This study investigated the rate of diffusion of the natural red dye betanin from beet juice into boiled eggs over time. Eggs were submerged in beet juice for periods of 1, 2, and 24 hours. Absorbance readings of the beet juice decreased over time, indicating dye was transferring into the eggs. Measurement of the eggs found dye had diffused deeper with increased time, reaching 3 mm after 1 hour, 4 mm after 2 hours, and 6 mm after 24 hours. COMSOL modeling simulated the diffusion at 1 and 2 hours, matching observed results.

1. Mass Transfer of Betanin Dye from Beet Juice to Boiled Eggs
By: Natalie Whitaker, Allison Barrera, Freddy Nocella
Biosystems Engineering, Clemson, SC, 29631
Abstract
This project looked at the rate of convective mass
transfer into boiled eggs. Three boiled eggs were
placed into beet juice and left for variable amounts
of time. One egg was left for 1 hour, a second for 2
hours, and the third for 24 hours. The length the dye
diffused into the eggs was then recorded and
compared to the COMSOL models.
Introduction
Beets are known to contain a natural red pigment
called betanin. Beetroot contains between 0.03-
0.06% betanin pigment. Betanin is the only FDA
approved natural dye and is widely used in food and
pharmaceutical applications. It does not have any
known health or environmental impacts. One
interesting way beet juice is applied is in coloring
boiled eggs for decoration. This project will
investigate this further to see how the length of
time the eggs are submerged in the beet juice
effects how deep the dye diffuses into the eggs. The
purpose of this project is to model the diffusion of
betanin into boiled eggs by varying the time in
which they are submerged.
Materials and Methods
• Eggs
• Hot plate
• Kettle
• Beet Juice
• Shallow Container
The eggs were hard-boiled, left to cool for 4 hours before
being peeled and submerged in a shallow dish of beet juice.
Eggs were left for 1, 2, and 24 hours. At the end of these
respective times, the eggs were cut in half and the length
the dye diffused into the egg was measured in
millimeters. The beet juice was also diluted 1:1 with DI
water, and the absorbance values were read at 752 nm at
each time point.
Results and Discussion - Diffusion of the
Beet Juice
From table 1, it is shown that as the dye diffuses into the
eggs, the absorbance readings of the beet juice decreases.
This is because the dye is leaving the solution and entering
the egg. This also results in the dye diffusing deeper into the
egg with time.
Table 1. Dye diffusion depth and absorbance readings
Results and Discussion- Analytical
solution using Heisler Approach
The modeling software COMSOL was used to model
the diffusion of the beet juice into the egg. Simulations ran for
1 hour and 2 hours. The color model (figure 1) and plots
(figure 2) are shown below.
The Heisler analytical solution technique was used to find how
long it would take for dye concentration in the center to reach
0.01 kg/m^3. Using the Rayleigh Number, Schmidt Number,
and Sherwood Number, the mass transfer coefficient for free
convection was found to be 1.44e-6 m/s. This number was then
used in the Heisler method to determine it would take 2 days
for the dye concentration at the center of the egg to reach 0.01
kg/m^3
Conclusion
Convection mass transfer was simulated by submerging peeled
hard-boiled eggs into a bath of beet juice for three-time
intervals of 1 hour, 2 hours, and 24 hours. From these results,
the diffusion mass depth increased over time. Following this
result, the beet juice absorbance values decreased
demonstrating mass transfer into the egg.
References
Drapcho, C. 2022. Lecture 14: Free Convection, Lecture 19, 20: Mass Transfer. Unpublished Lecture Notes, BE 4120, Clemson University, Clemson SC.
Time (hr) Beet Juice Abs.
Reading
Diffusion Depth
(mm)
1 0.060 3
2 0.051 4
24 0.037 6
Figure 1. Color COMSOL model of egg after 1 hour submerged in beet juice
Figure 2. Graphs of dye concentration from outside to center of the egg at 1
hour (left) and two hours (right)