# Intensification of a continuous powder mixing process by distributed and/or delayed feeding

Marie-Anne Batel, Lorenzo Contardo, Cendrine Gatumel, Henri Berthiaux

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Marie-Anne Batel, Lorenzo Contardo, Cendrine Gatumel, Henri Berthiaux. Intensification of a continuous powder mixing process by distributed and/or delayed feeding. Powder Technology, 2026, 473, pp.122229. 10.1016/j.powtec.2026.122229. hal-05533965

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# Intensification of a continuous powder mixing process by distributed and/or delayed feeding

Marie-Anne Batel, Lorenzo Contardo, Cendrine Gatumel, Henri Berthiaux*

RAPSODEE Research Center, UMR CNRS 5302, IMT Mines Albi, Campus Jarlard, 81013 Albi Cedex 09, France

## HIGHLIGHTS

* The impact of feeding strategies on continuous binary powder mixing is studied.

* A segregating component is fed through a distributed feeding system.

* Mass produced during transitory regime is measured.

* Mixture homogeneity is measured at the outlet.

* Both criteria can be dramatically improved using the right feeding strategy.

## GRAPHICAL ABSTRACT

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

## ARTICLE INFO

**Keywords:**

Blending

Particulate solids

Segregation

Start-up

Homogeneity

Process intensification

## ABSTRACT

Intensification of the continuous powder mixing process is intended to limit the effects of segregation, such as poor mixture homogeneity and long transient phases. Process intensification has mainly been developed for fluid processes, for example with staged or distributed feeding. In this work, we study the impact of distributed feeding of a segregating component along the entire length of a lab-scale continuous powder mixer. For this, a specific device is developed and tested for different feed configurations. We show that starting one of the feeders a few tenths of seconds after the beginning of the experiment reduces the mass of mixture produced during the transient regime at start-up. When using the optimal time delay, this mass is always lower than that obtained with conventional feeding. The feed configuration and the time delay of a feeder also have an impact on the homogeneity of the mixture at steady-state, due to the mixing and segregation mechanisms at play during process start-up.

## 1. Introduction

The mixing of powders and grains plays a key role in the production of a wide variety of products, ranging from food and pharmaceuticals to

construction materials and chemicals. The goal of this process is to create a homogeneous mixture at a desired scale while minimizing segregation. In this paper, we will use the terminologies “mixture homogeneity”, “mixture uniformity” or “mixture quality” that are

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: henri.berthiaux@mines-albi.fr (H. Berthiaux).</footnote>
<figure><img src="image_5.png" /><figcaption>Fig. 1. Illustration of conventional, shifted and distributed feeding.</figcaption></figure>

shortcuts -or somewhat imprecise words- to express the degree of mix-
edness of a mixture, as a mixture is always heterogeneous or homoge-
neous up to a certain extent.

Historically, powder mixing has been primarily performed in batch
mode. Nowadays, there exists a tendency towards continuous mode,
particularly to enhance process control and safety. As compared to batch
processes, continuous mixing reduces the number of transfers and
handling steps, which helps limit segregation, dust generation, and po-
tential contamination. Moreover, continuous operation allows for
improved product quality monitoring, as it enables more frequent
sampling with respect to batch methods, thanks to real-time control.

However, continuous powder mixing involves new difficulties, such as feeding a powder at a constant flow rate. A particulate flow rate fluctuates not only because of the discrete nature of powders, but also because of operational factors: presence of agglomerates in a cohesive powder, powder adhesion to the dosing screw or a screw pitch not adapted to the rotation speed or the control loop of a gravimetric feeder. In the aim to improve the feeding system, Kehlenbeck and Sommer [1] developed a rotating star-shaped grid attached to the feeder outlet. This grid improved powder dispersion in the case of a cohesive powder by causing an accumulation of powder at the end of the dosing tube, thus reducing flow rate fluctuations that may affect the homogeneity of the mixture at the mixer outlet if this latter is not able to attenuate those fluctuations. This study may be viewed as a first attempt at intensifying the mixing process, beginning by feeding. Although the authors showed the interest of adding a piece of equipment, such a rotating device may also add a periodic component to the flow rate and worsen of the quality of the mixture at the mixer outlet like rotating blades within the mixer (Batel et al. [2]). Another possibility for stabilizing the flow rate before the mixing equipment would be to insert an on-line static mixer, but this has never been investigated truly.

Mixing powders of different physical properties, such as particle size,
leads to segregation, which in turn affects the mixture homogeneity at
the mixer outlet as well as the duration of transient phases for which the
mixture is usually out-of-specification. Several studies have been carried
out on different feed configurations in the aim of reducing the effects of
segregation. Mizonov et al. [3] studied the intensification of batch
powder mixing by optimizing the initial distribution of components in a
vibratory mixer. The loading of powders differing in particle size into
the mixer included pre-mixing, as components are loaded as a sequence
of several layers. The number of layers of each component should then
be optimized to reduce loading and mixing time. In the case of contin-
uous powder mixing, the process may be intensified by acting on the
position of the feeders, for example. In the theoretical study by Mizonov
et al. [4], the continuous mixer is first filled with one of the powders,
then a second powder is fed at a point between the mixer inlet and
outlet. The authors have shown that the position of the second powder
feeding influences the quality of the mixture at the mixer outlet, and that
there would be an optimum position depending on the segregability of
the powder mixture. The basis for this theoretical study was a two-
dimensional Markov chain model. Our previous experimental work
(Batel et al. [5]) confirmed the impact of the feed configuration on the
outlet mixture characteristics, particularly on the duration of the tran-
sient regime during start-up. In this work, we studied a mixture of two
powders of different grain sizes. We showed that shifting the feeding of

one or both powders to the middle of the mixer or towards the mixer
outlet had little impact on the mixture homogeneity at steady-state, but
it did on the duration of the transient regime during start-up. Shifted
feeding, illustrated in Fig. 1, therefore modifies the mass of mixture
produced during the transient phase, which would be discarded in an
industrial context. What would definitely help counteract particle
segregation during the starting phase, would result in making grains of
both powders arrive at the mixer outlet at the same time. Consequently,
not only shifting feeders is worth studying, but also time-delaying
feeders or more complex configurations.

After studying space-shifted feeding, i.e. along a mixer, we now
propose to investigate the effects of both time-shifting, or delayed-
feeding, as well as that of distributed feeding of one of the powders. In
this latter case, this means that a powder is not fed at a single point, but
over the whole length of the equipment, much more progressively than
in conventional feeding, as illustrated in Fig. 1. Under such a configu-
ration, grains of different types fed at the mixer inlet would spend a
significant amount of time in the mixer before exiting, while similar
grains fed near the outlet would spend less time in the mixer before
exiting. In fact, even though the mixer is not a plug flow system, back-
mixing is actually not efficient enough to allow the system to reach
perfect mixing. Feeding one of the powders progressively may also
change the way the two powders come into contact in the equipment,
which could have an impact on the mixture homogeneity at the mixer
outlet.

Intensification through staged or distributed feeding has not been
studied for powder mixing, but for many other processes such as crys-
tallization, chemical reaction and polymer mixing. For crystallization, it
has been reported that staged feeding provides better control of super-
saturation to favor crystallization over precipitation [6]. In fact, it en-
ables reagent concentrations to be controlled through several additions
along the crystallizer. Regarding chemical reactions, staged feeding has
been employed for parallel reactions, also known as competitive re-
actions, as it favors one of the mechanisms. It can improve selectivity
and yield [7], as in the case of oxidative coupling of methane, where
oxygen is kept as the limiting reactant by staged feeding [8,9]. Another
notable application is temperature control in a reactor where an
exothermic reaction is taking place [10]. Guillou et al. [11] have studied
the staged feeding of hydrogen in Fischer-Tropsch synthesis, which aims
to convert syngas into a wide range of hydrocarbons by also producing
water and CO2. Among the many parallel reactions, a few are the ones to
be favored to obtain a certain fraction of hydrocarbons. This requires an
optimum local H2/CO ratio throughout the reactor. One possible
configuration is to distribute the feeding along the entire length of the
reactor by feeding through a membrane. In the field of polymer mixing,
staged feeding is known to improve mixture homogeneity when mixing
two polymers of different viscosities. This method has been used for
mixing rubber and nylon, as rubber is much more viscous in the molten
state than nylon. Staged feeding of nylon resulted in a fine dispersion of
rubber in the nylon matrix [12].

For powder mixing, we may expect that changing the conventional
feed configuration for a staged/distributed one could have an impact on
mixture homogeneity, as well as on the duration of transient phases such
as start-up. Indeed, feeding two powders at different points above the
mixer implies different residence time distributions for the particles. For
the same reason, the introduction of a time delay between the start of the
feeders may have a beneficial impact on process indicators.

The aim of this study is to investigate experimentally the impact of
distributed feeding and time delays on the duration of the transient
phase during start-up and mixture homogeneity at steady-state. For this,
our work will be supported by a binary mixture of free-flowing powders
of different grain sizes.
<caption>**Table 1**</caption>

Main physical characteristics of the powders used. Particle size has been determined by Malvern® Mastersizer 3000 with dry dispersion, true density by He pycnometer and apparent bulk densities by Erweka® “taptap” volumen-ometer. Carr index is deduced from apparent densities.

<table><thead><tr><th>Property</th><th>Semolina</th><th>Couscous colored black</th></tr></thead><tbody><tr><td>d<sub>10</sub> (μm)</td><td>197</td><td>830</td></tr><tr><td>d<sub>50</sub> (μm)</td><td>307</td><td>1430</td></tr><tr><td>d<sub>90</sub> (μm)</td><td>473</td><td>2470</td></tr><tr><td>Bulk density (kg.m<sup>-3</sup>)</td><td>709</td><td>765</td></tr><tr><td>Tapped apparent density (kg.m<sup>-3</sup>)</td><td>765</td><td>803</td></tr><tr><td>True density (kg.m<sup>-3</sup>)</td><td>1458</td><td>1426</td></tr><tr><td>Carr index (-)</td><td>7.3</td><td>4.7</td></tr></tbody></table>

<figure><img src="image_6.png" /><figcaption>**Fig. 2.** virtual subdivision of the mixer into five cells.</figcaption></figure>

## 2. Material and methods

### 2.1. Powders

To investigate the effect of particle segregation, free-flowing powders of different grain sizes, namely semolina and couscous, have been chosen. Table 1 shows the main physical characteristics of the powders. The Carr indices are below 10, demonstrating the excellent flow properties of both powders. The densities are similar but the $d_{50}$ ratio is 4.7. The two powders can be separated by sieving, enabling them to be reused from one experiment to another. It can be said that those two powders only differ by their particle size, so that the distinction semolina/couscous can be viewed as fine/coarse particles.

The mixture's segregability has been assessed through a segregation test developed by Massol-Chaudeur et al. [13]. Runs, fully described in Batel et al. [5], confirmed that the mixture segregability depends on its composition, with a maximum for the mixture containing 30% semolina. It is therefore waited that segregation is likely to take place at a higher extent in regions of an equipment in which the mixture composition reaches this value.

### 2.2. Mixer and feeders

The convective mixer used in this study is a lab-scale mixer designed at the RAPSODEE laboratory, again fully described in Batel et al. [5]. Main characteristics will however be remained in the following:

- Tank volume: 2.9 L

- Tank shape: semi-cylindrical

- Tank outlet: 1.8 cm height, 2.0 cm width

- Stirring device: shaft fitted with 16 blades, first 14 blades inclined 5° forward, last 2 inclined 70° forward.

- Mixing conditions: Froude number fixed at 0.3 (rotational speed 8.1 rad.s⁻¹).

- Feeders: GLD87 gravimetric feeders by Gericke (15 L hopper).

- Feed rate configuration: semolina and couscous feeders both set at 5 g.s⁻¹.

Since the feed rates for couscous and semolina are identical, the

<figure><img src="image_7.png" /><figcaption>**Fig. 3.** Studied feed configurations with distributed feeding.</figcaption></figure>

overall mass ratio of the output mixture at steady state is 1:1.

In the conventional feed configuration, the feeders are positioned at the mixer inlet section, which means as far as possible from the outlet. In this work, we are interested in staged or distributed feeding, which consists in feeding a powder all along the mixer, being the other feeder placed at different locations. To figure this more properly, we divided the mixer into five virtual cells, as shown in Fig. 2. These are of different sizes, depending on the position of the blades. As feeders cannot be positioned above cells 1 and 5, the conventional feeding position is therefore in cell 2. The spatial combination of distributed and shifted feeding configurations tests is listed in Fig. 3. To study the impact of time-delays in feeders, an experiment is first started with a single feeder, then the second feeder is started after a few tens of seconds (10 s to 40 s), as illustrated in Fig. 4. Each feed configuration with a certain time delay will be performed 5 times.

### 2.3. Distributed feeding device

We have developed a distributed feeding device that allows powder feeding to be distributed all along the mixer, as shown in Fig. 5. Powder exiting the feeder first passes through a funnel fitted with a Y-shaped connector to split the powder flow into two flows. Both connector outlets are inclined at a 30° angle to the vertical. The powder then arrives on a metal plate inclined at a 40° angle to the vertical, on which magnets have been positioned to form obstacles. These distribute the powder along the entire length of the mixer. The angle of inclination of the plate limits the speed of the grains, to better control impact with the obstacles and avoid unwanted rebounds. The plate is 260 mm wide and 298 mm high. Part of the plate is covered with squared paper to position the magnets. Parallel to this steel plate is a PMMA plate to prevent the grains from being thrown out of the mixer.

The 12 mm-long, 3 mm-diameter magnets were positioned so that the feeding was distributed over the whole mixer length. To achieve this, preliminary laboratory tests were carried out by placing the device on the top of a 29.5 cm-wide tray divided into 9 compartments (Fig. 6). The tray was lined with paper to prevent static electricity effect. The number of magnets and their position were determined by trial and error to optimize powder distribution in the compartments. For each trial, 50 g of powder were poured by hand into the funnel, then the contents of each compartment were collected and weighed. We selected one magnet configuration for semolina distribution and another one for couscous distribution (Fig. 7). The magnet configurations are different between the two powders because they behave differently when they encounter an obstacle. When a couscous grain encounters a magnet, its trajectory is strongly deflected. Few magnets are therefore needed to distribute the powder between the compartments. Conversely, the trajectory of a semolina grain is only slightly deviated when it hits a magnet. Many magnets are therefore needed to guide a few grains towards
<figure><img src="image_8.png" /><figcaption>Fig. 4. Time delays studied for distributed feeding configurations.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 5. Distributed feeding device installed on the mixer with distributed semolina and conventional couscous feeding.</figcaption></figure>

compartments 1 and 9.

The magnet configurations enable powders to be distributed across the 9 compartments of the tray during laboratory testing. Fig. 8 shows the distribution of distributed powders in the laboratory. For both powders, the distribution is symmetrical with respect to compartment 5, which is the central compartment.

## 2.4. On-line mixture analysis

Homogeneity at the mixer outlet is studied using an image analysis system that has been originally developed by Demeyre [14], perfected by Ammarcha [15] and fully described in our recent paper (Batel et al. [2]). The lack of homogeneity of a mixture at a defined scale of scrutiny can be quantified by the composition variance and sometimes its RSD, as its degree of heterogeneity or segregation intensity. When full homogeneity is reached, the degree of heterogeneity is at its lowest and the variance equals that of a random mixture. At the opposite, a fully heterogeneous mixture will correspond to the maximum variance $\sigma_0^2 = p$ (1-p), p being the composition in key ingredient.

A greyscale camera is positioned above a conveyor belt at the mixer outlet to film the mixture during the entire experiment. The frequency of acquisition of this camera is 14 frames per second. The couscous is

<figure><img src="image_10.png" /><figcaption>Fig. 6. Distributed feeding device in the laboratory to define the position of the magnets used to distribute the powder into the 9 compartments.</figcaption></figure>

previously colored in black, so the images show black couscous grains and yellow semolina grains. A double thresholding method is employed to determine, in each image, the number of white pixels corresponding to semolina and the number of black pixels corresponding to couscous. This method allows the calculation of the fraction of white pixels $x_i$ in an image and its time-evolution during each experiment. While the fraction of white pixels cannot be directly related to the semolina fraction in the mixture, we consider that fluctuations in the fraction of white pixels reflect fluctuations in the semolina fraction.

The sampling protocol consists in considering n consecutive images in a sliding window. The average of the white pixel fractions of the n images is then calculated by eq. 1. The moving standard deviation $\sigma_i$ defined by eqs. 2 is then calculated and compared with two thresholds.

$$ \bar{x}_i = \frac{1}{n} \sum_{k=i}^{i+\frac{n-1}{2}} x_k \quad (1) $$
<figure><img src="image_11.png" /><figcaption>Fig. 7. Position of magnets for (a) semolina and (b) couscous distribution with graduations in cm.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Fig. 8. Distribution of the powder in the 9 compartments of the laboratory tray.</figcaption></figure>

$$ \sigma_i = \sqrt{\frac{1}{n-1} \sum_{k=i-\frac{n-1}{2}}^{i+\frac{n-1}{2}} (x_k - \bar{x}_i)^2} \quad (2) $$

The beginning of steady-state is identified thanks to the evolution of the fraction in white pixels, which is first smoothed thanks to a Savitzky-Golay filter as explained in our previous work [2]. Steady-state begins when one point is below the lower threshold and none of the following points are above the upper threshold.

As stated earlier, the mass of mixture produced during the transient start-up regime is generally considered out-of-specification and is discarded. From an industrial perspective, determining the mass of mixture to be discarded can be more relevant than determining the time during which the mixture must be discarded, particularly for high value-added products. A weighing scale, connected to a data acquisition system, is positioned under the container at the end of the conveyor belt. This setup allows us to calculate the mass of the mixture that exits the mixer during its start, considering that it takes 2.8 s for the mixture to go from the camera to the scale. For each feed configuration, we carried out 5 identical trials. Given that steady-state detection is a sensitive process, it is possible for one of the trials to yield a significantly different result from the others. To prevent this and for each feed configuration, we therefore retained the 4 trials with the closest results.

Image analysis can also be used to study the homogeneity of the mixture at the mixer outlet. In this work, we considered a homogeneity criterion based on the fraction of white pixels. Depending on the feed configuration and the time delay, steady-state was reached between 100 s and 200 s. The calculation of mixture homogeneity was performed by systematically analyzing the data obtained between 250 s and 350 s.

<figure><img src="image_13.png" /><figcaption>Fig. 9. Evolution of the fraction of white pixels in the mixture at the mixer outlet when semolina is distributed and couscous is fed into cell 2.</figcaption></figure>

Each mixing experiment was then stopped after 360 s. The average relative standard deviation (RSD), which is the most common indicator for mixture homogeneity, has been calculated using eq. 3 with the window size $n = 20$ and $n_{SS}$ the number of points between startSS = 250 s and endSS = 350 s. The method has been detailed in Batel et al. [5].

$$ \text{Average RSD} = \frac{1}{n_{SS}} \sum_{i=\text{startSS}}^{\text{endSS}} \frac{\sigma_i}{\bar{x}_i} \quad (3) $$

# 3. Results and discussion

## 3.1. Mass of powder produced during start-up

As stated above, an important criterium for continuous mixing efficiency evaluation lays in the amount of powder produced during the start of the mixer, a mass that would be usually discarded.

As an example of the whole experimental set, Fig. 9 shows results of the mixture characteristics at the mixer outlet, in terms of white pixels fraction, when semolina is distributed and couscous is fed into cell 2. In this experiment, both feeders start at the same time. At the beginning of the experiment, no grain leaves the mixer as it is filling up, then the first grains leaving the mixer are mostly semolina grains. The powder layer on the conveyor belt is thin, which can skew the image analysis. As the mixture during start-up spread out more than at steady-state, the fine semolina grains cover a larger surface area, leading to an overestimation of the fraction of white pixels. For this reason, we were unable to calibrate the fraction of white pixels in relation to the semolina fraction. Experimentally, the mixture at the mixer outlet will therefore appear poorer in couscous than it is really. In this case, the beginning of steady-
<figure><img src="image_14.png" /></figure>

<figure><img src="image_15.png" /></figure>

<figure><img src="image_16.png" /></figure>

<figure><img src="image_17.png" /></figure>

<figure><img src="image_18.png" /></figure>

<figure><img src="image_19.png" /><figcaption>**Fig. 10.** Impact of the time delay on the mass of mixture produced during the transient regime at start-up for configurations with distributed feeding of semolina or couscous. The time delay indicates the number of seconds elapsed between the beginning of the experiment and the start-up of a feeder.</figcaption></figure>
<table><caption>**Table 2**
Optimal time delay and minimum mass of mixture produced during start-up with distributed feeding.</caption><thead><tr><th></th><th>Minimum mass of mixture produced during start-up</th></tr></thead><tbody><tr><td>Distributed semolina and couscous fed into cell 2</td><td>Semolina fed after 40 s 668 g</td></tr><tr><td>Distributed semolina and couscous fed into cell 3</td><td>Semolina fed after 20 s 491 g</td></tr><tr><td>Distributed semolina and couscous fed into cell 4</td><td>Couscous fed after 50 s 521 g</td></tr><tr><td>Distributed couscous and semolina fed into cell 2</td><td>Couscous fed after 20 s 375 g</td></tr><tr><td>Distributed couscous and semolina fed into cell 3</td><td>Semolina fed after 10 s 629 g</td></tr><tr><td>Distributed couscous and semolina fed into cell 4</td><td>Semolina fed after 40 s 579 g</td></tr></tbody></table>

state is detected at 145 s, which represents a mass of powder produced during start-up of 1022 g.

For each feed configuration, we tested several time delays on each feeder and measured the mass of powder produced during the transient regime at start-up (Fig. 10), in order to determine the best conditions for this criterium.

In all the cases studied, there exists an optimal time-delay that minimizes this mass. When the fine particles are distributed along the mixer, this time must be applied to either one feeder or the other, depending on the location of the coarse particle's feeder. The closer to the inlet the coarse feeder is, the later the fine feeder must be switched on. This is not a surprise since during the time needed for the coarse particles to reach the outlet, all the fines that exited the mixer are lost. When the coarse feeder is placed in cell 2, the distributed fine particle's feeder must wait approximately 40 s, when it is placed in cell 3, this delay is nearly 20 s and when it is placed in cell 4, the delay will be -50 s, meaning that, this time, the coarse feeder must be delayed.

When the coarse particles are distributed along the mixer, a symmetrical situation takes place. This time, the closer to the inlet the fine feeder is placed, the later the coarse feeder must be switched on, again unsurprisingly. When the fine particle's feeder is placed on cell 2, the distributed coarse feeder must wait around 20 s to be started, when it is placed in cell 3, the delay is -10 s and when it is in cell 4, the delay is close to -40 s, meaning that this the fine feeder which is, in fact, delayed.

From the sole perspective of the mass criteria, it looks better to place the coarse feeder in cell 3 if the fines are distributed, while leaving the fine feeder in cell 2 is the best option when the coarse particles are distributed. This may be explained by an axial segregation phenomenon that takes place because of differences in particle size. The coarse couscous particles are slowed down by the semolina particles due to their geometrical inability to pass through a bed of fine particle and therefore mix even worse if they are fed “behind” fines or if they have to recirculate through fines. Conversely, the semolina's behavior depends slightly on the presence or absence of couscous, so leaving the fine particles feeder close to the inlet will remain the best configuration. In addition, the Carr index of semolina is higher than that of couscous, meaning that semolina exhibits lower flowability, which limits the mobility of semolina grains to rearrange and mix efficiently with couscous grains.

When a powder is distributed and the other one is fed into cell 4, the phenomena involved seem different. A certain quantity of distributed powder must be present in cell 4 when the undistributed powder is fed, so that the powders are homogenized before leaving the mixer. In this configuration, the time needed for steady-state establishment is longer, as mixing in the rest of the tank can only be established by the re-circulation of the powders. Fig. 10e and Fig. 10f both show that the feeding of a powder into cell 4 must be started 40 s or 50 s after the beginning of the other powder's distributed feeding.

With a conventional feed configuration, i.e. both feeders placed in cell 2, the average mass of mixture produced during start-up is 885 g. For the 6 feed configurations tested in this study, a time delay applied on the appropriate feeder is always beneficial and results in a mass of mixture produced during start-up of less than 700 g, as shown in Table 2. Overall,

<figure><img src="image_20.png" /><figcaption>**Fig. 11.** Side-view of the continuous mixer while operating, showing the extent of segregation.</figcaption></figure>

<figure><img src="image_21.png" /><figcaption>**Fig. 12.** Identified segregation mechanisms at the surface of the bed and at its core.</figcaption></figure>

the best configuration is: coarse particles distributed, fine particles fed into cell 2, 20 s delay applied to the coarse particle feeder. This leads to a minimum mass of 375 g. The worst case is: fine particles distributed, coarse particles fed into cell 4, 10 s delay applied to the fine particle feeder, leading to a maximum of 1438 g, nearly four times higher.

Videos taken for all the configurations, as well as the above attempts of physical explanations, suggests that at least three segregation phenomena seem to take place inside the tank (Figs. 11 and 12):

- In the radial-or downwards-direction, fine semolina particles can percolate through coarse couscous ones, the contrary being much harder, due to geometrical hindrance. This “Brazil nuts” effect is well known and can explain why we see a significant amount of couscous particles at the surface and then a thick layer mostly composed of semolina. At the bottom of the tank, a more balanced mixture is present, because of the motion of the blades that convey surface particles towards the bottom.

In the axial direction, the coarse particles that are present at the surface of the bulk are hit by the blades and sent to a larger distance than fine particles. This phenomenon, known as segregation by trajectory, is enhanced by avalanches at the bed surface. Still in the axial direction but in the core of the powder, another percolation effect takes place. When placed behind semolina particles, coarse couscous particles have difficulty passing through them, whereas it is the contrary for fine semolina. As a result, not only are the coarse “core” particles slowed down in the inlet-outlet direction, but they can also hardly recirculate. This can be qualified as an axial percolation mechanism.

This discarded mass can finally be compared to hold-up mass, which is the mass that is retained in the tank when the process is at steady-state. The hold-up mass is almost constant, as operating conditions, in terms of mass flow rate and rotational frequency of the stirring device, are the same, and is experimentally equal to 400 g. This mass ratio is a way to link the size of the mixer to the quantity of powder that is lost during the transient regime. In the worst feed configuration (couscous in cell 4, semolina staged and started 10 s later), the ratio is 3.73, meaning that a 10-time bigger mixer would result in a powder loss of
<figure><img src="image_22.png" /><figcaption>**Fig. 13.** Mixture homogeneity at steady-state for configurations with distributed feeding of semolina or couscous. The time-shifting indicates the number of seconds elapsed between the beginning of the experiment and the start-up of a feeder.</figcaption></figure>

3.73*400*10 = 14,379 g. In the other hand, best conditions (couscous staged, semolina feeder in cell 2 started 20 s later) correspond to a ratio of 0.86 that would only result in a 3750 g loss for a mixer of this size.

To reduce the mass of mixture produced during start-up, changes in the feeding system configuration like those above-mentioned are looking beneficial. However, we need to investigate whether these changes have any detrimental effect on the homogeneity of the mixtures at the outlet of the tank.

<table><caption>**Table 3**
Average and standard deviation for the average RSD over all time delays.</caption><thead><tr><td></td><td>Average</td><td>Standard deviation</td></tr></thead><tbody><tr><td>Distributed semolina and couscous fed into cell 2</td><td>11.8%</td><td>0.9%</td></tr><tr><td>Distributed semolina and couscous fed into cell 3</td><td>13.2%</td><td>0.7%</td></tr><tr><td>Distributed semolina and couscous fed into cell 4</td><td>12.2%</td><td>0.7%</td></tr><tr><td>Distributed couscous and semolina fed into cell 2</td><td>9.6%</td><td>0.5%</td></tr><tr><td>Distributed couscous and semolina fed into cell 3</td><td>10.2%</td><td>0.8%</td></tr><tr><td>Distributed couscous and semolina fed into cell 4</td><td>10.3%</td><td>0.8%</td></tr></tbody></table>
<figure><img src="image_23.png" /><figcaption>**Fig. 14.** Overall impact of feed configuration on process acceptability criteria. Plain symbols indicate cases of coarse product distribution along the mixer, empty symbols those of fine product distribution. The star symbol corresponds to the conventional configuration.</figcaption></figure>

## 3.2. Homogeneity at steady-state

Fig. 13 and Table 3 show the mixture homogeneity at the mixer outlet at steady-state for the 6 feed configurations studied with time delays, each experiment being repeated 5 times. With conventional feeding, the average RSD at steady-state was 11.1%.

When fine particles are fed through the distribution setup, the impact of time delays on the homogeneity of the mixture is negligible if coarse particles are fed in cells 3 and 4, e.g. close to the outlet. In those cases, the mixtures produced are of equal to worse quality than with the conventional feeding configuration. The large amounts of coarse particles placed close to the outlet of the tank demonstrate difficulty in recirculating towards the inlet, as to encounter fine particles, therefore producing a bad mixture outside the mixer. The situation only gets better when the coarse feeder is placed at the mixer inlet without applying any delay. In any case, the average RSD lays between 11.8% and 13.2%. Indeed, while the distributed feeding of the small particles was beneficial to the mass produced criterium, it is not the case for the homogeneity criterium, meaning that such configuration is not advisable.

The situation changes dramatically when the coarse particles are distributed along the mixer. In all cases where coarse particles are distributed, the average RSD lays significatively below the value obtained in conventional feeding. The distribution of coarse particles along the mixer compensates the limited internal recirculation of these particles that is hindered by axial segregation. The best configuration regarding the sole RSD criterion corresponds to a placement of the fine particle's feeder close to the outlet but started 50 s earlier. However, this configuration leads to a mass produced of more than 773 g, due to the amounts of fine particles leaving the mixer before the start of the couscous feeder, as commented before. If fines are fed into cell 3 or 4, applying a time-delay on this feeder helps lower the average RSD to attain a value around 9.5%, a value that can be reached without time-delay if the semolina feeder is still at its conventional location (cell 2).

Fig. 14 summarizes the impact of the different configurations studied in the present work and on that of Batel et al. [5] on the two criteria chosen. Distributing the coarse particles along the mixer and placing the fine particles inlet in cell 2 with a 20 s time-delay is the configuration that looks to offer the best compromise between a small RSD and a small mass produced. It appears clearly at the bottom right of this graph and corresponds to a 9.6% RSD and a 375 g mass of mixture lost.

## 4. Concluding remarks

In the present work, we studied the influence of numerous feeding configurations, that can be seen as space and time delays, on two important criteria in continuous segregating binary powder mixing processing. From this study, we want to draw attention to the following remarks and perspectives.

For any given feed configuration, there is an optimal time delay that minimizes the mass of mixture produced during start-up. When using the optimal time delay, this mass is significantly lower than that obtained with conventional feeding, down to 58%. If this can be scaled up to an industrial mixer 10 to 20 times larger than our lab equipment, the powder mass savings would be in the range of 10–20 kg per run. In pharmaceutical production, this already represents tenths of thousands of tablets that would have been destroyed each time. In the cosmetic industry, where the product prices are usually higher, the resulting financial loss is sizable. The most suitable configuration for minimizing the discarded mass also provides a significant improvement (1.5% in RSD) in mixture homogeneity, which is a somewhat surprising win-win situation. There is no doubt that such a change is worth trying in a real pharmaceutical case.

Indeed, understanding the phenomena at play shed light on the way one can approach a powder mixing problem like this one. In such mixers, segregation takes place through mechanisms at the surface of the mixture and in the core of it through “steric” effects. Coarse particles are less likely to get through fines in either direction, axial or radial, and less able to recirculate in the tank, which is strongly detrimental to mixture quality. This effect can be efficiently counteracted by distributing these coarse particles along the mixer through controlled feeding.

A significant improvement can be achieved by control feeding of a segregating component at the right location and in the right quantities in a piece of equipment, what we believe fits within the definition of process intensification. However, we must bear in mind that we have employed a trial-and-error method in defining the feeding configurations to test, meaning that even better configurations could be reached. For example, while giving goods results, the powder distribution setup is uncontrolled and gives uneven repartition of the powder along the mixer (Fig. 8). An improvement of it would be a way to control flows in the different sections. And of course, the impact of having a setup of this type for each powder is worth studying.

It would be worthwhile to study the residence time distribution (RTD) for all feed configurations, and for both powders. In particular, RTD experiments performed with uncolored couscous particles tracked by colored couscous particles while semolina particles are still present,
contrasted with the same experiment without semolina, would help
understand the effect of particle segregation. Flow modeling could be
performed through RTD or Markovian cell models that should involve as
many cells as there are blades or group of blades in the longitudinal
direction, and at least three cells in the radial direction to figure out the
phenomenon outlined in the present work. DEM models would also
provide great help in determining the internal flows to integrate into the
above scheme.

The extent of segregation in the mixer is significant and seems
difficult to counteract. While the idea of performing a batch before
starting the feeders to fill the mixer is worth trying, it is very likely to fail
to provide a good mixture inside the tank. Again, modeling and simu-
lation would help testing those situations.

CRediT authorship contribution statement

**Marie-Anne Batel:** Writing – original draft, Methodology, Investi-
gation, Data curation, Conceptualization. **Lorenzo Contardo:** Investi-
gation. **Cendrine Gatumel:** Supervision. **Henri Berthiaux:** Writing –
review & editing, Supervision, Conceptualization.

Declaration of competing interest

The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence
the work reported in this paper.

Data availability

Data will be made available on request.

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