---
author:
- Elena Blanco
- 'Daniel J. M. Hodgson'
- Michiel Hermes
- Rut Besseling
- 'Gary L. Hunter'
- 'Paul M. Chaikin'
- 'Michael E. Cates'
- Isabella Van Damme
- 'Wilson C. K. Poon'
bibliography:
- 'Blanco\_Conching2019.bib'
title: 'Conching chocolate: A prototypical transition from frictionally jammed solid to flowable suspension with maximal solid content'
---

he incorporation of liquid into dry powder with primary particle size in the granular range ($\sim 10$-) to form a flowing suspension with solid volume fraction $\phi \gtrsim 50\%$ is important in many industries [@Kaye1997]. Often, maximising solid content is a key goal. Cements for building or bone replacement and ceramic ‘green bodies’ are important examples, where higher $\phi$ improves material strength [@Green2004]. Another example is chocolate manufacturing, where high solid content (= lower fat [@Tao2016]) is achieved by ‘conching’.

Conching [@Gutierrez2017], invented by Rodolphe Lindt in 1879, is important for flavor development, but its major physical function is to turn an inhomogeneous mixture of particulates (including sugar, milk solids and cocoa solids) and cocoa butter (a triglyceride mixture) into a homogeneous, flowing suspension (liquid chocolate) by prolonged mechanical action and the staged addition of dispersants. In this paper, we focus on this effect, and seek to understand how mechanical action and dispersants together transform a non-flowing, inhomogeneous mixture into a flowing suspension, a process that has analogs in, e.g., the ceramics and pharmaceuticals sectors [@Kaye1997].

We find that the key physical processes are friction-dominated flow and jamming. Specifically, two of the key rheological parameters in chocolate manufacturing, the yield stress, $\sigma_\textrm{y}$, and the high-shear viscosity, $\eta_\textrm{2}$, are controlled by how far the volume fraction of solids, $\phi$, of the chocolate formulation is situated from the jamming volume fraction, $\phi_{\textrm{J}}$. We demonstrate that the first part of the conche breaks apart particulate aggregates, thus increasing $\phi_{\rm J}$ relative to the fixed mass fraction. In the second part of the conche, the addition of a small amount of dispersant reduces the inter-particle friction and further raises $\phi_{\rm J}$, in turn reducing $\sigma_{\rm y}$ and $\eta_2$, resulting in fluidization of the suspension, i.e. a solid to liquid transition. Such ‘$\phi_{\rm J}$ engineering’ is common to diverse industries that rely on the production of high-solid-content dispersions.

Shear thickening suspensions {#shear-thickening-suspensions .unnumbered}
============================

We first review briefly recent advances in granular suspension rheology [@Seto2013; @WC1; @WC2; @mari2014shear; @Guy2015; @Lin2015; @Royer2016; @Hermes2016; @Colin2017; @clavaud2017revealing]. The viscosity of a high-$\phi$ granular suspension increases from a low-stress Newtonian value when the applied stress, $\sigma$, exceeds some onset stress, $\sigma^\star$, reaching a higher Newtonian plateau at $\sigma \gg \sigma^\star$: the suspension shear thickens. The low- and high-stress viscosities, $\eta_1$ and $\eta_2$, diverge as $$\label{eq:krieger-dougherty}
  \eta_{\textrm{r}} = A \left( 1 - \frac{\phi}{\phi^\mu_{\textrm{J}}(\sigma)} \right)^{-\lambda},$$ where $\eta_{\textrm{r}} = \eta_{1,2}/\eta_0$ with $\eta_0$ the solvent viscosity, $A\simeq 1$, and $\lambda \simeq 2$ for spheres [@Maron1956; @KD1959]. The jamming point, $\phi_{\textrm{J}}$, is a function of both the inter-particle friction coefficient, $\mu$, and the applied stress, $\sigma$. The latter begins to press particles into contact when it exceeds $\sigma^\star$. With $\mu \to 0$, no shear thickening is observed, and $\eta_{\textrm{r}}$ diverges at random close packing, $\phi_{\textrm{J}} = \phi_{\textrm{rcp}}$. At finite $\mu$, the low-stress viscosity $\eta_1(\phi)$ still diverges at $\phi_{\textrm{rcp}}$, but $\eta_2(\phi)$, the high-stress viscosity, now diverges at some $\phi_{\textrm{J}} = \phi_{\textrm{m}}^\mu < \phi_{\textrm{rcp}}$. For monodisperse hard spheres, (a), $\phi_{\textrm{rcp}} \approx 0.64$ and $\phi_{\textrm{m}}^{\mu \to \infty} \approx 0.54$ (where ‘$\infty$’ in practice means $\mu \gtrsim 1$) [@silbert2010jamming; @mari2014shear]. (Below we drop the ‘$\mu$’ in $\phi_{\textrm{m}}^\mu$ unless it is needed.) A granular suspension at $\phi > \phi_{\textrm{m}}$ cannot flow at high stress either steadily or homogeneously [@Hermes2016]: it shear-jams [@WC2]. Instead, theory [@WC2] and experiments [@Hodgson2015] suggest that it granulates.

![(a) The high-shear viscosity of suspensions of granular hard spheres normalised by the solvent viscosity, $\eta_{\textrm{r}}$, plotted against the volume fraction $\phi$, with friction coefficient increasing from $\mu = 0$ (red), diverging at $\phi_{\textrm{rcp}}$, to $\mu \to \infty$ (blue), diverging at $\phi_{\textrm{m}}^{\mu \to \infty}$. Inset: The jamming volume fraction, $\phi_{\textrm{J}}$, where $\eta_{\textrm{r}}$ diverges, as a function of the coefficient of static friction $\mu$ (replotted from [@silbert2010jamming]). (b) The jamming state diagram of a frictional granular suspension with inter-particle adhesion. The adhesive strength is set by $\sigma_{\textrm{a}} \gg \sigma^\star$. Shaded region = jammed. The flow curve of a suspension with volume fraction $\varphi$ is shown in the inset: it has a yield stress $\sigma_{\textrm{y}}(\varphi)$.[]{data-label="fig:FrictionDependentPhiJ"}](Fig1a.pdf){width="0.72\columnwidth"}

![(a) The high-shear viscosity of suspensions of granular hard spheres normalised by the solvent viscosity, $\eta_{\textrm{r}}$, plotted against the volume fraction $\phi$, with friction coefficient increasing from $\mu = 0$ (red), diverging at $\phi_{\textrm{rcp}}$, to $\mu \to \infty$ (blue), diverging at $\phi_{\textrm{m}}^{\mu \to \infty}$. Inset: The jamming volume fraction, $\phi_{\textrm{J}}$, where $\eta_{\textrm{r}}$ diverges, as a function of the coefficient of static friction $\mu$ (replotted from [@silbert2010jamming]). (b) The jamming state diagram of a frictional granular suspension with inter-particle adhesion. The adhesive strength is set by $\sigma_{\textrm{a}} \gg \sigma^\star$. Shaded region = jammed. The flow curve of a suspension with volume fraction $\varphi$ is shown in the inset: it has a yield stress $\sigma_{\textrm{y}}(\varphi)$.[]{data-label="fig:FrictionDependentPhiJ"}](Fig1b.pdf){width="0.75\columnwidth"}

The onset stress, $\sigma^\star$, correlates with the force to overcome an inter-particle repulsive barrier; typically $\sigma^* \sim d^{-\nu}$ with $\nu \lesssim 2$, where $d$ is the particle diameter [@Guy2015]. For granular suspensions, $\sigma^{\star}$ is far below stresses encountered in liquid-powder mixing processes, so that they always flow with viscosity $\eta_2(\phi,\mu)$, which diverges at $\phi_\textrm{m} < \phi_\textrm{rcp}$. To formulate a flowable granular suspension with maximum solid content is therefore a matter of maximising $\phi_\textrm{m}$, e.g., by lowering $\mu$, (a) (inset).

Inter-particle adhesion introduces another stress scale, $\sigma_{\textrm{a}}$, characterising the strength of adhesive interactions [@guy2018constraint]. A yield stress, $\sigma_{\textrm{y}}$, emerges above some $\phi_{\textrm{a}}^\mu < \phi_{\textrm{m}}^\mu$ that is dependent on both adhesion and friction [@liu2017; @guy2018constraint] (hence the $\mu$ superscript, which, again, we will drop unless needed), and diverges at $\phi_{\textrm{m}}^\mu$.

Competition between friction and adhesion gives rise to a range of rheologies [@guy2018constraint]. If $\sigma^{\star}/\sigma_{\textrm{a}}\ll 1$, the suspension shear thins at $\sigma > \sigma_{\textrm{y}}$ to the frictional viscosity, $\eta_2$. The state diagram such a system is shown schematically in (b); the inset shows a typical flow curve. However, a suspension with $\sigma^{\star}/\sigma_{\textrm{a}}\gg1$ first shear thins at $\sigma > \sigma_{\textrm{y}}$, and then shear thickens as $\sigma$ exceeds $\sigma^\star$. Surfactants can increase $\sigma^{\star}/\sigma_{\textrm{a}}$ and change the first type of behavior to the second type [@brown2010].

![Schematic of a planetary mixer. A blade (bold) rotates inside a bowl, full circle, which counter rotates. Shearing occurs in the gap between the blade and the bowl. []{data-label="fig:Planetary"}](Fig2.pdf){width="0.45\columnwidth"}

Conching phenomenology {#conching-phenomenology .unnumbered}
======================

We worked with a simplified chocolate formulation of ‘crumb powder’ dispersed in sunflower oil with lecithin [@vanDamme2009]. For one experiment, we also added a second surfactant, polyglycerol polyricinoleate (PGPR). Crumb is manufactured by drying a water-based mixture of sucrose crystals, milk and cocoa mass followed by milling [@Beckett2003]. To perform a laboratory-scale conche, we used a planetary mixer, , to prepare batches. The total lecithin added was 0.83 wt%. In the first step, the ‘dry conche’, we mixed the solids with the oil and 0.166 wt% of lecithin (20% of the total) in the planetary mixer at $\approx 100$ rpm until the material smears around the bowl right after it has cohered into a single lump around the blade. At $\phi = 0.55$, this took $\approx \SI{40}{\minute}$. Then, for the ‘wet conche’, the remaining lecithin was added and mixed for a further 20 min.

Conched samples were prepared with solid concentrations in the range $0.4 \lesssim \phi \lesssim 0.6$, with $\phi$ calculated using measured densities (see Materials and Methods), so that a weight fraction of 74% converts to $\phi = 0.55$ (assuming all the fat contained in the crumb melts during conching). In each case, the flow curves of the as-conched sample as well as that of samples successively diluted with pure oil were measured using parallel-plate rheometry (see Materials and Methods).

(A-H) show the phenomenology of conching a mixture with solid volume fraction[^1] $\phi_0 = 0.55$ (or 74 wt.%) to which initially 20% of the final total of 0.83 wt.% of lecithin has been added; the accompanying plots show the power consumption of the planetary mixer as well as measured densities of the sample as conching proceeds. Almost immediately after addition of the sunflower oil to the crumb powder ($t=\SI{0}{\minute}$), all the liquid appeared to have been absorbed. The sample then proceeded to granulate, with the granule size increasing with time. The first granules were visually matt and dry, , A-C, and do not stick to each other during mixing.

[Fig3\_upper.pdf]{}

(26,50)[![*Top* Power consumption ([(0,0) – (0.3,0);]{}), skeletal density ([(0,0) – (0.3,0);]{}) and envelope density ([(0,0) – (0.3,0);]{}) as a function of mixing time for a typical model chocolate formulation with $\phi_{0} = 0.55$ ($\equiv$ 74 wt.%). Red box: the density of the grey shaded cluster is the skeletal density. Blue box: the average density inside the black dashed circle is the envelope density. Red dash line denotes time at which second shot of lecithin is added and the transition from dry to wet conche. *Bottom* Visual appearance of samples taken out of the planetary mixer at various stages of the conche. Letter labels correspond in the upper and lower panels. Scale bars are . Granule size increases A–E; by F, the granule size has diverged to the size of the system.[]{data-label="fig:conche"}](Fig3_upper_inset1.pdf "fig:"){height="1cm" width="1cm"}]{}

(34.5,18)[![*Top* Power consumption ([(0,0) – (0.3,0);]{}), skeletal density ([(0,0) – (0.3,0);]{}) and envelope density ([(0,0) – (0.3,0);]{}) as a function of mixing time for a typical model chocolate formulation with $\phi_{0} = 0.55$ ($\equiv$ 74 wt.%). Red box: the density of the grey shaded cluster is the skeletal density. Blue box: the average density inside the black dashed circle is the envelope density. Red dash line denotes time at which second shot of lecithin is added and the transition from dry to wet conche. *Bottom* Visual appearance of samples taken out of the planetary mixer at various stages of the conche. Letter labels correspond in the upper and lower panels. Scale bars are . Granule size increases A–E; by F, the granule size has diverged to the size of the system.[]{data-label="fig:conche"}](Fig3_upper_inset2.pdf "fig:"){height="1cm" width="1cm"}]{}

![*Top* Power consumption ([(0,0) – (0.3,0);]{}), skeletal density ([(0,0) – (0.3,0);]{}) and envelope density ([(0,0) – (0.3,0);]{}) as a function of mixing time for a typical model chocolate formulation with $\phi_{0} = 0.55$ ($\equiv$ 74 wt.%). Red box: the density of the grey shaded cluster is the skeletal density. Blue box: the average density inside the black dashed circle is the envelope density. Red dash line denotes time at which second shot of lecithin is added and the transition from dry to wet conche. *Bottom* Visual appearance of samples taken out of the planetary mixer at various stages of the conche. Letter labels correspond in the upper and lower panels. Scale bars are . Granule size increases A–E; by F, the granule size has diverged to the size of the system.[]{data-label="fig:conche"}](Fig3_lower.pdf){width="\columnwidth"}

The skeletal density of a material, (red-box inset in plot), is the mass of mesoscopic condensed phases (solids and liquids) it contains divided by the volume occupied by these phases, and therefore excludes externally connected air pores. The skeletal density sharply decreased during the first few minutes, converging rapidly to the system average bulk density of the solid and liquid components. The envelope density, (blue-box inset in plot), defined as the mass of a sample divided by its macroscopic volume, including air- and liquid-filled pores, increased over the first as the granules compacted, and converged to the skeletal density. The power consumption increased slowly.

After $\simeq \SI{15}{\minute}$ the granules became visibly moist and coalesced into larger ‘raspberry-like’ structures, (D), that somewhat resemble washing powder manufactured by granulation [@Salman2006]. The envelope density decreased slightly, presumably due to air incorporation as granules coalesced, and then remained constant: compactification had finished by stages E and F. The power consumption sharply peaked at $\simeq \SI{30}{\minute}$, when all of the material had formed into a ball adhering to the blade. Thereafter, the power consumption rapidly decreased, and the material became a paste that did not flow easily, (G). Soon after this (red dashed line in the plot) the remaining 80% of lecithin is added, and the ‘dry conche’ transitions to the ‘wet conche’. The sample rapidly fluidised into a glossy, pourable suspension, (H). A sharp decrease in power consumption accompanied this fluidisation.

Similar phenomenology is widely reported in wet granulation [@Salman2006], where liquid is gradually added to a dry powder to manufacture granules for applications ranging from agrochemicals to pharmaceuticals. A similar sequence of events to that in A-H is seen as the amount of added liquid increases. However, the system would typically become ‘overwet’, i.e. turn into a flowing suspension, at the peak of the power curve (equivalent to our stage F) [@Betz2003], rather than later (as in our case, at stage H). We note especially that there is a striking visual similarity in the time-lapsed images and power curves for concrete mixing at fixed liquid content [@cazacliu2009]. Such similarities across diverse sectors suggest that the incorporation of liquid into powder to form a flowing suspension via various stages of granulation may be underpinned by generic physics, which we seek to uncover through rheology.

Effect of conching on chocolate rheology {#sec:rheology .unnumbered}
========================================

() shows the flow curve, $\eta(\sigma)$, of a fully-conched crumb mixture with $\phi_0 = 0.54$ (73 wt.%). Below a yield stress, $\sigma_{\textrm{y}} \approx \SI{40}{\pascal}$, $\eta \to \infty$. Above $\sigma_{\textrm{y}}$ the sample shear thins towards a Newtonian plateau at $\lesssim \SI{5}{\pascal\second}$. However, just before reaching this value, the surface of the sample breaks up and it is no longer contained between the rheometer tools. This occurs at an approximately $\phi_0$-independent $\sigma_{\rm frac} \approx \SI{400}{\pascal}$, close to the stress, $\sim 0.1\Sigma/a$ ($\approx \SI{300}{\pascal}$ for our system with $a \approx \SI{10}{\micro\meter}$ and $\Sigma \approx \SI{30}{\milli\newton\per\meter}$), where particles may be expected to poke out of the free suspension-air interface [@brown2014shear].

![Model chocolate flow curves. (): $\sigma^{\star}/\sigma_{\textrm{a}} \ll 1$, crumb conched with lecithin ($\phi_0 = 0.55$). (): $\sigma^{\star}/\sigma_{\textrm{a}} \gg 1$; as before, but with PGPR. Intermediate curves for intermediate PGPR contents. Dashed lines guide the eye to high-shear viscosity at $\sigma > \sigma_{\textrm{frac}}$.[]{data-label="fig:rheology"}](Fig4.pdf){width="0.8\columnwidth"}

Interestingly, if PGPR is added together with the ‘second shot’ of lecithin at the beginning of the wet conche, a different rheology is obtained, (): $\sigma_{\textrm{y}}$ is dramatically lowered (here, to $\sigma_{\textrm{y}}^\prime \sim \SI{E-2}{\Pa}$), revealing shear thickening with an onset stress of $\sigma^\star \gtrsim \SI{2}{\pascal}$. This suggests that in the sample conched with lecithin only, shear thickening is masked [@brown2010; @guy2018constraint] by $\sigma_{\textrm{y}} > \sigma^\star$, but the high-shear viscosity is nevertheless the shear-thickened, frictional-contacts dominated $\eta_2$.

![(a) Relative high shear viscosity of chocolate suspensions [*vs*]{} solid volume fraction. (): $\eta_{\textrm{fc}}^{[\phi_0]}$, suspensions fully conched in the planetary mixer. *Filled circles*: Diluted fully-chonched suspensions: (): diluted from $\phi_0 = 0.596$. (): diluted from $\phi_0 = 0.586$. (): diluted from $\phi_0 = 0.576$. (): diluted from $\phi_0 = 0.536$. Matching-color vertical dotted lines: $\phi_{\rm m}$ from fitting to these four data sets. Thin red curves: with $\lambda = 1,73$ consistent with single open red circle data points. *Inset* Frictional jamming $\phi_{\textrm{J}}$ of chocolate suspensions as a function of the conched volume fraction $\phi_0$. Symbols as in main figure. (b) Replotted data of Lewis and Nielson [@lewis1968] for 30- glass spheres suspended in Aroclor, with each data set fitted to ; aggregate size increases from $\aleph$ and then A to K.[]{data-label="fig:dilution"}](Fig5a.pdf){width="0.73\columnwidth"}

![(a) Relative high shear viscosity of chocolate suspensions [*vs*]{} solid volume fraction. (): $\eta_{\textrm{fc}}^{[\phi_0]}$, suspensions fully conched in the planetary mixer. *Filled circles*: Diluted fully-chonched suspensions: (): diluted from $\phi_0 = 0.596$. (): diluted from $\phi_0 = 0.586$. (): diluted from $\phi_0 = 0.576$. (): diluted from $\phi_0 = 0.536$. Matching-color vertical dotted lines: $\phi_{\rm m}$ from fitting to these four data sets. Thin red curves: with $\lambda = 1,73$ consistent with single open red circle data points. *Inset* Frictional jamming $\phi_{\textrm{J}}$ of chocolate suspensions as a function of the conched volume fraction $\phi_0$. Symbols as in main figure. (b) Replotted data of Lewis and Nielson [@lewis1968] for 30- glass spheres suspended in Aroclor, with each data set fitted to ; aggregate size increases from $\aleph$ and then A to K.[]{data-label="fig:dilution"}](Fig5b.pdf){width="0.75\columnwidth"}

This high-shear viscosity, $\eta_{\textrm{fc}}^{[\phi_0]}$, of model chocolates fully-conched (fc) with lecithin at nine different solid fractions, $\phi_0$, is plotted in (a) (). In four cases, we successively diluted the conched samples and measured the high-shear viscosity along each dilution series, $\eta_{\textrm{fc}}^{[\phi_0]}(\phi)$. Each data set can be fitted to with $A=1$, (a) (solid lines), confirming what is already obvious from inspection, viz., that these data sets diverge at different points: $\phi_{\textrm{m}} = 0.639$ ($\lambda=1.88$) for $\phi_0 = 0.596$, $\phi_{\textrm{m}} = 0.627$ ($\lambda=1.78$) for $\phi_0 = 0.586$, $\phi_{\textrm{m}} = 0.612$ ($\lambda=1.72$) for $\phi_0 = 0.576$, $\phi_{\textrm{m}} = 0.562$ ($\lambda = 1.53$) for $\phi_0 = 0.536$. In each remaining case, we estimate $\phi_{\textrm{m}}$ without generating a full dilution series at each $\phi_0$ by fitting through each of the five $\eta_{\textrm{fc}}^{[\phi_0]}$ data points using the averaged exponent from the four full dilution series $\lambda = \bar \lambda = 1.73$, (a) (thin red curves).

Plotting all available pairs of $(\phi_0, \phi_{\textrm{m}})$, (a) (inset), confirms that $\phi_{\textrm{m}}$ increases as we conche the mixtures at higher solid fraction $\phi_0$. That is to say, conching at a higher solid fraction gives rise to a higher jamming volume fraction. There is, however, an upper bound to such $\phi_{\rm m}$ optimisation, which we can estimate by noting that, empirically, $\phi_{\textrm{m}}(\phi_0)$ is approximately linear in our range of $\phi_0$. A linear extrapolation shows that $\phi_{\textrm{m}} = \phi_0$ at $\phi_0^{\textrm{max}} \approx 0.8$. This is likely an overestimate: the approximately linear relation shown in the inset of (a) probably becomes sub-linear and perhaps saturates at higher $\phi_0$. Nevertheless, the existence of some $\phi_0^{\rm max} < 0.8$ beyond which conching will not increase $\phi_{\textrm{m}}$ seems to be a reasonable inference from our data.

Conching as jamming engineering {#sec:description .unnumbered}
===============================

Conching reduces aggregate size and increases $\phi_{\textrm{m}}$ {#conching-reduces-aggregate-size-and-increases-phi_textrmm .unnumbered}
-----------------------------------------------------------------

Interestingly, our observations may be interpreted in terms of an ‘inverse conching’ experiment performed some 50 years ago. Lewis and Nielsen [@lewis1968] measured the viscosity of 30- glass spheres suspended in Aroclor (a viscous Newtonian organic liquid) as a function of volume fraction, (b) (data set $\aleph$), and repeated the measurements with glass beads that have been increasingly aggregated by sintering before dispersal in Aroclor, (b), giving average number of primary particles in an aggregate $N$ of 1.8 (A), 5 (C), 8 (D), 12 (E) and 200-300 (K). Neutral silica in an apolar solvent likely has a vanishingly small $\sigma^\star$, so that Lewis and Nielsen were measuring $\eta_2(\phi)$, the shear-thickened viscosity, which diverges at $\phi_{\textrm{m}}$. Thus, $\phi_{\rm m}$ is clearly lowered by aggregation.

We interpret our data, (a), as ‘Lewis and Nielsen in reverse’. The primary particles in raw crumb are aggregated due to stacking in storage, moisture, etc. [@pietsch2004agglomeration]. Conching reduces aggregation and therefore increases $\phi_{\textrm{m}}$, with the effect being progressively more marked as the material is being conched at higher $\phi_0$. The latter effect is probably because the same external stress generates higher particle pressure at higher $\phi$ [@Boyer2011; @Hermes2016], which breaks up aggregates more effectively.

The linear relation in the inset of (a) extrapolates to a finite intercept at $(0, 0.11\pm0.02)$, suggesting that the viscosity of unconched crumb powder would diverge at $\phi_{\textrm{m}} = 0.11$. This value is perhaps unrealistically low: the real $\phi_{\textrm{m}}(\phi_0)$ dependence probably becomes sub-linear at low $\phi_0$ and saturates at some value $> 0.11$. Nevertheless, there seems little doubt that unconched, aggregated crumb suspensions jam at volume fractions considerably below those used for real chocolate formulations ($\phi_0 \gtrsim 0.55$). The change in aggregation during the liquid-powder mixing process is often monitored by laser light scattering. This method would not have separated Lewis and Nielsen’s samples $\aleph$, A, C, D and E. Highly accurate data at very low scattering angles are needed to distinguish $N$-mers with small $N$ even when the primary particles are quasi-monodisperse. (See the instructive study of monomers and dimers by Johnson [*et al.*]{} [@Johnson2005].) Similarly, light scattering will be at best a crude tool for studying conching. In fact, measuring changes in $\phi_{\textrm{m}}$ by rheology is likely a good, albeit indirect, method to detect changes in low $N$-mer aggregation.

![The conching process represented as shifts in the jamming state diagram (cf. (b)). (a) The formulation at $\phi_0$ is considerably more concentrated than the jamming point of the unconched suspension, $\phi_{\textrm{m}}^\mu(\mbox{init})$. (b) It granulates under mechanical agitation, simultaneously breaking up aggregates and increasing both $\phi_{\textrm{m}}^\mu$ and $\phi_{\textrm{a}}^\mu$, thus shifting the jamming boundary to the right. At the end of the dry conche, the suspension could in principle flow, $\phi_0 < \phi_{\textrm{m}}^\mu(\mbox{dry})$, but in fact cannot do so, because $\sigma_{\textrm{frac}} < \sigma_{\textrm{y}}(\mbox{dry})$. (c) Addition of the ‘second shot’ of lecithin reduces the inter-particle friction coefficient to $\mu^\prime < \mu$ and the adhesive interaction to $\sigma_{\textrm{a}}^\prime < \sigma_{\textrm{a}}$, thereby shifting the jamming boundary further to the right and down, dropping $\sigma_{\textrm{y}}(\mbox{wet})$ below $\sigma_{\textrm{frac}}$. Since $\phi_0$ is now considerably below $\phi_{\textrm{m}}^{\mu^\prime}\mbox{(wet)}$, the system is now a flowing suspension. []{data-label="fig:schematic"}](Fig6.pdf){width="0.9\columnwidth"}

From granules to flowing suspension {#from-granules-to-flowing-suspension .unnumbered}
-----------------------------------

We can now describe the whole conching process in terms of suspension rheology. Consider a crumb-oil-lecithin mixture at $\phi_0 = 0.576$, somewhat higher than in . The jamming point of the initial mixture at time $t = 0$, $\phi_{\textrm{m}}^\mu(\mbox{init})$, is substantially lower (our lower-bound estimate, the $y$-intercept of (a) (inset), being $0.11$). This initial mixture therefore cannot flow homogeneously. In state-diagram terms, the starting system is deep inside the jammed region, (a), where, under mechanical agitation, it granulates [@WC2], (B-D). The granulation process is controlled by the kinetics of cluster-cluster collisions and the mechanical properties of the clusters [@Iveson1998; @Iveson2001; @Salman2006]. In parallel, aggregates are being broken up, so that both $\phi_{\textrm{m}}^\mu$ and $\phi_{\textrm{a}}^\mu$ steadily increase, until $\phi_{\textrm{m}}^\mu$ just exceeds $\phi_0$.

At this point, we may expect the system to turn into a flowable suspension, albeit with a very high viscosity. This is indeed what happens in many systems: the power is observed to peak just as the material becomes (in granulation jargon) ‘overwet’ [@Betz2003], i.e. a flowing suspension with a shiny surface. In our case, at the power peak (stage F in ), the suspension still does not flow easily and appears visually matt. This is probably because the sample fractures before it can yield to flow homogeneously, i.e., $\sigma_{\textrm{y}} > \sigma_{\textrm{frac}}$ (cf. the earlier discussion of $\sigma_{\textrm{frac}}$ associated with ).

Further conching continues to increase $\phi_{\textrm{m}}$ until at the end of the dry conche, the yield stress, $\sigma_{\textrm{y}}(\mbox{dry})$, only just exceeds the fracture stress, $\sigma_{\textrm{frac}}$, (b). Here, the addition of the ‘second shot’ of lecithin has a dramatic effect. We suggest that this is because the additional lecithin lowers $\mu$ and $\sigma_{\textrm{a}}$ to $\mu^\prime$ and $\sigma_{\textrm{a}}^\prime$. The jamming boundary abruptly shifts to the right and drops down, (c). The resulting dramatic lowering of the yield stress to $\sigma_{\textrm{y}}(\mbox{wet}) < \sigma_{\textrm{frac}}$ in a system where, now, $\phi_0$ is considerably below $\phi_{\textrm{m}}(\mbox{wet})$, immediately produces a flowing suspension, liquid chocolate.

Lecithin as a lubricant {#lecithin-as-a-lubricant .unnumbered}
-----------------------

We have suggested that the lecithin added in the ‘second shot’ lowers $\mu$ and therefore increases both $\phi_{\textrm{m}}^\mu$ and $\phi_{\textrm{a}}^\mu$. To provide direct experimental evidence for this role, we prepared a dry conche with the first shot of lecithin omitted, which again produced a non-flowing paste. Various amounts of lecithin was mixed into aliquots of this paste, which liquified. The high-shear viscosity, $\eta_2$, of the resulting suspensions decreases with lecithin concentration, . To check that this was not due to the oils in lecithin lowering the sample volume fraction, we repeated the experiment added an equivalent volume of oil corresponding to the maximum lecithin concentration (1.4%). This failed to liquify the paste. We may therefore conclude that lecithin causes this effect by lowering $\mu$ and so increasing the jamming point, $\phi_{\textrm{J}} = \phi_{\textrm{m}}^\mu$, (inset).

![High-shear viscosity of model chocolate at $\phi_0 = 0.557$ dry-conched without lecithin as a function of subsequently-added lecithin. []{data-label="fig:RoleOfLecithin"}](Fig7.pdf){width="0.7\columnwidth"}

Summary and conclusions {#summary-and-conclusions .unnumbered}
=======================

Creating flowable solid-in-liquid dispersions of maximal solid content is a generic goal across many industrial sectors. We have studied one such process in detail, the conching of crumb powder and sunflower oil into a flowing model chocolate. We interpreted our observations and measurements using existing knowledge from the granulation literature as well as an emerging new understanding of shear thickening and jamming in granular dispersions. The resulting picture is summarised in . The essential idea is that conching, and more generally wet milling, is about ‘jamming engineering’ – manipulating $\phi_{\textrm{m}}^\mu$ and $\phi_{\textrm{a}}^\mu$ by changing the state of aggregation, and ‘tuning’ the inter-particle friction coefficient $\mu$ and the strength of inter-particle adhesion, $\sigma_{\textrm{a}}$. Importantly, many additives ostensibly acting as dispersants to reduce inter-particle attraction and so lower $\sigma_{\rm a}$ may, in fact, function primarily as lubrications to lower $\mu$ and so increase $\phi_{\rm m}$. Our scheme, , with appropriate shifts in $\sigma_{\textrm{frac}}$, can be used to understand liquid incorporation into powders in many different specific applications.

Our proposed picture for conching/wet milling poses many questions. For example, the rheology of a suspension at the end of dry conche, in which flow is in principle possible ($\phi_0 < \phi_{\textrm{m}}$) but in practice ruled out by surface fracture occurring before bulk yielding, has not yet been studied in any detail. Neither is the role of changing $\phi_{\textrm{m}}$ during the granulation process understood. Our results therefore constitute only a first step towards a unified description of liquid incorporation, wet milling and granulation.

[^1]: That is, the ratio of solid volume to total solid plus liquid volume, discounting any air that may be present; this differs from the granulation literature, where the air is typically taken into account.
