdown caused by $Q_{evap}$ during the drying phase and the RoR surge caused by $Q_{rxn}$ after the first crack, thereby achieving uniform roast degrees and optimal flavor profiles.