# About Aguilera et al. (2004): chocolate, migration of lipids, diffusion and capillarity,

Hervé This, Vo Kientza

► To cite this version:

Hervé This, Vo Kientza. About Aguilera et al. (2004): chocolate, migration of lipids, diffusion and capillarity,. International Journal of Molecular and Physical Gastronomy, 2023, 11, pp.1_9. 10.17180/ijmpg-2023-art11. hal-04197297

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Submitted on 6 Sep 2023

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# About Aguilera et al. (2004): chocolate, migration of lipids, diffusion and capillarity,

Hervé This, Vo Kientza

<figure><img src="image_1.png" /></figure>

## To cite this version:

Hervé This, Vo Kientza. About Aguilera et al. (2004): chocolate, migration of lipids, diffusion and capillarity,. International Journal of Molecular and Physical Gastronomy, 2023, 11, pp.1_9. 10.17180/ijmpg-2023-art11. hal-04197297v2

HAL Id: hal-04197297

https://hal.inrae.fr/hal-04197297v2

Submitted on 16 Jul 2024

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_2.png" /></figure>
# About Aguilera et al. (2004): chocolate, migration of lipids, diffusion and capillarity

Hervé This vo Kientza¹,²*

1. Université Paris-Saclay, INRAE, AgroParisTech, UMR 0782 SayFood, 22 place de l'agronomie, 91120, Palaiseau, France.

2. Inrae-AgroParisTech International Centre for Molecular and Physical Gastronomy, https://icmpg.hub.inrae.fr/.

*Correspondence: herve.this@inrae.fr

## Abstract

An article published in 2004 by Aguilera et al. is useful for science and technology education, because it shows the difference between diffusion and capillarity as two important mechanisms of mass transfer. It is also an opportunity to recommend supplementing the physical descriptions of food systems (using the dispersed system formalism) by a thorough analysis of their chemical compositions.

## Keywords

chocolate, diffusion, capillarity, microstructure

The purpose of this commentary article is not only to show why an article published about 20 years ago by Aguilera et al., although old, remains useful for food science, food technology and food engineering education, but it is also an opportunity to use recent data to examine how the microstructure of chocolate is changing as a function of temperature.

Often review articles begin with an introductory paragraph explaining a question dealt with in an article; they go on explaining its context, then they present the ideas of the article reviewed in the order in which they appear in the article (Gülpınar and Güçlü, 2023), and they conclude by an evaluation of the document, the interpretations being separated from the facts. Here, the organization of this commentary will be different: it will be first explained why the chosen article, about lipid migration in chocolate, is useful for food science and food technology education, but then a scientific question dealt with in the article, about chocolate microstructure, will be discussed. So it is not so much an evaluation but more a scientific discussion.

## Diffusion vs capillarity

The title of the article reviewed is *Fat migration in chocolate: diffusion or capillary flow in a*
<figure><img src="image_3.png" /></figure>

Inrae-AgroParisTech
International Centre for Molecular and Physical Gastronomy

International Journal
of
Molecular and Physical Gastronomy

**Authors**

Hervé This

**Title of the work**

About Aguilera et al. (2004): chocolate, migration of lipids, diffusion and capillarity

Year 2023, 9(1) 11, pp. 1-9

DOI: 10.17180/ijmpg-2023-art11

**Published online:**

31 August 2023,

https://icmpg.hub.inrae.fr/international-activities-of-the-international-centre-of-molecular-gastronomy/international-journal-of-molecular-and-physical-gastronomy/1-news/book-article-reviews/about-aguilera-et-al.-2004-chocolate-migration-of-lipids-diffusion-and-capillarity

About Aguilera et al. (2004): chocolate, migration of lipids, diffusion and capillarity © 2023 by

Hervé This vo Kientza is licensed under Attribution 4.0 International

<figure><img src="image_4.png" /></figure>
Commentary

particulate solid?—A hypothesis paper, by
Aguilera et al. (2004). Since its publication, the
students in our university have been invited to
study it, because it explains various concepts that
are useful for food science, food technology and
food engineering. To make it short, the article
discusses - as is well said in the title - diffusion
and capillarity in "chocolate" (it will be explained
later why quotation marks are used here for the
word chocolate), in particular during fat blooming,
i.e., the formation of a whitish haze on the surface
due to recrystallization of cocoa butter when
chocolate is stored at elevated temperatures,
depriving it from a smooth appearance, bright
color, and gloss (Hartel 1999).

Chocolate is made of cocoa butter, as the most
important ingredient, i.e., a mixture of triglycerides
for which the fatty acid residues are mainly those
of oleic acid (cis-octadec-9-enoic acid, 35 %),
stearic acid (n-octadecanoic acid, 34 %), palmitic
acid (hexadecanoic acid, 26 %), plus linoleic acid
((9Z,12Z)-octadeca-9,12-dienoic acid) and
arachidonic acid ((5Z,8Z,11Z,14Z)-5,8,11,14-
eicosatetraenoic acid) (Longchampt and Hartel,
2004).

Having different compositions in their three fatty
acid residues, the various triglycerides of cocoa
butter can melt at different temperatures. At "room
temperature" (again, the reason why there are
quotation marks will be discussed later), some
triglycerides - those melting at temperatures lower
than "room temperature" - can make a liquid
phase, whereas others, melting at higher
temperatures, can make a solid phase. By the
way, as the first are "oils", the title of the article
should perhaps have included "oil migration",
instead of "fat migration" (IFST, 2023), as in
Galdamez et al. (2009).

In certain circumstances, the oil (i.e., liquid)
fraction of lipids migrates inside the "crystal
structure" made by the lipid crystals (Miquel et al.,
2001; Howard, 2020). The main question
discussed by Aguilera et al. is: how does this
"migration" take place? This question is very
broad, because the possible mechanisms for
molecular motions and mass transfers are many,
but the authors discuss in particular the question:

can we speak of "diffusion", or is it better to
speak of "capillarity"? The word "diffusion" is
ubiquitous in molecular gastronomy studies
(Burke et al., 2021), and, more generally, in food
science, food technology and food engineering.
A review of the scientific literature in these fields
shows that one should be cautious about this
word, and also about the meaning of "diffusion
coefficients"... because often it means an
effective coefficient rather than what is
recommended by the International Union of Pure
Chemistry and Applications of Chemistry
(IUPAC).

One of the best starting point, for such a
discussion of the terminology, is the consultation
of the *Compendium of Chemical Terminology* (so
called “Gold Book”) of IUPAC (2009a). It
provides various definitions including the word
“diffusion”, beginning with “*The spreading or*

<figure><img src="image_1.png" /><figcaption>Figure 1. For lipids, the solid content decreases regularly from 100% at about -10 °C toward 0% at more than 55 °C, due to the great number of different triglycerides, each having a particular melting point (from This, 2022). Here the melting curve of cocoa butter is compared to the one for butter and for the fraction of butter that melts at the highest temperature, as determined by various analytical methods such as nuclear magnetic resonance spectroscopy (from Shenk and Peschar, 2004; Lopez and Ollivon, 2009; This, 2014).</figcaption></figure>
# About Aguilera et al. (2004): chocolate, migration of lipids, diffusion and capillarity

Hervé This vo Kientza¹²*

1. Université Paris-Saclay, INRAE, AgroParisTech, UMR 0782 SayFood, 22 place de l'agronomie, 91120, Palaiseau, France.

2. Inrae-AgroParisTech International Centre for Molecular and Physical Gastronomy, https://icmpg.hub.inrae.fr/.

*Correspondence: herve.this@inrae.fr

**Abstract**

An article published in 2004 by Aguilera et al. is useful for science and technology education, because it shows the difference between diffusion and capillarity as two important mechanisms of mass transfer. It is also an opportunity to recommend supplementing the physical descriptions of food systems (using the dispersed system formalism) by a thorough analysis of their chemical compositions.

**Keywords**

chocolate, diffusion, capillarity, microstructure

The purpose of this commentary article is not only to show why an article published about 20 years ago by Aguilera et al., although old, remains useful for food science, food technology and food engineering education, but it is also an opportunity to use recent data to examine how the microstructure of chocolate is changing as a function of temperature.

Often review articles begin with an introductory paragraph explaining a question dealt with in an article; they go on explaining its context, then they present the ideas of the article reviewed in the order in which they appear in the article (Gülpınar and Güçlü, 2023), and they conclude by an evaluation of the document, the interpretations being separated from the facts. Here, the organization of this commentary will be different: it will be first explained why the chosen article, about lipid migration in chocolate, is useful for food science and food technology education, but then a scientific question dealt with in the article, about chocolate microstructure, will be discussed. So it is not so much an evaluation but more a scientific discussion.

**Diffusion vs capillarity**

The title of the article reviewed is *Fat migration in chocolate: diffusion or capillary flow in a*
International Journal of Molecular and Physical Gastronomy
(IJMPG)

Commentary

scattering of a gaseous or liquid material. [...] Molecular diffusion is the net transport of molecules which results from their molecular motions alone in the absence of turbulent mixing; it occurs when the concentration gradient of a particular gas in a mixture differs from its equilibrium value".

Diffusion phenomena are quantitatively characterized by diffusion coefficients, but according to IUPAC, "the diffusion coefficient is the proportionality constant D, relating the flux of amount of entities B to their concentration gradient":

$$J_n = -D \nabla c_B$$

There are other diffusion coefficients, such as rotational diffusion coefficient, differential diffusion coefficients, chemical diffusion coefficient, interdiffusion coefficient, and, most importantly, the self-diffusion coefficient $D_i^*$, which is defined as the diffusion coefficient of species i in the absence of a chemical potential gradient. It is related to the diffusion coefficient by:

$$D_i^* = D_i \frac{\partial \ln(c_i)}{\partial \ln(a_i)}$$

where $a_i$ is the activity of i in the solution, and $c_i$ is the concentration of i.

Aguilera et al. do not go into such details, but they could have done it, because when the oil in chocolate makes a continuous liquid phase, and even when it is restricted to small oil isolated pockets within a solid framework, the triglycerides of this oil exhibits molecular diffusion.

But the authors should not be criticized, because the article focuses on mass transfer, occurring often faster than by diffusion (Quéré et al., 1999). Indeed, to understand their goal, the best is to quote them: "Molecular or Fickian diffusion is widely used (and abused) by food engineers as a general model for mass transfer, most notably in drying, leaching, and frying. The approach has the advantage that by plotting experimental data in the form of log (unaccomplished ratio of mass transferred) against time, an apparent or effective diffusion coefficient, $D_{eff}$, can be determined from the straight portion of the curve (Schwartzberg, 1987). The simplicity of the method has resulted

in that during a 20-y period over 170 papers from only 5 journals have reported data of $D_{eff}$ or moisture transfer in food materials (Saravacos and Maroulis, 2000). The parameter (which may be correctly redefined as a mass transfer coefficient) actually encompasses all possible forms of mass transfer involved in the process, not only diffusional ones. A major drawback of this practice is that no efforts are made to resolve microstructural aspects, understand the process, and find out actual mechanisms of mass transfer involved (Aguilera and Stanley 1999)."

As said, one virtue of this text is to compare Fickian (some write "Fickian") diffusion with capillarity, i.e., the tendency of liquids to be drawn into the confined space of a narrow tube or between at least two surfaces (Von Honschoten et al., 2010). The article considers the case of flow in porous media, generated by an interfacial pressure gradient (as when there is meniscus).

More generally, the article explains both phenomena of diffusion and capillarity, giving examples of food science or food technology where they occur, and it discusses some general equations for mass transfer. In both cases, a fast increase is followed by an asymptotical behaviour, but the slopes in the time-mass diagrams can be different. For the Fickian case, the ratio of the mass at instant t by the mass when equilibrium is reached is proportional to the square root of the time... and the same holds for capillarity as described through the Lucas-Washburn equation (Zhmud et al., 2000; De Gennes et al., 2004).

After discussing this, the articles goes on examining the experimental data obtained at the time it was published, in order to propose the importance of capillarity for liquid lipids ("oil") moving through the solid lipid framework ("a continuous phase of solid and liquid fat"). Here it should be added that other conclusions were favored later (Deka et al., 2006; Galdamez et al., 2009): observations of oil migration through chocolate using magnetic resonance imaging have shown that the dominant mechanism is
Commentary

particulate solid? —A hypothesis paper, by
Aguilera et al. (2004). Since its publication, the
students in our university have been invited to
study it, because it explains various concepts that
are useful for food science, food technology and
food engineering. To make it short, the article
discusses - as is well said in the title - diffusion
and capillarity in "chocolate" (it will be explained
later why quotation marks are used here for the
word chocolate), in particular during fat blooming,
i.e., the formation of a whitish haze on the surface
due to recrystallization of cocoa butter when
chocolate is stored at elevated temperatures,
depriving it from a smooth appearance, bright
color, and gloss (Hartel 1999).

Chocolate is made of cocoa butter, as the most
important ingredient, i.e., a mixture of triglycerides
for which the fatty acid residues are mainly those
of oleic acid (cis-octadec-9-enoic acid, 35 %),
stearic acid (n-octadecanoic acid, 34 %), palmitic
acid (hexadecanoic acid, 26 %), plus linoleic acid
((9Z,12Z)-octadeca-9,12-dienoic acid) and
arachidonic acid ((5Z,8Z,11Z,14Z)-5,8,11,14-
eicosatetraenoic acid) (Longchampt and Hartel,
2004).

Having different compositions in their three fatty
acid residues, the various triglycerides of cocoa
butter can melt at different temperatures. At "room
temperature" (again, the reason why there are
quotation marks will be discussed later), some
triglycerides - those melting at temperatures lower
than "room temperature" - can make a liquid
phase, whereas others, melting at higher
temperatures, can make a solid phase. By the
way, as the first are "oils", the title of the article
should perhaps have included "oil migration",
instead of "fat migration" (IFST, 2023), as in
Galdamez *et al*. (2009).

In certain circumstances, the oil (i.e., liquid)
fraction of lipids migrates inside the "crystal
structure" made by the lipid crystals (Miquel *et al.*,
2001; Howard, 2020). The main question
discussed by Aguilera *et al.* is: how does this
"migration" take place? This question is very
broad, because the possible mechanisms for
molecular motions and mass transfers are many,
but the authors discuss in particular the question:

can we speak of "diffusion", or is it better to
speak of "capillarity"? The word "diffusion" is
ubiquitous in molecular gastronomy studies
(Burke *et al.*, 2021), and, more generally, in food
science, food technology and food engineering.
A review of the scientific literature in these fields
shows that one should be cautious about this
word, and also about the meaning of "diffusion
coefficients"... because often it means an
effective coefficient rather than what is
recommended by the International Union of Pure
Chemistry and Applications of Chemistry
(IUPAC).

One of the best starting point, for such a
discussion of the terminology, is the consultation
of the *Compendium of Chemical Terminology* (so
called “Gold Book”) of IUPAC (2009a). It
provides various definitions including the word
“diffusion”, beginning with “*The spreading or*

<figure><img src="image_5.png" /><figcaption>Figure 1. For lipids, the solid content decreases regularly from 100% at about -10 °C toward 0% at more than 55 °C, due to the great number of different triglycerides, each having a particular melting point (from This, 2022). Here the melting curve of cocoa butter is compared to the one for butter and for the fraction of butter that melts at the highest temperature, as determined by various analytical methods such as nuclear magnetic resonance spectroscopy (from Shenk and Peschar, 2004; Lopez and Ollivon, 2009; This, 2014).</figcaption></figure>
Commentary

diffusion, and that if capillary pressure is involved,
it is a minor contributor. However it is not the goal
of this commentary article to discuss this matter:
rather the chocolate microstructure is considered.
The authors describe chocolate as a "particulate
system", but what does it mean? And is it correct?
Comparing chocolate to butter is useful for a
better understanding of the microstructure of
chocolate.

Butter: which microstructure?

The composition of cocoa butter having been
given before, it has now to be observed, for
comparison, that the triglycerides content of milk
lipids is much more heterogeneous than for
chocolate, with a total number of fatty acid
residues reaching 400 (Jensen, 2002). The main
residues are: butyric, caproic, caprylic, capric,
auric, myristic, pentadecanoic, palmitic,
pamitoleic, margaric, stearic, oleic, linoleic,
linolenic.

In order to describe the microstructure of butter
(and of chocolate), it is convenient to use the
"dispersed system formalism" (This vo Kienza,
2021a), using the letters G, O, S, W respectively
for describing gas phases, liquid lipid phases
("oils"), solid phases (for example, ice, lipid
crystals, etc.) and aqueous solutions. The symbol
"/" stands for random dispersion, and the symbol
"x" describes the interweaving of two continuous
phases. For example, an emulsion is written O/W,
or W/O; a dispersion of liquid pockets inside a
solid is written O/S, or W/S, and a gelatin gel, with
two continuous phases, is described by SxW
(when the operator is commutative, the letters are
in the alphabetical order). When needed, the
physical "dimension" of the various objects being
considered is described by D₀, D₁, D₂, or D₃,
respectively for dimensions 0, 1, 2, 3, after a
reference size is chosen.

Using this formalism, it is possible to analyse what
many textbooks in food science and food
technology (Friberg et al., 2003; McClements,
2006; Khader, 2016) have been publishing, i.e.,
that butter is an "emulsion". According to the Gold

Book of IUPAC, an emulsion is "a fluid colloidal
system in which liquid droplets and/or liquid
crystals are dispersed in a liquid. The droplets
often exceed the usual limits for colloids in size".
Following the IUPAC definition, milk (from the
female of Bos taurus in particular) can be an
emulsion or not, depending on temperature.
Indeed milk is mainly a dispersion of lipids (as D₀
structures) in an aqueous solution D₃(W), but the
issue is to know what is the physical state of the
lipids: if they are in a liquid phase (O), then milk
is indeed an emulsion D₀(O)/D₃(W), but if they
make fully solid structures (D₀(S)/D₃(S)) or if they
make complex structures with both liquid and
solid phases, such as in a (D₀(S)@D₀(O))/D₃(S)
system, then milk would be a "suspension"
(IUPAC, 2009b; 2009c).

In order to decide which system describes milk,
one has to look at the melting curve of milk lipids
(Figure 1). At temperatures lower than - 10 °C,
milk lipids are entirely solid (as well as water),
and butter is a solid suspension D₀(S₁)/D₃(S₂), S₁
and S₂ standing respectively for ice and for solid
lipids, but at temperatures higher than 60 °C, all
the milk lipids are melted and butter is either an
emulsion (D₀(O)/D₃(W) or D₀(W)/D₃(O))
depending on the way it has been obtained) or a
biphasic liquid (D₃(O)σD₃(W)) (here σ stands for
superposition).

What about milk at "room temperature"? This is
not well defined, as the summer temperatures in
hot countries are very different from the
temperatures in cold countries in winter: at a
"room temperature" of 15 °C, the solid lipid
content would be slightly higher than 50 %, but
at a room temperature of 30 °C, it would be less
than 15 % (Jacques et al., 1999). Anyway, in
both cases, milk is a suspension (because of the
solid component of the dispersed structures)
rather than an emulsion.

From milk, cream is recovered, and butter is
produced by churning. After butter production,
some of the aqueous solution (limited to 16 % w
by international regulations) (EC, 1998) can
remain in the system, but the liquid lipid fraction
(O)/solid lipid fraction (S) ratio still depends on
temperature, and the system can be a "gel", with
International Journal of Molecular and Physical Gastronomy
(IJMPG)

Commentary

scattering of a gaseous or liquid material. [...] Molecular diffusion is the net transport of molecules which results from their molecular motions alone in the absence of turbulent mixing; it occurs when the concentration gradient of a particular gas in a mixture differs from its equilibrium value".

Diffusion phenomena are quantitatively characterized by diffusion coefficients, but according to IUPAC, "the diffusion coefficient is the proportionality constant D, relating the flux of amount of entities B to their concentration gradient":

$$J_n = -D \nabla c_B$$

There are other diffusion coefficients, such as rotational diffusion coefficient, differential diffusion coefficients, chemical diffusion coefficient, interdiffusion coefficient, and, most importantly, the self-diffusion coefficient $D_i^*$, which is defined as the diffusion coefficient of species i in the absence of a chemical potential gradient. It is related to the diffusion coefficient by:

$$D_i^* = D_i \frac{\partial \ln(c_i)}{\partial \ln(a_i)}$$

where $a_i$ is the activity of i in the solution, and $c_i$ is the concentration of i.

Aguilera et al. do not go into such details, but they could have done it, because when the oil in chocolate makes a continuous liquid phase, and even when it is restricted to small oil isolated pockets within a solid framework, the triglycerides of this oil exhibits molecular diffusion.

But the authors should not be criticized, because the article focuses on mass transfer, occurring often faster than by diffusion (Quéré et al., 1999). Indeed, to understand their goal, the best is to quote them: "Molecular or Fickian diffusion is widely used (and abused) by food engineers as a general model for mass transfer, most notably in drying, leaching, and frying. The approach has the advantage that by plotting experimental data in the form of log (unaccomplished ratio of mass transferred) against time, an apparent or effective diffusion coefficient, $D_{eff}$, can be determined from the straight portion of the curve (Schwartzberg, 1987). The simplicity of the method has resulted

in that during a 20-y period over 170 papers from only 5 journals have reported data of $D_{eff}$ or moisture transfer in food materials (Saravacos and Maroulis, 2000). The parameter (which may be correctly redefined as a mass transfer coefficient) actually encompasses all possible forms of mass transfer involved in the process, not only diffusional ones. A major drawback of this practice is that no efforts are made to resolve microstructural aspects, understand the process, and find out actual mechanisms of mass transfer involved (Aguilera and Stanley 1999)."

As said, one virtue of this text is to compare Fickian (some write "Fickian") diffusion with capillarity, i.e., the tendency of liquids to be drawn into the confined space of a narrow tube or between at least two surfaces (Von Honschoten et al., 2010). The article considers the case of flow in porous media, generated by an interfacial pressure gradient (as when there is meniscus).

More generally, the article explains both phenomena of diffusion and capillarity, giving examples of food science or food technology where they occur, and it discusses some general equations for mass transfer. In both cases, a fast increase is followed by an asymptotical behaviour, but the slopes in the time-mass diagrams can be different. For the Fickian case, the ratio of the mass at instant t by the mass when equilibrium is reached is proportional to the square root of the time... and the same holds for capillarity as described through the Lucas-Washburn equation (Zhmud et al., 2000; De Gennes et al., 2004).

After discussing this, the articles goes on examining the experimental data obtained at the time it was published, in order to propose the importance of capillarity for liquid lipids ("oil") moving through the solid lipid framework ("a continuous phase of solid and liquid fat"). Here it should be added that other conclusions were favored later (Deka et al., 2006; Galdamez et al., 2009): observations of oil migration through chocolate using magnetic resonance imaging have shown that the dominant mechanism is
Commentary

two kinds of liquid droplet ($D_0$(O), $D_0$(W)) inside a continuous solid lipid matrix $D_3$(S) (IUPAC, 2009c), or a suspension if the oil phase is continuous. Metastabilizing phenomena such as supercooling effects can occur (Castro-Alayo et al., 2023), adding to the allotropy that is well known for lipid crystals, and the proportion and distribution of liquid and solid lipid fractions depend not only on the temperature, but also on the history of the product (Ronholt et al., 2014). Finally sintering of lipid crystals can make it likely that butter is a complex gel (continuous solid phase) when the temperatures are those at which butter is usually consumed by humans (Johansson and Bergenstahl, 1995; This, 2016).

As chocolate includes cocoa butter, the same question arise, concerning its microstructure: is it a suspension, or a gel, with respectively a continuous liquid lipid phase, or a continuous solid lipid phase? The melting curve of cocoa butter is narrower than the melting curve for butter (Figure 1), and here, the two solid contents to be considered for answering the question are 90 % at 15 °C, and 20 % at 30 °C. These values can be compared with the maximum packing coefficient (74 %) for spheres all of the same diameter, and the unlikely100 % value when spheres of all sizes are present (so called Apollonian packing) (Kasner and Supnick, 1943), or to other values when polydispersity is taken into account (Howe et al., 1997). Of course, the full packing is not possible, because one has to consider the presence of liquid lipids, and a 92 % maximum solid content is more realistic (Kwok et al., 2020).

Aguilera et al. seem to assume a suspension system, based on some articles that do not indicate the temperature at which their measurements were made (Loisel et al., 1997; Hartel, 1998; Babin et al., 2005; Hartel et al., 2016; Howard and Maleky, 2022), but keeping in mind the 92 % limit, and taking into account the sugar crystals and plant solid particles, which increase to solid volume fraction, one could doubt of their assumption. Indeed, lipid crystals can undergo sintering in chocolate as in butter (Johansson and Bergenstahl, 1995), and because chocolate is made from an initial melted mass

(during conching), percolation phenomena should be taken into account in order to envision a possible suspension-to-gel transition (De Gennes, 1979). Moreover the fact that "chocolate chantilly" (This vo Kientza, 2021b) can be obtained only when it is cooled corroborates the assumption that a continuous solid network is established at these temperatures (Figure 2).

Let us conclude temporarily this discussion by quoting the old controversy between Plato and Aristoteles: for Plato, chocolate would have been an entity, but for Aristoteles, "chocolate" does not exist, and there are rather chocolates... perhaps with different microstructures depending on the temperature at which they are stored.

Back to capillarity

Aguilera et al. promote the idea of capillarity as a mechanism for oil migration within the chocolate "matrix", but what is this matrix? As seen before, an important preliminary question is to know if

<figure><img src="image_2.png" /><figcaption>Figure 2. When an emulsion of chocolate in water is whipped, an aerated system called "chocolate chantilly" is obtained only when the system is cooled: this indicates that a continuous solid network is probably established, as these temperatures (This vo Kientza, 2021b).</figcaption></figure>
Commentary

diffusion, and that if capillary pressure is involved,
it is a minor contributor. However it is not the goal
of this commentary article to discuss this matter:
rather the chocolate microstructure is considered.
The authors describe chocolate as a "particulate
system", but what does it mean? And is it correct?
Comparing chocolate to butter is useful for a
better understanding of the microstructure of
chocolate.

Butter: which microstructure?

The composition of cocoa butter having been
given before, it has now to be observed, for
comparison, that the triglycerides content of milk
lipids is much more heterogeneous than for
chocolate, with a total number of fatty acid
residues reaching 400 (Jensen, 2002). The main
residues are: butyric, caproic, caprylic, capric,
auric, myristic, pentadecanoic, palmitic,
pamitoleic, margaric, stearic, oleic, linoleic,
linolenic.

In order to describe the microstructure of butter
(and of chocolate), it is convenient to use the
"dispersed system formalism" (This vo Kienza,
2021a), using the letters G, O, S, W respectively
for describing gas phases, liquid lipid phases
("oils"), solid phases (for example, ice, lipid
crystals, etc.) and aqueous solutions. The symbol
"/" stands for random dispersion, and the symbol
"x" describes the interweaving of two continuous
phases. For example, an emulsion is written O/W,
or W/O; a dispersion of liquid pockets inside a
solid is written O/S, or W/S, and a gelatin gel, with
two continuous phases, is described by SxW
(when the operator is commutative, the letters are
in the alphabetical order). When needed, the
physical "dimension" of the various objects being
considered is described by D₀, D₁, D₂, or D₃,
respectively for dimensions 0, 1, 2, 3, after a
reference size is chosen.

Using this formalism, it is possible to analyse what
many textbooks in food science and food
technology (Friberg et al., 2003; McClements,
2006; Khader, 2016) have been publishing, i.e.,
that butter is an "emulsion". According to the Gold

Book of IUPAC, an emulsion is "a fluid colloidal
system in which liquid droplets and/or liquid
crystals are dispersed in a liquid. The droplets
often exceed the usual limits for colloids in size".
Following the IUPAC definition, milk (from the
female of Bos taurus in particular) can be an
emulsion or not, depending on temperature.
Indeed milk is mainly a dispersion of lipids (as D₀
structures) in an aqueous solution D₃(W), but the
issue is to know what is the physical state of the
lipids: if they are in a liquid phase (O), then milk
is indeed an emulsion D₀(O)/D₃(W), but if they
make fully solid structures (D₀(S)/D₃(S)) or if they
make complex structures with both liquid and
solid phases, such as in a (D₀(S)@D₀(O))/D₃(S)
system, then milk would be a "suspension"
(IUPAC, 2009b; 2009c).

In order to decide which system describes milk,
one has to look at the melting curve of milk lipids
(Figure 1). At temperatures lower than - 10 °C,
milk lipids are entirely solid (as well as water),
and butter is a solid suspension D₀(S₁)/D₃(S₂), S₁
and S₂ standing respectively for ice and for solid
lipids, but at temperatures higher than 60 °C, all
the milk lipids are melted and butter is either an
emulsion (D₀(O)/D₃(W) or D₀(W)/D₃(O))
depending on the way it has been obtained) or a
biphasic liquid (D₃(O)σD₃(W)) (here σ stands for
superposition).

What about milk at "room temperature"? This is
not well defined, as the summer temperatures in
hot countries are very different from the
temperatures in cold countries in winter: at a
"room temperature" of 15 °C, the solid lipid
content would be slightly higher than 50 %, but
at a room temperature of 30 °C, it would be less
than 15 % (Jacques et al., 1999). Anyway, in
both cases, milk is a suspension (because of the
solid component of the dispersed structures)
rather than an emulsion.

From milk, cream is recovered, and butter is
produced by churning. After butter production,
some of the aqueous solution (limited to 16 % w
by international regulations) (EC, 1998) can
remain in the system, but the liquid lipid fraction
(O)/solid lipid fraction (S) ratio still depends on
temperature, and the system can be a "gel", with
Commentary

they assume that it is a continuous one. For sure,
capillarity can occur both with suspensions
between the solid particles, or with connected
gels, inside the solid network (This vo Kientza,
2021c), and mercury porosimetry can be
performed for the two systems (Loisel et al.,
1997). But another question is to know if
capillarity is occurring in the same way or
differently in the two kinds of systems? It is
interesting that whereas the chemical bonds
between the triglycerides of the liquid fraction and
the compounds making up the surface of the
"solids" in presence are highly determinant, as
well as the size of the "pores", the chemical
question is not discussed: the discussion in the
article is mainly from a physical point of view. For
sure, the classical dichotomy diffusion/capillarity is
well analyzed (even if there are other possibilities
than the Lucas-Washburn equation), but can the
oil migration be discussed without going down to
molecular description? And what about other
mechanisms, such as depletion mechanisms,
Ostwald ripening, etc. (Zhao and Tahkar, 2017)?
What about the influence of sugar crystals
(perhaps covered with a water layer) and plant
particles (Shen et al., 2023)?

All that being written, I shall continue to advise
students to read the article reviewed here, for it is
a direction in which they will not stray, in particular
if they go beyond what was written when it was
published (about 20 years ago): they will be
invited to use any word of the article as a
possibility to ask scientific questions, and to
discover the advances since the time of its
publication. They will be invited to question every
word and every concept, and to supplement their
reading with bibliographical research into recent
works on chocolate, in particular using new
analytical tools such as confocal microscopy,
electron miscrocopy, small angle X-ray or neutron
scattering (Metilli et al., 2020; Jeffries et al., 2021;
Pugh et al., 2023). But they will also be invited to
look beyond the physics-chemistry dichotomy and
always seek out the relationships between the two
separate descriptions: let's stand on our two feet,
physics *and* chemistry!

Two experiments are proposed, as a conclusion

to the discussion given here. The first is giving a
hint to the solution of the gel versus suspension
question: it consists in putting chocolate into oil;
as a suspension will be diluted, solid particles
would separate spontaneously, whereas a gel
will keep its structure. The second experiment is
to put a piece of chocolate in water, and to
observe the whitening of the surface. Why?
Indeed, chocolates (observe the plural) are still
wonderfully mysterious.

References

Aguilera JM, Michel M, Mayor G. 2004. Fat migration in chocolate: diffusion or capillary flow in a particulate solid?—A hypothesis paper, *Journal of food science*, 69(7), R167-174.

Bouteille R, Gaudet M, Lecanu B, This H. 2013. Monitoring lactic acid production during milk fermentation by in situ quantitative proton nuclear magnetic resonance spectroscopy, *Journal of Dairy Science*, 96(4), 2071-2080. DOI: 10.3168/jds.2012-6092.

Burke R, Kelly A, Lavelle C, This vo Kientza H. 2021. *Handbook of molecular gastronomy*, CRC Press, Boca Raton (FL). https://doi.org/10.1201/9780429168703.

Castro-Alayo EF, Balcazar-Zumaeta CR, Torrejon-Valquia L, Medina-Mendoza M, Cayo-Colca IS, Cardenas-Toro FP. 2023. Effect of tempering and cocoa butter equivalents on crystallization kinetics, polymorphism, melting, and physical properties of dark chocolates, *LWT - Food Science and Technology*, 173, 114402. DOI: 10.3390/foods11121769.

De Gennes PG. 1979. *Scaling concepts in polymer physics*, Cornell University Press, New York.

De Gennes PG, Brochard-Wyart F, Quere D.
Commentary

two kinds of liquid droplet (D₀(O), D₀(W)) inside a
continuous solid lipid matrix D₃(S) (IUPAC,
2009c), or a suspension if the oil phase is
continuous. Metastabilizing phenomena such as
supercooling effects can occur (Castro-Alayo et
al., 2023), adding to the allotropy that is well
known for lipid crystals, and the proportion and
distribution of liquid and solid lipid fractions
depend not only on the temperature, but also on
the history of the product (Ronholt et al., 2014).
Finally sintering of lipid crystals can make it likely
that butter is a complex gel (continuous solid
phase) when the temperatures are those at which
butter is usually consumed by humans
(Johansson and Bergenstahl, 1995; This, 2016).

As chocolate includes cocoa butter, the same question arise, concerning its microstructure: is it a suspension, or a gel, with respectively a continuous liquid lipid phase, or a continuous solid lipid phase? The melting curve of cocoa butter is narrower than the melting curve for butter (Figure 1), and here, the two solid contents to be considered for answering the question are 90 % at 15 °C, and 20 % at 30 °C. These values can be compared with the maximum packing coefficient (74 %) for spheres all of the same diameter, and the unlikely100 % value when spheres of all sizes are present (so called Apollonian packing) (Kasner and Supnick, 1943), or to other values when polydispersity is taken into account (Howe et al., 1997). Of course, the full packing is not possible, because one has to consider the presence of liquid lipids, and a 92 % maximum solid content is more realistic (Kwok et al., 2020).

Aguilera et al. seem to assume a suspension
system, based on some articles that do not
indicate the temperature at which their
measurements were made (Loisel et al., 1997;
Hartel, 1998; Babin et al., 2005; Hartel et al.,
2016; Howard and Maleky, 2022), but keeping in
mind the 92 % limit, and taking into account the
sugar crystals and plant solid particles, which
increase to solid volume fraction, one could doubt
of their assumption. Indeed, lipid crystals can
undergo sintering in chocolate as in butter
(Johansson and Bergenstahl, 1995), and because
chocolate is made from an initial melted mass

(during conching), percolation phenomena
should be taken into account in order to envision
a possible suspension-to-gel transition (De
Gennes, 1979). Moreover the fact that
"chocolate chantilly" (This vo Kientza, 2021b)
can be obtained only when it is cooled
corroborates the assumption that a continuous
solid network is established at these
temperatures (Figure 2).

Let us conclude temporarily this discussion by
quoting the old controversy between Plato and
Aristoteles: for Plato, chocolate would have been
an entity, but for Aristoteles, "chocolate" does not
exist, and there are rather chocolates... perhaps
with different microstructures depending on the
temperature at which they are stored.

Back to capillarity

Aguilera et al. promote the idea of capillarity as a
mechanism for oil migration within the chocolate
"matrix", but what is this matrix? As seen before,
an important preliminary question is to know if

<figure><img src="image_6.png" /><figcaption>Figure 2. When an emulsion of chocolate in water is whipped, an aerated system called "chocolate chantilly" is obtained only when the system is cooled: this indicates that a continuous solid network is probably established, as these temperatures (This vo Kientza, 2021b).</figcaption></figure>
Commentary

2004. *Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves*, Springer, Heidelberg (Germany, chapter 5).

Deka K, MacMillan B, Ziegler GR, Marangoni AG, Newling B, Balcom B. 2006. Spatial mapping of solid and liquid lipid in confectionery products using a 1D centric SPRITE MRI technique, *Food Research International*, 39, 365–371. DOI: 10.1016/j.foodres.2005.08.009.

EC. 1998. 98/582/EC: Council Decision of 6
October 1998 amending Commission Decision
97/80/EC laying down provisions for the
implementation of Council Directive 96/16/EC on
statistical surveys of milk and milk products,
Official Journal, L 281, 17/10/1998 P. 0036 - 0038.

Friberg S, Larsson K, Sjoblom J. 2003. *Food Emulsions*, CRC Press, Boca Raton (FL).

Galdamez JR, Szlachetka K, Duda JL, Ziegler GR. 2009. Oil migration in chocolate: A case of non-Fickian diffusion, *Journal of Food Engineering*, 92, 261–268. DOI: 10.1016/j.jfoodeng.2008.11.003.

Gülpinar O, Güçlü AG. 2023. How to write a review article?, *Turkish Journal of Urology*, 39(S1), 44-8. doi:10.5152/tud.2013.054.

Hartel RW. 1999. Chocolate: Fat bloom during storage. The influence of structural elements. *Manufacturing Confectioner*, 79(5), 89-99.

Hartel RW, Jin J, Jaures E. 2016. Particulate effects on storage bloom in chocolate, *Manufacturing Confectioner*, 96, 59-64.

Howard BD. 2020. *Shear and Composition Effects on Porous Network Properties and the Permeability of Lipid Films*, Master's thesis, Ohio State University, 2020.
http://rave.ohiolink.edu/etdc/view?
acc_num=osu1593680466745792.

Howard BD, Maleky F. 2022. Quantification of

Porous Properties of Shear Crystallized Lipids,
*Molecules*, 27, 631. DOI: 10.3390/molecules27030631.

Howe AM, Clarke A, Whitesides TH. 1997. Viscosity of emulsions of polydisperse droplets with a thick adsorbed layer, *Langmuir*, 13, 2617-2626. https://doi.org/10.1021/la960871f

IFST. 2023. *Oils and fats*,
https://www.ifst.org/resources/information-statements/oils-and-fats.

IUPAC. 2019a. diffusion, *Compendium of Chemical Terminology*, 2nd ed. (the "Gold Book"), 61, 2167.
https://doi.org/10.1351/goldbook.

IUPAC. 2009b. emulsions, *Compendium of Chemical Terminology*, 2nd ed. (the "Gold Book"), 62, 2167.
https://doi.org/10.1351/goldbook.

IUPAC. 2009c. suspensions, *Compendium of Chemical Terminology*, 2nd ed. (the "Gold Book"), 61, 2167.
https://doi.org/10.1351/goldbook.

IUPAC. 2009d. gels, *Compendium of Chemical Terminology*, 2nd ed. (the "Gold Book"), 61, 2167. https://doi.org/10.1351/goldbook.

Jacques H, Gascon A, Arul J, Boudreau A, Lavigne C, Bergeron J. 1999. Modified milk fat reduces plasma triacylglycerol concentrations in normolipidemic men compared with regular milk fat and nonhydrogenated margarine, *American Journal of Clinical Nutrition*, 70, 983-91. doi: 10.1093/ajcn/70.6.983.

Jeffries CM, Ilavsky J, Martel A, Hinrichs S, Meyer A, Pedersen JS, Sokolova AV, Svergun DI. 2021. mall-angle X-ray and neutron scattering, *Natural Reviews Methods Primers 1*, 70, https://doi.org/10.1038/s43586-021-00064-9.

Jensen RG. 2002. The composition of bovine
**Commentary**

they assume that it is a continuous one. For sure, capillarity can occur both with suspensions between the solid particles, or with connected gels, inside the solid network (This vo Kientza, 2021c), and mercury porosimetry can be performed for the two systems (Loisel et al., 1997). But another question is to know if capillarity is occurring in the same way or differently in the two kinds of systems? It is interesting that whereas the chemical bonds between the triglycerides of the liquid fraction and the compounds making up the surface of the "solids" in presence are highly determinant, as well as the size of the "pores", the chemical question is not discussed: the discussion in the article is mainly from a physical point of view. For sure, the classical dichotomy diffusion/capillarity is well analyzed (even if there are other possibilities than the Lucas-Washburn equation), but can the oil migration be discussed without going down to molecular description? And what about other mechanisms, such as depletion mechanisms, Ostwald ripening, etc. (Zhao and Tahkar, 2017)? What about the influence of sugar crystals (perhaps covered with a water layer) and plant particles (Shen et al., 2023)?

All that being written, I shall continue to advise students to read the article reviewed here, for it is a direction in which they will not stray, in particular if they go beyond what was written when it was published (about 20 years ago): they will be invited to use any word of the article as a possibility to ask scientific questions, and to discover the advances since the time of its publication. They will be invited to question every word and every concept, and to supplement their reading with bibliographical research into recent works on chocolate, in particular using new analytical tools such as confocal microscopy, electron miscrocopy, small angle X-ray or neutron scattering (Metilli et al., 2020; Jeffries et al., 2021; Pugh et al., 2023). But they will also be invited to look beyond the physics-chemistry dichotomy and always seek out the relationships between the two separate descriptions: let's stand on our two feet, physics and chemistry!

Two experiments are proposed, as a conclusion

to the discussion given here. The first is giving a hint to the solution of the gel versus suspension question: it consists in putting chocolate into oil; as a suspension will be diluted, solid particles would separate spontaneously, whereas a gel will keep its structure. The second experiment is to put a piece of chocolate in water, and to observe the whitening of the surface. Why? Indeed, chocolates (observe the plural) are still wonderfully mysterious.

**References**

Aguilera JM, Michel M, Mayor G. 2004. Fat migration in chocolate: diffusion or capillary flow in a particulate solid?—A hypothesis paper, *Journal of food science*, 69(7), R167-174.

Bouteille R, Gaudet M, Lecanu B, This H. 2013. Monitoring lactic acid production during milk fermentation by in situ quantitative proton nuclear magnetic resonance spectroscopy, *Journal of Dairy Science*, 96(4), 2071-2080. DOI: 10.3168/jds.2012-6092.

Burke R, Kelly A, Lavelle C, This vo Kientza H. 2021. *Handbook of molecular gastronomy*, CRC Press, Boca Raton (FL). https://doi.org/10.1201/9780429168703.

Castro-Alayo EF, Balcazar-Zumaeta CR, Torrejon-Valquia L, Medina-Mendoza M, Cayo-Colca IS, Cardenas-Toro FP. 2023. Effect of tempering and cocoa butter equivalents on crystallization kinetics, polymorphism, melting, and physical properties of dark chocolates, *LWT - Food Science and Technology*, 173, 114402. DOI: 10.3390/foods11121769.

De Gennes PG. 1979. *Scaling concepts in polymer physics*, Cornell University Press, New York.

De Gennes PG, Brochard-Wyart F, Quere D.
International Journal of Molecular and Physical Gastronomy
(IJMPG)

Commentary

milk lipids: January 1995 to December 2000,
*Journal of Dairy Science*, 85, 295-350. doi:
10.3168/jds.S0022-0302(02)74079-4.

Johansson D, Bergenstahl B.1995. Sintering of fat
crystal networks in oil during post-crystallization
processe, *Journal of the American Oil Chemist's
Society*, **72**(8), 911-920.
DOI:10.1007/BF02542069.

Kasner E, Supnick F. 1943. The Apollonian
packing of circles, *Proceedings of the National
Academy of Sciences*, 29 (11) 378-384.

Khader V. 2016. Textbook of food science and technology, *Indian Council of Agricultural Research*, New Delhi.

Kwok S, Botet R, Shglabow A, Cabane B. 2020. Apollonian emulsions. *EPL - Europhysics Letters*, 130 (3), 38001.

Lonchampt P, Hartel RW. 2004. Fat bloom in
chocolate and compound coatings, *European
Journal of Lipid Science and Technology*, **106**,
241-274. https://doi.org/10.1002/ejlt.200400938

Loisel C, Lecq G, Ponchel G, Keller G, Ollivon M. 1997. Fat bloom and chocolate structure studied by mercury porosimetry, *Journal of Food Science*, 62(4), 781-788.

Lopez C, Ollivon M. 2009. Triglycerides obtained by dry fractionation of milk fat. 2. Thermal properties and polymorphic evolutions on heating, *Chemistry and Physics of Lipids*, 159, 1-12.

McClements DJ. 2006. Food Emulsions, CRC Press, Boca Raton (FL).

Metilli L, Francis M, Povey M, Lazidis A, Marty-
Terrade S, Ray J, Simine E. 2020. Latest
advances in imaging techniques for characterizing
soft, multiphasic food materials, *Advances in
Colloid and Interface Science*, 279, 102154.
https://doi.org/10.1016/j.cis.2020.102154

Miquel ME, Carli S, Couzens PJ, Wille HJ, Hall
LD. 2001. Kinetics of the migration of lipids in
composite chocolate measured by magnetic
resonance imaging, *Food Research
International*, 34 (2001) 773-781.

Pugh MJ, Hamlett CAE, Fairhurst DJ. 2023. A
short overview of bubbles in foods and
chocolate, *Advances in Colloid and Interface
Science*, 314, 102835.
https://doi.org/10.1016/j.cis.2023.102835

Quéré D, Raphaël E, Ollitrault JY. 1999.
Rebounds in a capillary tube, *Langmuir*, 15 (10),
3679-3682.

Rønholt S, Kierkensgaard JJK, Mortensen K,
Knudsen JC. 2014. Effect of cream cooling rate
and water content on butter microstructure
during four weeks of storage, *Food
Hydrocolloids*, 34, 169-176.

Shen L, Jin J, Ye X, Li Y, Zhang C, Jiang L, Zhao
L. 2023. Effects of sucrose particle size on the
microstructure and bloom behavior of chocolate
model systems, *Food Structure*, 36, 100323.

Schenk H, Peschar R. 2004. Understanding the
structure of chocolate, *Radiation Physics and
Chemistry*, 71, 829-835.

This H. 2014. *Mon histoire de cuisine*, Belin,
Paris (France).

This H. 2016. What can “Artificial Meat” be?,
Note by note cooking offers a variety of answers,
*Notes Académiques de l'Académie d'agriculture
de France / Academic Notes from the French
Academy of Agriculture (N3AF)*, 2(4), 1-10.
https://doi.org/10.58630/pubac.not.a196614

This vo Kientza H. 2021a. DSF. In Burke R, Kelly A, Lavelle C, This vo Kientza H, *Handbook of molecular gastronomy*, CRC Press, Boca Raton (FL).

This vo Kientza H. 2021b. Chantillys. In Burke R,
Commentary

2004. *Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves*, Springer, Heidelberg (Germany, chapter 5).

Deka K, MacMillan B, Ziegler GR, Marangoni AG, Newling B, Balcom B. 2006. Spatial mapping of solid and liquid lipid in confectionery products using a 1D centric SPRITE MRI technique, *Food Research International*, 39, 365–371. DOI: 10.1016/j.foodres.2005.08.009.

EC. 1998. 98/582/EC: Council Decision of 6 October 1998 amending Commission Decision 97/80/EC laying down provisions for the implementation of Council Directive 96/16/EC on statistical surveys of milk and milk products, *Official Journal*, L 281, 17/10/1998 P. 0036 - 0038.

Friberg S, Larsson K, Sjöblom J. 2003. *Food Emulsions*, CRC Press, Boca Raton (FL).

Galdamez JR, Szlachetka K, Duda JL, Ziegler GR. 2009. Oil migration in chocolate: A case of non-Fickian diffusion, *Journal of Food Engineering*, 92, 261–268. DOI: 10.1016/j.jfoodeng.2008.11.003.

Gülpinar O, Güçlü AG. 2023. How to write a review article?, *Turkish Journal of Urology*, 39(S1), 44-8. doi:10.5152/tud.2013.054.

Hartel RW. 1999. Chocolate: Fat bloom during storage. The influence of structural elements. *Manufacturing Confectioner*, 79(5), 89–99.

Hartel RW, Jin J, Jaures E. 2016. Particulate effects on storage bloom in chocolate, *Manufacturing Confectioner*, 96, 59-64.

Howard BD. 2020. *Shear and Composition Effects on Porous Network Properties and the Permeability of Lipid Films*, Master's thesis, Ohio State University, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1593680466745792.

Howard BD, Maleky F. 2022. Quantification of

Porous Properties of Shear Crystallized Lipids, *Molecules*, 27, 631. DOI: 10.3390/molecules27030631.

Howe AM, Clarke A, Whitesides TH. 1997. Viscosity of emulsions of polydisperse droplets with a thick adsorbed layer, *Langmuir*, 13, 2617-2626. https://doi.org/10.1021/la960871f

IFST. 2023. *Oils and fats*, https://www.ifst.org/resources/information-statements/oils-and-fats.

IUPAC. 2019a. diffusion, *Compendium of Chemical Terminology*, 2nd ed. (the "Gold Book"), 61, 2167. https://doi.org/10.1351/goldbook.

IUPAC. 2009b. emulsions, *Compendium of Chemical Terminology*, 2nd ed. (the "Gold Book"), 62, 2167. https://doi.org/10.1351/goldbook.

IUPAC. 2009c. suspensions, *Compendium of Chemical Terminology*, 2nd ed. (the "Gold Book"), 61, 2167. https://doi.org/10.1351/goldbook.

IUPAC. 2009d. gels, *Compendium of Chemical Terminology*, 2nd ed. (the "Gold Book"), 61, 2167. https://doi.org/10.1351/goldbook.

Jacques H, Gascon A, Arul J, Boudreau A, Lavigne C, Bergeron J. 1999. Modified milk fat reduces plasma triacylglycerol concentrations in normolipidemic men compared with regular milk fat and nonhydrogenated margarine, *American Journal of Clinical Nutrition*, 70, 983–91. doi: 10.1093/ajcn/70.6.983.

Jeffries CM, Ilavsky J, Martel A, Hinrichs S, Meyer A, Pedersen JS, Sokolova AV, Svergun DI. 2021. mall-angle X-ray and neutron scattering, *Natural Reviews Methods Primers 1*, 70, https://doi.org/10.1038/s43586-021-00064-9.

Jensen RG. 2002. The composition of bovine
**International Journal of Molecular and Physical Gastronomy**
(IJMPG)

**Commentary**

Kelly A, Lavelle C, This vo Kientza H, Handbook of molecular gastronomy, CRC Press, Boca Raton (FL).

This vo Kientza H. 2021c. Gels. In Burke R, Kelly A, Lavelle C, This vo Kientza H, Handbook of molecular gastronomy, CRC Press, Boca Raton (FL).

This vo Kientza H. 2022. Calculating and problem solving through culinary experimentation, CRC Press, Boca Raton (FL), 237.

Van Honschoten JW, Brunets N, Tas NR. 2010. Capillarity at the nanoscale, Chemical Society Reviews, 39, 1096–1114. https://doi.org/10.1039/B909101G.

Zhao Y, Takhar PS. 2017. Freezing of Foods: Mathematical and Experimental Aspects. Food Engineering Reviews, 9, 1–12. https://doi.org/10.1007/s12393-016-9157-z.

Zhmud G, Tiberg F, Hallstensson K. 2002. Dynamics of capillary rise, Journal of Colloid and Interface Science, 228(2), 263-269.

**Edited by**

Volker Hessel, Professor in Sustainable Chemical Engineering, School of Chemical Engineering, Faculty of Sciences, Engineering and Technology University of Adelaide, Australia.

**Reviewed by**

1. Alan Kelly, professor at the School of Food and Nutritional Sciences, University College Cork, Cork (Ireland), vice-dean External Engagement and vice-head of the College of Science, Engineering and Food Science.

2. Paola Pittia, Professor at the University of Teramo (Italy), Delegate of the Rector for International Affairs.

**Received**

15 June 2022

**Published**

31 August 2023

**Cite as :**

This vo Kientza H. 2023. About Aguilera et al. (2004): chocolate, migration of lipids, diffusion and capillarity, *International Journal of Molecular and Physical Gastronomy*, 11, 1-9.
International Journal of Molecular and Physical Gastronomy
(IJMPG)

Commentary

milk lipids: January 1995 to December 2000,
*Journal of Dairy Science*, 85, 295-350. doi:
10.3168/jds.S0022-0302(02)74079-4.

Johansson D, Bergenstahl B.1995. Sintering of fat
crystal networks in oil during post-crystallization
processe, *Journal of the American Oil Chemist's
Society*, **72**(8), 911-920.
DOI:10.1007/BF02542069.

Kasner E, Supnick F. 1943. The Apollonian
packing of circles, *Proceedings of the National
Academy of Sciences*, 29 (11) 378-384.

Khader V. 2016. Textbook of food science and technology, *Indian Council of Agricultural Research*, New Delhi.

Kwok S, Botet R, Shglabow A, Cabane B. 2020. Apollonian emulsions. *EPL - Europhysics Letters*, 130 (3), 38001.

Lonchampt P, Hartel RW. 2004. Fat bloom in
chocolate and compound coatings, *European
Journal of Lipid Science and Technology*, **106**,
241–274. https://doi.org/10.1002/ejlt.200400938

Loisel C, Lecq G, Ponchel G, Keller G, Ollivon M. 1997. Fat bloom and chocolate structure studied by mercury porosimetry, *Journal of Food Science*, 62(4), 781-788.

Lopez C, Ollivon M. 2009. Triglycerides obtained by dry fractionation of milk fat. 2. Thermal properties and polymorphic evolutions on heating, *Chemistry and Physics of Lipids*, 159, 1–12.

McClements DJ. 2006. Food Emulsions, CRC Press, Boca Raton (FL).

Metilli L, Francis M, Povey M, Lazidis A, Marty-
Terrade S, Ray J, Simine E. 2020. Latest
advances in imaging techniques for characterizing
soft, multiphasic food materials, *Advances in
Colloid and Interface Science*, 279, 102154.
https://doi.org/10.1016/j.cis.2020.102154

Miquel ME, Carli S, Couzens PJ, Wille HJ, Hall
LD. 2001. Kinetics of the migration of lipids in
composite chocolate measured by magnetic
resonance imaging, *Food Research
International*, 34 (2001) 773-781.

Pugh MJ, Hamlett CAE, Fairhurst DJ. 2023. A
short overview of bubbles in foods and
chocolate, *Advances in Colloid and Interface
Science*, 314, 102835.
https://doi.org/10.1016/j.cis.2023.102835

Quéré D, Raphaël E, Ollitrault JY. 1999.
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Commentary
**International Journal of Molecular and Physical Gastronomy**
(IJMPG)

**Commentary**

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**Edited by**

Volker Hessel, Professor in Sustainable Chemical Engineering, School of Chemical Engineering, Faculty of Sciences, Engineering and Technology University of Adelaide, Australia.

**Reviewed by**

1. Alan Kelly, professor at the School of Food and Nutritional Sciences, University College Cork, Cork (Ireland), vice-dean External Engagement and vice-head of the College of Science, Engineering and Food Science.

2. Paola Pittia, Professor at the University of Teramo (Italy), Delegate of the Rector for International Affairs.

**Received**

15 June 2022

**Published**

31 August 2023

**Cite as :**

This vo Kientza H. 2023. About Aguilera et al. (2004): chocolate, migration of lipids, diffusion and capillarity, *International Journal of Molecular and Physical Gastronomy*, 9(1) 11, 1-9. DOI: 10.17180/ijmpg-2023-art11