# Nanoprecipitation through solvent-shifting using rapid mixing: Dispelling the Ouzo boundary to reach large solute concentrations

Kevin Roger, Nataliya Shcherbakova, Lison Raynal

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Kevin Roger, Nataliya Shcherbakova, Lison Raynal. Nanoprecipitation through solvent-shifting using rapid mixing: Dispelling the Ouzo boundary to reach large solute concentrations. Journal of Colloid and Interface Science, 2023, 650, pp.2049-2055. 10.1016/j.jcis.2023.07.065. hal-04276955

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# Nanoprecipitation through solvent-shifting using rapid mixing: Dispelling the Ouzo boundary to reach large solute concentrations

Kevin Roger*, Nataliya Shcherbakova, Lison Raynal

Laboratoire de Génie Chimique, Université de Toulouse, CNRS, INPT, UPS, Toulouse, 31432, France

## GRAPHICAL ABSTRACT

<figure><img src="image_2.png" /></figure>

## ARTICLE INFO

**Keywords:**

Nanoprecipitation

Mixing

Continuous flow

Kinetics

Phase diagram

Ouzo

Boundary

Solvent-shifting

## ABSTRACT

**Hypothesis:** The addition of a non-solvent to a solute in good solvent solution leads to nanoprecipitation, which is the spontaneous formation of nanodomains. Yet, increasing solute concentration usually leads to the formation of macrodomains that quickly separate into a bulk phase, which is a severe process limitation. The corresponding concentration threshold, often termed as the Ouzo boundary, remains a mystery that could find its origin in the complex interplay between nanoprecipitation and mixing.

**Experiments:** We performed a systematic investigation of nanoprecipitation thermodynamics and kinetics as well as its interplay with mixing hydrodynamics for the hexadecane-acetone-water system, in the presence of the non-ionic $C_{16}EO_8$ surfactant. The binodal curve and its underlying tie-lines were obtained using Raman spectroscopy, allowing the computation of the spinodal curve. Kinetics were probed using a continuous flow setup that combines two sequential rapid mixers. The impact of mixing efficiency was probed systematically by varying the oil concentration for respectively slow and rapid mixing, while the uncoupling from mixing and nanoprecipitation was quantified by modifying systematically the flow rate in a continuous flow approach.

**Findings:** We elucidate the nature of the Ouzo boundary that marks the maximal solute concentration leading to nanoobjects. Rather than a thermodynamic boundary, as evidenced by its uncorrelation to the spinodal curve, it results from the coupling of nanoprecipitation and mixing when both processes occur within the same time range, leading to heterogeneous conditions and the escape of some objects to the macroscale. Increasing the solute concentration speeds up nanoprecipitation and thus requires increasingly faster mixing times to uncouple both processes. Accordingly, if the mixing efficiency is large enough, it is possible to dispel the Ouzo boundary and reach very large solute concentrations. Implementing rapid mixing strategies in continuous flow approaches is thus the solution to overcome the most stringent condition of nanoprecipitation and open the way to scale-
# 1. Introduction

Nanoprecipitation by solvent-shifting, the Ouzo effect, is a bottom-up approach to spontaneously obtain colloidal particles [1,2]. In practice, a solute is first molecularly dissolved in a good solvent, to which is then added a non-solvent that is miscible with the good solvent. This triggers precipitation, which can be constrained to the colloidal scale in the presence of interfacially active species such as surfactants [3,4] or polymer end-groups [5], which hinder aggregation [2,6–8]. Despite its apparent simplicity, which notably does not require any mechanical energy input or chemical reactions to obtain nano-objects, the Ouzo effect suffers from a severe practical shortcoming. Indeed, increasing the solute concentration above typically 0.01% usually results in rapid macroscopic phase separation. This concentration threshold was recognized in the earliest works by Katz, Ganachaud, and coworkers on the topic 20 years ago and named the ‘Ouzo boundary’, a curve separating the ‘Ouzo domain’ in which nanoobjects are obtained from macroscopic phase separation [2,1,9,10]. The nature of this boundary has been a matter of debate, with some works arguing that it matched the spontaneous decomposition boundary [1], or spinodal curve, and others showing instead that these two boundaries were not matching [2]. This latter conclusion was reinforced by a kinetic study by Roger and coworkers evidencing that the Ouzo effect proceeded by nucleation/aggregation rather than nucleation followed by monomer growth [6,7]. Therefore, a mechanistic understanding of this Ouzo boundary remains lacking, which considerably limits the industrial applications of the Ouzo effect. Nevertheless, the COVID-19 pandemic brought to light lipid-based nanocarriers of mRNA, which are precisely made by the Ouzo effect. Indeed, the process involves the mixing of an ethanolic solution of lipids with an aqueous solution of the polynucleotide, leading to the spontaneous precipitation of lipids, followed by their self-assembly, concomitantly with the complexation of the polynucleotide by cationic lipids [11,12]. Actually, the Ouzo effect is a unique method to produce various nanocomposites [9,13–15] through multiple assembly processes, as pioneered by Ganachaud and coworkers, which would be hardly achievable using mechanical means. In the case of high-end products such as vaccines, this advantage can be sufficient to overcome industrially the low concentration constraint. Still, to really deploy its generic potential, a solution must be found to achieve larger concentrations. In this respect and in contrast with most of the literature, the extensive research effort by the Prud’homme group did not really evidence this Ouzo boundary. The objects were found to grow larger when increasing solute concentrations but nanoobjects were still obtained up to 1% of solute [16]. The major difference lies in the processing of the Ouzo effect, which was performed using a continuous flow method and rapid mixers in the Prud’homme group, while most other groups use batch methods with basic mixing tools. This brings out an interesting question when dealing with the Ouzo effect, which is why hydrodynamics would impact a spontaneous process that relies on molecular interactions for making the particles and stabilizing them. The purpose of this work is to answer this question, in close relationship with elucidating the nature of the Ouzo boundary. To achieve this, we will first present a thermodynamic characterization of the model system we investigate, water-acetone-hexadecane. The resulting phase diagram will settle the issue of the spinodal curve vs. Ouzo boundary. Then, we will characterize the kinetics of the Ouzo effect by an original ex-situ method, which will highlight the millisecond timescale associated with the Ouzo effect. Since a stabilizer is needed to maintain droplets in a metastable state, we deliberately added a known amount of a purified surfactant, $C_{16}EO_8$, at an acidic pH = 2 to avoid any influence from the well-documented fatty acid impurities that otherwise adsorb

at oil/water interfaces [4]. From the characterization of nanoprecipitation kinetics, we will then examine the interplay of hydrodynamics and nanoprecipitation by investigating the impact of varying mixing efficiency and solute concentration on the final objects’ size. This will demonstrate how the simultaneous control of hydrodynamics and physical chemistry enables reaching high solute concentration, and thus boost up the range of applicability of the Ouzo effect.

# 2. Materials and methods

## 2.1. Materials

Hexadecane (>99% purity), Acetone (>99.9% purity, HPLC grade), Hydrochloric Acid were purchased from Merck. We used milli-Q water obtained from a purelab option Q device. Octaethylenehexadecyl ether ($C_{16}EO_8$) was purchased from Nikko Chemicals.

## 2.2. Continuous flow setup

We used tangential millifluidic mixers as described in a previous work [17]. Each unit consists of four inlets meeting tangentially in a mixing chamber and exiting orthogonally, as first described by Hartridge and Roughton. We prepared an aqueous solution at pH = 2 by adding an adequate amount of hydrochloric acid in milliQ water, while the organic solution was prepared by dissolving hexadecane and $C_{16}EO_8$ in acetone. These two solutions were pushed through a mixer by using Nemsys syringe pumps (Cetoni Gmbh), with adjustable flow rates.

## 2.3. Light scattering for droplet size assessment

Droplet size distributions of emulsions were measured using a static light scattering instrument (Mastersizer 3000, Malvern) with a 633 nm laser wavelength. An emulsion sample was diluted in circulating water until an obscuration value between 1 and 10% was obtained, in order to avoid multiple scattering. The average droplet diameter was determined as the volume-surface mean diameter $d[3,2]$ or Sauter diameter. Each measurement was repeated in triplicate at room temperature.

## 2.4. Binodal curve determination

Tie-lines were determined by separating the two phases and then analyzing them using Raman spectroscopy. We compared systematically the spectra obtained with a calibration matrix obtained by measuring the Raman spectra of ternary mixtures of known concentrations. Since acetone, water and hexadecane display distinct spectral signature, this procedure was highly precise. We also determined the envelope of the binodal curve by first preparing a mixture in the two-phase region and then adding acetone until the mixture became transparent. These two methods were highly consistent. In contrast, the determination of the binodal curve by looking at the onset of turbidity when adding water to an acetone-hexadecane solution lead to a significant offset.

## 2.5. Computation of the spinodal curve

Computing the spinodal curve is straightforward once an expression of the system’s free energy is obtained. Indeed, the spinodal curve is just a locus of points where the Hessian of the free energy is singular. However, obtaining this expression is much more challenging. Our strategy was to first obtain a high-quality data set composed of 14 tie-lines. Then we used a modified Flory-Huggins equation, containing a
<figure><img src="image_3.png" /><figcaption>Fig. 1. Hexadecane/Acetone/Water phase diagram. A) The ternary phase diagram was determined experimentally by measuring with Raman spectroscopy the binodal curve (green line) as an ensemble of tie-nodes connected by a tie-line (dotted black lines). This method is consistent with a determination of the curve's envelope by solubilization observations (grey dots). The numerical derivation of this ensemble of tie-lines leads to a free energy model that reproduces with accuracy the experimental binodal curve as shown by the numerical tie-lines (grey lines). The spinodal curve is then readily obtained (orange line). Note that this phase diagram displays two miscibility gaps (dotted red line) on the binary axis hexadecane-water and acetone-water. B) The same diagram can be plotted using a semi-log scale, which is more adequate to describe the solute concentration range that can be used. Blue lines represent dilution lines upon water addition with the final point corresponding to the experiments performed in this manuscript ($\phi_{water}$ = 0.75). The Ouzo boundary reported from literature [13] is also plotted as a purple line.</figcaption></figure>

triple interaction term to compensate for the simplifying hypothesis of the unmodified model, notably that binary coefficients are composition-independent and that volume is conserved. The excess free energy of mixing per volume unit is then:

$$g = \phi_w \ln \phi_w + \frac{1}{N_a} \phi_a \ln \phi_a + \frac{1}{N_h} \phi_h \ln \phi_h + \chi_{wa} \phi_w \phi_a + \chi_{wh} \phi_w \phi_h + \chi_{ah} \phi_a \phi_h + \beta \phi_w \phi_a \phi_h$$

with $N_a$ and $N_h$ are the number of segments in the molecules of acetone and hexadecane with respect to the water segment, $\chi_{ij}$, $i, j \in \{a, w, h\}$ are binary interaction coefficients and $\beta$ corresponds to the additional triple interaction term. The model depends linearly on 6 scalar parameters that are assumed to be constant, $\chi_{ij}$, $\beta$, $N_a^{-1}$ and $N_h^{-1}$. We found these parameters by solving a non-linear optimization problem associated to a specially constructed minimization criterion which takes into account the intrinsic geometry of the binodal curve, in particular its relation to the one-parametric family of connodal points on the graph of the energy surface associated to the function $g$.

From the final expression of $g$, the computation of binodal and spinodal curves simply consists in the integration of systems of ordinary differential equations. A detailed description of this method can be found in a recent work [18]. In particular, by choosing the mole fractions $\phi_a$ and $\phi_h$ as independent variables, the spinodal curve turns to be the integral curve of the vector field ($\nabla_{\phi} H)^{\perp}$, where $H$ is the Hessian of $g$:

$$H = \left[ \frac{\partial^2 g}{\partial \phi_i \partial \phi_j} \right]_{i,j \in a,h}$$

All computations were realized using Mathematica 9 package.

### 3. Results and discussion

#### 3.1. Equilibrium phase diagram, boundaries and pathways

From a thermodynamic standpoint, nanoprecipitation corresponds to the phase separation of a ternary mixture. More specifically, the ternary mixture consists of two incompatible species, the solute and the non-solvent, that are both compatible to a significant extent with

a third species, the solvent. Starting from a solution of the solute in the good solvent, the addition of the non-solvent will ultimately lead to phase separation when crossing the solubility boundary. Each phase will display a composition given by the two nodes of the tie-line, and the solubility boundary is thus also termed the binodal curve. A second thermodynamic boundary exists at higher contents in the non-solvent, and corresponds to the vanishing of the nucleation barrier that must be crossed by the system to effectively undergo phase separation. In contrast with the binodal curve, which tells at which composition phase separation becomes the equilibrium state, this spinodal curve thus rather tells at which composition phase separation proceeds without any kinetic barriers. A longstanding issue when dealing with the Ouzo effect has been the relationship between the spinodal curve and the so-called Ouzo boundary, the latter being a phenomenological boundary corresponding to the sharp increase in particle size. Yet, the spinodal curve can not be simply assessed experimentally, and must rather be calculated from the system's free energy. The latter can be obtained from knowing the binodal curve if one really determines tie-lines and not simply the envelope of the boundary.

We thus measured systematically the binodal curve of our system, hexadecane-acetone-water, by making samples at different water content in the two-phase regions, and then by characterizing the composition of each separating phase by Raman spectroscopy. We verified that the resulting binodal curve matched the envelope determined by observing the redissolution of all species into a single phase upon adding acetone. We would like to stress here, that this method should always be preferred to its more common opposite, which is monitoring the amount of water necessary to trigger phase separation. Indeed, the kinetic barrier to precipitation is much stronger than to dissolution. The two methods thus yield two different boundaries, with a significant offset. But only the dissolution method yields an envelope consistent with the proper determination of dozens of tie-lines and their conjugated nodes.

The results are displayed in Fig. 1A in a triangular plot. In contrast with the simplest case usually displayed in textbooks (one miscibility gap), one may observe that our phase diagram is slightly more complex (two miscibility gaps, displayed as dotted red lines in Fig. 1A). The underlying reason is that hexadecane is not fully miscible with
acetone, resulting in a miscibility gap on the binary axis hexadecane-acetone (displaying an upper critical separation temperature UCST at around 27°C [19]), in addition to the expected gap on the binary axis hexadecane-water. At ambient temperature, the two gaps extend in the ternary mixture and merge into a single two-phase region, while no critical point is observed. Tie-lines slopes are also significantly impacted, with the practical result that the phase separation results in a phase comprised nearly of pure oil and another consisting of acetone and water. This important data set allows extracting with confidence an expression of the free energy, which we chose as a modification of the Flory-Huggins expression with a ternary cross-term for simplicity. From this expression, the spinodal curve is readily calculated. It is useful at this stage to redraw the diagram in a semi-log plot, see Fig. 1B, as is often done when investigating nanoprecipitation by solvent-shifting. On this plot, we have also drawn some tie-lines and some dilution lines, which both display unusual shapes due to the semi-log scale. We also plotted the Ouzo boundary determined by Fu et al. some years ago using light scattering [13]. As discussed in the past for other systems, there is no clear correlation between the spinodal curve and the Ouzo boundary, neither in shape nor in location. We would thus like to stress again and definitively that the spinodal curve does not underlie a change from small particles to large particles when performing solvent-shifting. To express it otherwise, the formation of well-defined nanoparticles does not coincide with a composition located in between the binodal and the spinodal curve and is often associated with nucleation followed by a monomer growth mechanism. Such a fact is consistent with the in situ monitoring of the nanoprecipitation process that we performed a decade ago and evidencing that growth proceeds through a nucleation-aggregation process [6].

We are then still left at this stage with a phenomenological boundary, the Ouzo boundary, of practical importance, as it severely limits the achievable solute concentration, which can not be explained by thermodynamics although the process is primarily triggered by thermodynamics. To explain this apparent paradox, we will first shed some elements of the process kinetics.

## 3.2. Kinetics of droplets formation

The Ouzo effect proceeds notoriously fast, and is often described as occurring 'instantaneously'. Of course, nothing is instantaneous and this expression actually means that it occurs faster than a human experimentalist can monitor. It is consistently delicate to probe its exact time scale, with one past attempt made by small-angle X-ray scattering with a stopped-flow device for a PMMA-water-acetone mixture [6]. There, the kinetics were probed from 10 ms to 1 s, at which growth was nearly achieved, so that the whole process can be termed as a sub-second one. Yet, during the same beamtime, we never managed to characterize the kinetics of the hexadecane-water-acetone system. Indeed, from the first data point at around 10 ms, we obtained the same scattering curve as for the latter times. This means that the time scale must be much shorter than for polymers. Here, we would like to present an alternate experimental approach, which consists in estimating kinetics through an arrest strategy. The idea is that the amount of stabilizer, here the surfactant $C_{16}EO_8$, controls to some extent the final size at which droplets are metastable. Comparing two surfactant concentrations, all other parameters being constant, we indeed observe a significant change in the droplet size. Now, if one triggers solvent-shifting at a low surfactant concentration but then injects a higher surfactant concentration at a later time, two situations are expected. Firstly, if the surfactant is injected much later than the formation of droplets, the droplet size will not change. In practice, the excess surfactant arrived too late to cover the forming interfaces and thus restrain growth. Secondly, if the surfactant is injected much faster than the formation of droplets, the droplet size will be the one obtained if all the surfactant was present from the start.

<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Probing formation kinetics. The use of two sequential rapids mixers allows probing nanoprecipitation kinetics ex-situ. For this, nanoprecipitation is triggered at the first mixer and is arrested at a second mixer, adjusting the tubing length between the two mixers, by injecting a large surfactant excess. The reference at time 0 corresponds to the injection of surfactant excess at the first mixer. At time towards infinity, it corresponds to the addition of the excess surfactant after 1 min. While this experiment does not tell us about the initial stage of nanoprecipitation, nor about the true kinetic law, it does provide the characteristic formation time. For instance, we observe for the chosen set of conditions that after 10 ms, the nanodroplets are nearly completely formed. The main advantage of this approach compared to previously performed kinetic monitoring with synchrotron SAXS experiments [6] is its comparative simplicity.</figcaption></figure>

Experimentally, this strategy is not straightforward to deploy but we have precisely recently developed a continuous-flow setup that enables us to perform rapid sequential additions [17,20]. The setup consists of two rapid mixers in series (see Fig. 2A), with the first mixer adding a water-surfactant solution to a hexadecane-acetone solution and the second mixer adding a more concentrated water-surfactant solution to this mixture. By modulating the length of tubing between the two mixers, it is possible to modulate the delay separating the addition of an excess of surfactant. The two extreme cases are easily obtained by adding the surfactant either all at once or a few minutes after initial precipitation. Fig. 2B displays all the corresponding results, showing that the final mean diameter increases with delaying the excess surfactant addition. As expected, the two extreme cases lead to respectively the minimum and the maximum achievable sizes for this set of conditions. While this data set does not give us directly the true kinetic law, it yields the characteristic time at which the system is not influenced anymore by a change in composition. From the data, we see that the mean diameter is nearly at its maximal value at around 10 ms, so we can conclude that the overall kinetics proceed faster than this. Interestingly, this is consistent with our previous experience using in situ SAXS monitoring in a stopped-flow cell, which did not seem to evolve after the first point obtained at 10 ms.

From this emerges the interesting observation that if all conditions are constant otherwise, the nanoprecipitation of polymers proceeds comparatively slower than the nanoprecipitation of short oils.
This observation may notably have practical consequences when co-
precipitating oils and polymers in a single solvent-shifting process.

We will now turn to the implication of such small time scales re-
garding the mixing of the two fluids and its interplay with the Ouzo
boundary or said otherwise the limitation of nanoprecipitation to small
concentrations.

3.3. *The Ouzo boundary and its relationship to mixing efficiency*

So far, we have presented the physical chemistry, thermodynam-
ics and kinetics, of the phase separation process triggered by solvent-
shifting, the Ouzo effect. An interesting idea at this stage is that nano-
precipitation may proceed within 10 ms in rather dilute conditions but
ultimately requires first that the different species are brought in con-
tact to obtain the (unstable) ternary solution. This requires the mixing
of two liquid streams, which means that hydrodynamics should also be
considered. Indeed, two characteristic times are in fact at play, one re-
lated to nanoprecipitation itself, t_nano, that was quantified above, and
one related to mixing, t_mix, that rather describes how fast a homoge-
neous mixture would be achieved (even if ultimately unstable) [8].
The relative value of these two characteristic times determines whether
nanoprecipitation proceeds in homogeneous conditions (t_mix < t_nano)
or rather in heterogeneous ones (t_mix > t_nano). Indeed, if nanoprecipita-
tion occurs simultaneously with mixing, the local composition will vary
over the whole sample and precipitation conditions will thus become
spatially dependent [7].

In practice, the existing literature describes these two situations.
Most studies have used simple mixing methods that all come down to
mixing two volumes with some mechanical agitation, which we will
name here the manual method. This method is simple to implement
in any chemistry laboratory, which probably explains its spread, but is
prone to variability depending on the exact setup and operator. The sit-
uation of rapid mixing was rather achieved with a chemical engineering
approach pioneered by the Prud'homme group, using a continuous flow
process and millifluidic mixers.

In order to explore the origin of the limitation to high solute con-
centrations, and thus the Ouzo boundary, we prepared samples of in-
creasing hexadecane fraction in acetone and maintained constant the
surfactant to oil ratio and the final water content. We specifically com-
pared the two types of methods, as displayed in Fig. 3, which reveals
several important observations. Firstly, at the lowest oil concentration,
the rapid mixing method yields a droplet size that is slightly higher than
what is expected if all the surfactant is adsorbed at interfaces [21,22]
but still approaches this value. The manual method yields in contrast
larger droplets, that still remain in the Brownian range. The two meth-
ods seem to converge towards this minimal size when extrapolating to
much lower oil concentrations. However, when increasing the oil con-
tent, there is a sharp difference between the two mixing methods. For
the rapid mixing method, the droplet diameter does increase but only
moderately, while for the manual mixing method, the droplet diameter
rises by two orders of magnitude. This escape to the macroscale corre-
sponds to the failure to produce a nanoemulsion that would display a
Brownian behavior. We have also plotted on the figure the location of
the Ouzo boundary reported by Ganachaud and coworkers [13] and see
it coincides with the onset of this escape to the macroscale.

The first strong conclusion of this figure is that it is possible to reach
very large oil fractions, while keeping sizes in the Brownian range,
when using rapid mixing. The second conclusion is that the same feat
is impossible to achieve with standard manual mixing methods, which
explains why most of the existing literature states that the Ouzo effect
is restricted to a fairly low concentration range. The third conclusion is
that the true nature of the Ouzo boundary is that of a kinetic artifact re-
sulting from poor mixing. While the exact location of this boundary is
an interplay of several factors, it is worth stressing here that it is located
at lower solute content than the spinodal curve but still in its vicinity.
Indeed, the escape to the macroscale will be favored by the existence of

<figure><img src="image_5.png" /><figcaption>**Fig. 3. Size with increasing solute concentration.** Solute initial concentration in the solvent is increased and the resulting droplet size is measured using laser granulometry. Two mixing methods are used: one in which liquids are poured into one another, and one using rapid mixing in continuous flow (1.6 mL/s total flow rate). While the first method quickly leads to macroscopic phase separation (the Ouzo boundary observed in literature), the second method allows to obtain nanoparticles at all concentrations. Note that the minimum size achievable that is calculated from the amount of surfactant available (4 times less than oil) is reached at low solute concentrations and rapid mixing.</figcaption></figure>

domains that are highly concentrated in oil and able to spontaneously
decompose through the formation of a bicontinuous network during
spinodal decomposition, resulting quickly in very large droplets that
can not be then reduced back to the nanoscale as more non-solvent and
surfactant arrive in their vicinity.

With these conclusions achieved, we will turn to the last remaining
point to precise, which is exactly how rapid should mixing be in practice
for a given formulation and how to assess it experimentally.

3.4. *Uncoupling mixing and nanoprecipitation to achieve homogeneous conditions*

To this purpose, we reproduce an experiment that has been stan-
dardly proposed by Prud'homme and collaborators, which is the varia-
tion of the mean diameter with the total flow rate that controls mixing
efficiency. Fig. 4 displays typical results for two oil concentrations span-
ning two orders of magnitude. In both cases, we observe that the mean
diameter decreases with increasing the flow rate, which is the clean
extension of comparing manual mixing with rapid mixing. At the low-
est oil content, the mean diameter eventually reaches a constant value,
which corresponds to the minimal achievable diameter, from a given
flow rate. In practice, this means that increasing mixing efficiency does
not impact any more nanoprecipitation and thus that t_mix ≪ t_nano
therefore that mixing and nanoprecipitation are effectively uncoupled.
For the larger oil fraction, a similar behavior is observed but we see
that the mean diameter continues to decrease at the highest flow rate,
indicating that we have actually not reached a full uncoupling of mix-
ing and hydrodynamics in this case. If mixing and nanoprecipitation
were uncoupled for the whole range, we rather expect that the diam-
eter would remain constant when increasing the oil content. However,
this becomes increasingly difficult to achieve experimentally. Indeed,
increasing the oil content drastically decreases t_nano as the collision fre-
quency increases, and spinodal decomposition with the formation of
a bicontinuous network may eventually occur. t_mix must thus become
even smaller. In practice, the moderate droplet size increase with in-
creasing oil content displayed for rapid mixing conditions in Fig. 3 thus
results from insufficiently rapid mixing (see also arrow in Fig. 3).
<figure><img src="image_6.png" /><figcaption>**Fig. 4.** Increasing flow rate. Variation of the droplet size upon increasing the flow rate and thus mixing efficiency, for two concentrations of solutes in acetone but the same surfactant/oil ratio (0.25). The droplet diameter reaches a plateau value in both cases albeit at a different critical flow rate. The threshold between decay and plateau corresponds to the uncoupling of mixing and nanoprecipitation. Better mixing is required when increasing solute concentration as precipitation time scales decrease drastically (through an increase in collision frequency and ultimately spinodal decomposition). Note that the minimum achievable size is reached at high flow rates for low solute concentration but seems complicated to reach otherwise, which corresponds to the transition to spinodal decomposition that probably hinders drastically surfactant adsorption at the onset and sets a minimal size that is likely already not that small.</figcaption></figure>

## 4. Conclusion

A change in solvent quality can lead to the spontaneous formation of solute-rich colloidal particles in the presence of a stabilizer [3]. Nevertheless, it can also lead to macroscopic phase separation, notably when attempting to increase the solute concentration. This behavior known as the Ouzo limit or boundary [1,9,2] limits the industrialization of this method and remained unexplained from a physical chemistry standpoint. Here, we showed, through a complete phase diagram determination with Raman spectroscopy and modelling, that this limit did not match the spinodal curve. This discards once and for all the popular explanation that the failure of the Ouzo effect at high solute content is related to spinodal decomposition. Rather, we focused on the conditions under which species are brought in contact, which precludes precipitation itself. Our postulate [7] was that the relative kinetics of mixing all species compared to the intrinsic precipitation kinetics determines whether precipitation occurs in homogeneous or heterogeneous conditions, which will crucially impact the final outcome. Throughout this work, we consistently showed that the Ouzo boundary corresponds to the coupling of hydrodynamics with precipitation, or expressed otherwise to mixing kinetics occurring on the same time scale as precipitation kinetics. Precipitation then occurs in heterogeneous conditions, with some regions reaching transiently extremely high solute concentrations leading to the rapid growth of a solute-rich phase before any interfacial stabilization can take place. Using rapid mixers in a continuous flow approach enables dispelling this Ouzo boundary by promoting homogeneous precipitation conditions. In practice, reachable solute concentrations can increase up to the order of 10% when mixing is fast enough and a sufficient amount of stabilizer is available. Using an original situ method, we showed that nanoprecipitation kinetics can be as fast as around 10 ms even for modest solute fractions, which means they are even faster upon increasing solute content. Achieving rapid mixing is thus all the more challenging as one tries to increase solute concentration. Continuous-flow approaches including millifluidic mixers, as pioneered by Prud'homme and co-workers, are thus an improvement over batch methods at low solute concentrations but a strict requirement at high solute concentrations. Despite resting on the spontaneous

bottom-up assembly of the solute into nanoobjects, controlled by physical chemistry, the Ouzo effect thus also requires chemical engineering and hydrodynamics to really be implemented to production scales. In practice, such a scale-up approach would benefit from calculating systematically mixing times for different flow rates and geometries and comparing them to precipitation times determined experimentally, for instance with the method displayed in our work. This systematic soft matter engineering approach should help realize the intrinsic potential of the Ouzo effect to produce nano-objects, including nanocrystals as the first stage of non-classical crystallization [23] also occurs through liquid-liquid phase separation. It will also be critical to manufacturing complex nanohybrid structures such as lipid-based nanocarriers of polynucleotides [11], which involves several assembly processes in addition to the precipitation induced by solvent-shifting.

### CRediT authorship contribution statement

**Kevin Roger:** Conceptualization, Methodology, Validation, Investigation, Data Curation, Writing, Visualization, Supervision, Project administration, Funding acquisition. **Nataliya Shcherbakova:** Software, Investigation. **Lison Raynal:** Validation, Investigation, Data Curation.

### Declaration of competing interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Kevin Roger reports financial support was provided by National Centre for Scientific Research.

### Data availability

Data will be made available on request.

### Acknowledgements

We thank Nouha El Amri for the discussions and technical help to perform the nanoprecipitation experiments, and the technical team of Laboratoire de Génie Chimique de Toulouse for manufacturing the mixers.

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[2] Julien Aubry, François Ganachaud, Jean-Pierre Cohen Addad, Bernard Cabane, Nanoprecipitation of polymethylmethacrylate by solvent shifting: 1. Boundaries, Langmuir 25 (4) (2009) 1970-1979.

[3] Hélène Lannibois, Anwar Hasmy, Robert Botet, Olivier Aguerre Chariol, Bernard Cabane, Surfactant limited aggregation of hydrophobic molecules in water, J. Phys. II 7 (2) (1997) 319-342.

[4] Kevin Roger, Bernard Cabane, Why are hydrophobic/water interfaces negatively charged?, Angew. Chem., Int. Ed. Engl. 51 (23) (2012) 5625-5628.

[5] Kevin Roger, Mohammed Eissa, Abdelhamid Elaissari, Bernard Cabane, Surface charge of polymer particles in water: the role of ionic end-groups, Langmuir 29 (36) (2013) 11244-11250.

[6] Kevin Roger, Robert Botet, Bernard Cabane, Coalescence of repelling colloidal droplets: a route to monodisperse populations, Langmuir 29 (19) (2013) 5689-5700.

[7] Robert Botet, Kevin Roger, How do interactions control droplet size during nanoprecipitation?, Curr. Opin. Colloid Interface Sci. 22 (2016) 108-112.

[8] J.G.J.L. Lebouille, R. Stepanyan, J.J.M. Slot, M.A. Cohen Stuart, R. Tuinier, Nanoprecipitation of polymers in a bad solvent, Colloids Surf. A, Physicochem. Eng. Asp. 460 (2014) 225-235.

[9] François Ganachaud, Joseph L. Katz, Nanoparticles and nanocapsules created using the Ouzo effect: spontaneous emulsification as an alternative to ultrasonic and high-shear devices, ChemPhysChem 6 (2) (2005) 209-216.

[10] Kevin Roger, Julien Aubry, François Ganachaud, Bernard Cabane, Le pastis dans tous ses états: l'effet ouzo et son extension à la synthèse de nouvelles émulsions, Bull. Union Phys. 919 (2009) 1081-1093.

[11] Xucheng Hou, Tal Zaks, Robert Langer, Yizhou Dong, Lipid nanoparticles for mrna delivery, Nat. Rev. Mater. 6 (12) (2021) 1078-1094.
[12] Marianna Yanez Arteta, Tomas Kjellman, Stefano Bartesaghi, Simonetta Wallin, Xiaoqiu Wu, Alexander J. Kvist, Aleksandra Dabkowska, Noémi Székely, Aurel Radulescu, Johan Bergenholtz, Lennart Lindfors, Successful reprogramming of cellular protein production through mrna delivered by functionalized lipid nanoparticles, Proc. Natl. Acad. Sci. 115 (15) (2018) E3351-E3360.

[13] Xibo Yan, Marco Delgado, Amy Fu, Pierre Alcouffe, Sébastien G. Gouin, Etienne Fleury, Joseph L. Katz, François Ganachaud, Julien Bernard, Simple but precise engineering of functional nanocapsules through nanoprecipitation, Angewandte Chemie International Edition 53 (27) (2014) 6910–6913.

[14] Ying Liu, Zhen Tong, Robert K. Prud'homme, Stabilized polymeric nanoparticles for controlled and efficient release of bifenthrin, Pest Management Science: Formerly Pesticide Science 64 (8) (2008) 808–812.

[15] Olivier Gazil, Nick Virgilio, Fabienne Gauffre, Synthesis of ultrasmall metal nanoparticles and continuous shells at the liquid/liquid interface in Ouzo emulsions, Nanoscale 14 (37) (2022) 13514–13519.

[16] Chuan Zhang, Vikram J. Pansare, Robert K. Prud'Homme, Rodney D. Priestley, Flash nanoprecipitation of polystyrene nanoparticles, Soft Matter 8 (1) (2012) 86–93.

[17] Kevin Roger, Nouha El Amri, Controlling nanoparticle formation from the onset of nucleation through a multi-step continuous flow approach, J. Colloid Interface Sci. 608 (2022) 1750–1757.

[18] N. Shcherbakova, K. Roger, J. Gergaud, O. Cots, Homotopic method for binodal curves computation in ternary liquid-liquid separation, Comput. Aided Proc. Eng. (2023).

[19] Stefano Farisè, Andrea Franzoni, Pietro Poesio, Gian Paolo Beretta, Heat transfer enhancement by spinodal decomposition in micro heat exchangers, Exp. Therm. Fluid Sci. 42 (2012) 38–45.

[20] Nouha El Amri, Kevin Roger, An alkanethiol-surfactant bilayer to prevent shape conversion of anisotropic silver nanoparticles and probe their formation mechanisms, Langmuir (2023).

[21] Kevin Roger, Bernard Cabane, Ulf Olsson, Formation of 10-100 nm size-controlled emulsions through a sub-pit cycle, Langmuir 26 (6) (2010) 3860–3867, PMID: 19899785.

[22] Kevin Roger, Ulf Olsson, Malin Zackrisson-Oskolkova, Peter Lindner, Bernard Cabane, Superswollen microemulsions stabilized by shear and trapped by a temperature quench, Langmuir 27 (17) (2011) 10447–10454.

[23] Marie Jehannin, Ashit Rao, Helmut Cölfen, New horizons of nonclassical crystallization, J. Am. Chem. Soc. 141 (26) (2019) 10120–10136, PMID: 31173682.