# Surface chemistry-based continuous separation of colloidal particles via diffusiophoresis and diffusioosmosis

Adnan Chakra, Christina Puijk, Goran Vladisavljević, Cécile Cottin-Bizonne, Christophe Pirat, Guido Bolognesi

► To cite this version:

Adnan Chakra, Christina Puijk, Goran Vladisavljević, Cécile Cottin-Bizonne, Christophe Pirat, et al. Surface chemistry-based continuous separation of colloidal particles via diffusiophoresis and diffusioosmosis. Journal of Colloid and Interface Science, 2025, 693, pp.137577. 10.1016/j.jcis.2025.137577. hal-05067444

HAL Id: hal-05067444

https://hal.science/hal-05067444v1

Submitted on 14 May 2025

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

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

<figure><img src="image_1.png" /></figure>
<figure><img src="image_2.png" /></figure>

Regular Article

# Surface chemistry-based continuous separation of colloidal particles via diffusiophoresis and diffusioosmosis

Adnan Chakra<sup>a, ID</sup>, Christina Puijk<sup>b, ID</sup>, Goran T. Vladisavljević<sup>c, ID</sup>, Cécile Cottin-Bizonne<sup>d, ID</sup>, Christophe Pirat<sup>d, ID</sup>, Guido Bolognesi<sup>b, ID, *</sup>

<figure><img src="image_3.png" /></figure>

## GRAPHICAL ABSTRACT

<figure><img src="image_4.png" /><figcaption>colloid separation based on COO⁻ surface concentration</figcaption></figure>

## ARTICLE INFO

Surface Chemistry-based Continuous Separation of Colloidal Particles via Diffusiophoresis and Diffusioosmosis (Original data)

**Keywords:**

Colloids

Microfluidics

Particle separation

Diffusiophoresis

Diffusioosmosis

Zeta potential

Surface conductance

## ABSTRACT

The separation of colloidal particles is of great importance in many fields, such as purification, sensing, and bioanalysis. However, separating particles based on their surface physico-chemical properties remains challenging. This study demonstrates through experimental and theoretical analyses that diffusiophoresis and diffusioosmosis enable the continuous separation of carboxylate polystyrene particles with similar sizes and zeta potentials but distinct surface concentrations of carboxyl groups. In the proposed approach, the particles are exposed to salt concentration gradients generated in a double-junction microfluidic device, fed with low and high electrolyte concentration streams. As the particles move across environments with varying salinity levels, their dynamics are affected by the sensitivity of their electrophoretic mobility – and consequently, their apparent zeta potential, which is proportional to it – to the local salt concentration. The apparent zeta potential, measured via electrophoretic light scattering, and its sensitivity to salt concentration are influenced by the ionic conduction occurring near the particle surface whose intensity depends, in turn, on the concentration of surface carboxyl groups. By harnessing these effects, colloids with comparable apparent zeta potentials but different surface concentrations of carboxyl groups are separated with high efficiency when they exhibit opposite apparent zeta potential sensitivities to salt. This simple approach, which relies on an easy-to-operate device with no external energy source, has discipline-spanning potential for the continuous separation of colloids distinguished solely

<footnote><sup>a</sup> Department of Chemistry, Imperial College London, London, W12 7TA, United Kingdom</footnote>

<footnote><sup>b</sup> Department of Chemistry, University College London, London, WCH1 0AJ, United Kingdom</footnote>

<footnote><sup>c</sup> Department of Chemical Engineering, Loughborough University, Loughborough, LE11 3TU, United Kingdom</footnote>

<footnote><sup>d</sup> Institut Lumière Matière, UMR5306 Université Claude Bernard Lyon 1, Villeurbanne, 69622, France</footnote>

<footnote>* Corresponding author.
E-mail address: g.bolognesi@ucl.ac.uk (G. Bolognesi).</footnote>
by surface properties like roughness, permeability, heterogeneity, and chemical composition that influence the sensitivities of their electrophoretic mobility and, thus apparent zeta potential, to the salt concentration.

# 1. Introduction

The separation of nano- and micro-particles based on their physical and chemical properties is of great importance in a wide range of applications, including diagnostics [1], drug delivery [2], chemical and biological analyses [3], food processing [4], biofuel production [5], pharmaceutical industry [6], and environmental monitoring and remediation [7]. Microfluidic-based particle separation methods offer several advantages compared to conventional bulk approaches [8]. Higher precision, smaller footprint, improved energy efficiency, and reduced consumption of costly or hazardous samples and reagents make microfluidic methods a more efficient, cost-effective, sustainable, and safer alternative. These methods are particularly advantageous for the rapid and continuous processing of small volumes of materials, such as biofluids or expensive nanomaterials.

Active microfluidic separation techniques rely on external fields and auxiliary equipment and are most effective in terms of high separation efficiency and throughput [9]. Conversely, passive hydrodynamic techniques rely on interactions between particles, flows and channel structures; they can easily operate with simpler experimental set-ups, but they are only adequate for separation based on particle size and elasticity [10,11]. Alternatively, electrolyte diffusiophoresis and diffusoosmosis – namely, the spontaneous relative motion between adjacent liquid and solid phases induced by a solute concentration gradient – have been successfully applied for the passive and continuous separation of colloids in microfluidic devices [12–18]. Since the diffusiophoresis mobility of colloids depends on particle size and zeta potential, diffusio-phoresis/osmosis-assisted microfluidic strategies have enabled the continuous separation based on particle size and surface charge properties. However, the small magnitude of the diffusiophoresis and diffusoosmosis velocities ($1-10 \ \mu\text{m s}^{-1}$) combined to the typically short residence times of the particles in the microfluidic devices (1-10 s) have implied that up to now only particles with significantly different size (i.e., at least one order of magnitude) [17,18] or zeta potential (i.e., oppositely charged surface groups) [13,14,16], could be separated efficiently under continuous flow settings.

The zeta potential $\zeta$ of a colloid or a solid wall depends on the physical and chemical properties of its surface and surrounding electrolyte solution. For particle and wall materials commonly used in microfluidics (e.g., silica, silicon, and polymers), the zeta potential varies with the ionic strength, and thus, electrolyte concentration of the solution [19,20]. This relationship is affected by the solution pH and the surface physico-chemical properties of the solid substrate, including type and concentration of surface ionizable groups, ion adsorption affinity, roughness, and permeability to ions and liquid. It is worth noting that the zeta potential of particles is often determined via electrophoretic light scattering measurements, whereby the particle's electrophoretic mobility, $\mu_E$, is calculated from the ratio of the measured particle's velocity and the applied electric field intensity. The value of $\zeta$ is then inferred through the Henry's formula [21], which establishes a linear relationship between $\mu_E$ and $\zeta$. However, under certain experimental conditions, such as high zeta potentials and low liquid medium conductivities, Henry's formula is no longer valid due to the onset of ionic conduction within the electric double layer at the particle surface – also referred to as surface conductance – which slows down the electrophoretic motion of the particle and leads to a reduced electrophoretic mobility [21–23]. In these circumstances, it is more appropriate to denote the particle's zeta potential extracted from the measured electrophoretic mobility and the Henry's formula as the *apparent zeta potential*.

The latter is directly proportional to the particle's electrophoretic mobility, but it differs from the actual value of the particle's zeta potential when Henry's formula is not valid and the real $\zeta$ is no longer proportional to $\mu_E$ [24].

In diffusiophoresis/osmosis microfluidic experiments, the difference in ionic strength between the lowest and highest concentration streams is typically of two or three orders of magnitude, potentially leading up to 10-fold variation of particle and wall zeta potential between the two streams [25]. Therefore, at least in principle, the continuous separation by diffusiophoresis/osmosis effects could be extended to particles that exhibit similar values of apparent zeta potentials $\zeta(c)$ at a given salt concentration $c$, but different apparent zeta potential sensitivity to varying salinity levels (i.e., $\partial\zeta/\partial c$). Indeed, as the particles are exposed to local environments with varying ionic strengths, their apparent zeta potential can also vary to a different extent, depending on $\partial\zeta/\partial c$, thus leading to different particle dynamics. If possible, this would enable the separation of particles with similar apparent zeta potentials at a given salt concentration but distinct surface physico-chemical properties that influence the relationship between apparent zeta potential and local salt concentration. In practice, the dependence of zeta potential on salt concentration is often neglected, and the assumption $\partial\zeta/\partial c = 0$ is commonly used in studies on diffusiophoresis/osmosis effects [18,12–17,26–35]. This is because constant potential models facilitate the theoretical work and also provide a good quantitative agreement with experimental observations in most cases [25], apart a few exceptions [36–38]. As a result, the anticipated opportunity for passive continuous separation of particles with similar zeta potentials but different surface physico-chemical properties seems to be out of reach.

In a previous study, we presented a physical mechanism whereby diffusiophoresis and diffusoosmosis are closely intertwined, leading to a strong transverse focusing of particles towards the central region of a straight channel under continuous and steady flow conditions. A double $\Psi$-junction device, generating salt concentration gradients from the merging of 0.1 mM and 10 mM LiCl aqueous streams, was developed to exploit this focusing mechanism for preconcentration, sorting, and characterization of liposomes and charged polystyrene beads with a diameter ranging from 20 nm to 1 $\mu\text{m}$ [18]. Again, under the examined conditions, a constant zeta potential model allows the quantitative prediction of the experimental results. Also, charge-based separation was only possible for oppositely charged particles, whereas size-based separation was achieved efficiently only between 20 nm and 1 $\mu\text{m}$ particles. In this study, we investigated the particle dynamics in the same device, but under varying ionic strengths, ranging from 0.01 mM to 100 mM. Remarkably, we found that in this wider range of salt concentrations, the effect of ionic strength on particle and wall zeta potential becomes apparent, and the experimental observations can be interpreted only by accounting for a salt concentration dependent zeta potential. More surprisingly, we discovered that similarly-sized carboxylate polystyrene particles exhibiting comparable values of apparent zeta potential but different surface concentration of carboxyl groups and thus opposite apparent zeta potential sensitivities to the local salt concentration, namely $\partial\zeta/\partial c > 0$ and $\partial\zeta/\partial c < 0$, can be continuously separated with high separation efficiency.

Our findings, supported by experimental and numerical analyses, open up unprecedented opportunities for the diffusiophoresis/osmosis-assisted microfluidic continuous separation of synthetic or biological particles, including macromolecules [29,39,40], liposomes [28,41–43], exosomes [33] and bacterial cells [44,45], based exclusively on their surface physico-chemical properties.
<figure><img src="image_5.png" /><figcaption>**Fig. 1.** (a) Schematic of the micro-chip for the manipulation of colloids via a salinity gradient. Inner inlet stream: LiCl solution at a low concentration ($c_L$ = 1 mM). Outer streams of upstream junction: LiCl solution at low concentration ($c_L$) seeded with red fluorescent ($d$ = 0.5 µm) carboxylate polystyrene particles, shown as red dots. The particle concentration was set to 0.002% (v/v). Outer streams of downstream junction: LiCl solution at high salt concentration ($c_H$ = 1 mM). Dashed lines represent the outer boundaries of the colloidal streams. The red shading represents the local level of salinity. (b) Epi-fluorescence micrographs at $z/w_m$ = 36 without (left) and with (right) a salinity gradient. Scale bar is 75 µm. White dashed lines represent the boundary of the micro-channel.</figcaption></figure>

## 2. Results

The double Ψ-junction micro-chip used for particle focusing in continuous flow settings [18] is illustrated in Fig. 1a. The device consists of a narrower (upstream) junction, where the inner inlet channel meets the middle inlet channels and merges into the middle channel of width $w_m$. This is followed by a wider (downstream) junction, where the middle channel meets the outer inlet channels and merges into the main channel (see Supplementary Text for channel sizes). The flow rates of the inner, middle and outer streams were fixed to 3.65 µL min⁻¹, and the particle dynamics was observed using an epi-fluorescent microscope. Lithium chloride (LiCl) salt was employed to establish solute gradients perpendicular to the flow, by injecting low-concentration LiCl solution ($c_L$) in the inner and middle inlets and either low or high-concentration LiCl solution ($c_H$) in the outer inlets. Colloidal particles were dispersed in the middle inlet stream only. Fig. 1 shows the typical dynamics of sub-micron beads ($d$ = 549.8 ± 6.8 nm and $\zeta_p$ = -50.4 ± 0.2 mV at 0.1 mM LiCl) when low and high salt concentrations are $c_L$ = 0.1 mM and $c_L$ = 10 mM, respectively. A reference coordinate system is introduced as shown in (Fig. 1a), with the origin located at the downstream junction and at the mid-point along the channel depth and width.

In the absence of a salt concentration gradient ($\nabla c = 0$) – namely, when all streams have the same low salinity level – the particles remain homogeneously dispersed in the colloidal bulk (Fig. 1b). However, when the outer flow streams are switched to a high salt solution, a steady state salt gradient is imposed ($\nabla c \neq 0$), driving the particles towards higher salt concentration regions along this direction, as illustrated by the dashed lines in Fig. 1a. This motion is driven by the x component of the diffusiophoretic velocity, $u_{DP,x} = \Gamma_{DP} \frac{\partial \ln c}{\partial x}$, with $\Gamma_{DP}$ the diffusio-phoresis mobility.

In addition, two highly intense peaks of accumulated colloids, separated by a distance $\Delta_p$, form at the entrance of the junction ($z/w_m$ = 0), and rapidly converge towards the center of the device, downstream of the junction. The dynamics of these accumulation peaks have been studied in our previous works [31,18], and Migacz and co-workers [46] and Liu and Pahlavan [47] have clarified further the underlying mechanisms. Briefly, the vertical (y-axis) component of the salt concentration gradient induces the formation of two symmetric accumulation peaks in close proximity to the top and the bottom walls of the microchannel. The dynamics of these peaks along the transverse direction is governed by the competition between the horizontal (x-axis) particle diffusiophoresis velocity, $u_{DP,x}$, which pushes the particle outwards, and the wall diffusioosmosis velocity, $u_{DO,x} = -\Gamma_{DO} \frac{\partial \ln c}{\partial x}$ – with $\Gamma_{DO}$ the diffusiophoresis mobility – which advects the particle inwards. The total transversal particle velocity can be approximated as $u_{p,x} = \Gamma_{eff} \frac{\partial \ln c}{\partial x}$, where $\Gamma_{eff} = \Gamma_{DP} - \Gamma_{DO}$ is the effective mobility. Hence, when $\Gamma_{eff} > 0$, diffusiophoresis is dominant and the particles accumulated near the wall

migrate towards the outer regions of the channel. Conversely, when $\Gamma_{eff} < 0$, diffusioosmosis is dominant and the particles migrate towards the central region of the channel [46,47]. For the particle type shown in Fig. 1b (i.e., 0.5 µm, red), the effective mobility $\Gamma_{eff}$ is negative for any salt concentration in the range from $c_L$ = 0.1 mM to $c_H$ = 10 mM, as shown in Figure S4. Consequently, this causes the displacement of the particle accumulation peaks towards the center, as it can be observed in the fluorescence micrographs in Fig. 1b.

### 2.1. Effects of ionic strength on particle dynamics

The ionic strength of the solution can alter the zeta potentials of both particles and channel walls, which in turn affect the diffusiophoretic and diffusioosmotic mobilities, respectively. Moreover, the ionic strength can drastically influence the thickness of the electric double layer and, consequently, the diffusiophoretic mobility. The investigation of the effect of ionic strength on the particle focusing mechanism was conducted by varying the intensity of the low ($c_L$) and high ($c_H$) salt concentration streams while maintaining a constant salt concentration ratio $c_H/c_L$, thereby an approximately constant relative solute gradient $\nabla(\ln c) = \nabla c/c$. This allows one to modify the effective mobility $\Gamma_{eff}$ without significantly altering $\nabla(\ln c)$. Thus, it is reasonable to expect that the formation and subsequent motion of particle peaks near the walls of the device could also be altered.

#### 2.1.1. Experimental analysis

The dynamics of carboxylate polystyrene particles of various nominal diameters (20 nm, 100 nm, 200 nm, 0.5 µm and 1 µm) were investigated. The low salt concentration of the streams injected in the upstream junction was varied to either $c_L$ = 0.01, 0.1 or 1 mM, while the salt concentration ratio was fixed at $c_H/c_L$ = 100 by adjusting the higher salt concentration $c_H$ of the outer flows of the downstream junction. Fig. 2a-c present the normalized fluorescence intensity profiles along the transverse direction x at a normalized distance $z/w_m$ = 36 (i.e., z = 9 mm) downstream of the junction for various particle sizes under different values of $c_L$. The normalized fluorescence intensity profiles $I(x^*)$ with $x^* = x/w_m$, provide a measure of the particle concentration along x, averaged over the depth of field of the microscope system and normalized with respect to the concentration of the solution injected into the device. Specifically, $I_{norm}(x) \approx 0$ where no particles are detected, whereas $I_{norm}(x) \approx 1$ where the depth-average particle concentration is close to the concentration $n_0$ of the colloidal solution injected into the device (see Supplementary Text for further details).

In the case of low ionic strength – namely, $c_L$ = 0.01 mM and $c_H$ = 1 mM, compactly expressed as 0.01–1 mM in the remainder of the paper – sub-micron particles do not form accumulation peaks, and they
<figure><img src="image_6.png" /><figcaption>**Fig. 2.** Normalized transverse fluorescent intensity profiles for particles of varying sizes under different ionic strength conditions. Each panel corresponds to different ion concentration fields where $c_L$ is (a) 0.01 mM, (b) 0.1 mM, and (c) 1 mM, with a fixed concentration ratio $c_H/c_L = 100$. In panel (a), the particle concentration at the inlet stream is 0.02% (v/v) for all particle type. In panels (b) and (c), the concentration of the 20 nm and 200 nm particles at the inlet is 0.02% (v/v), while for 0.5 µm and 1 µm particles it is 0.002% (v/v). Fluorescent intensity profiles were analyzed from epi-fluorescent micrographs taken at a distance of $z/w_m = 36$ (i.e., $z = 9$ mm) downstream of the junction. Insets: fluorescence micrographs showing the different dynamics of 0.5 µm and 1 µm particles.</figcaption></figure>

display only a weak particle drift towards the inner region of the channel (Fig. 2a). A particle accumulation effect is apparent instead for 1 µm colloids for which well-defined peaks – with a normalized average peak intensity of 1.3 – migrate slightly inward into the channel. Irrespective of the size, no particles are detected in the region $|x|/w_m < 0.1$, indicating a rather weak mobility of the particles along the transverse direction.

Conversely, under moderate ionic strength (0.1-10 mM, Fig. 2b), the accumulation effect is substantially amplified for all investigated particle sizes. In the case of sub-micron particles, the intensity of the colloidal front becomes more apparent, and the intensity profiles display intense fluorescent peaks that are otherwise absent under low electrolyte concentrations. Intriguingly, for 1 µm colloids, the normalized average peak intensity reaches a value of 2.9, almost two times greater than the peak intensity for the same particle size under low ionic strength condition. Consistently with the findings reported in our previous study [18], par-

ticles with similar apparent zeta potential but larger size exhibit more intense accumulation effects due to their higher diffusiophoretic mobilities, which promote faster migration toward the walls. This is because smaller particles have larger values of the electric double layer thickness to particle radius ratios $(\kappa a)^{-1}$, which hinder their diffusiophoretic migration. The diminished particle accumulation effect under lower ionic strength conditions could be attributed to a reduced diffusiophoresis mobility, which is responsible for the particle migration along the channel depth-wise (y) direction and the accumulation at the top and bottom walls of the device. This interpretation is supported by the numerical simulations reported in the Supplementary Text, and it justifies why the observed particle manipulation mechanism is severely restricted in the salt concentration range 0.01-1 mM. Therefore, such conditions are not suitable for particle manipulation applications.

The transversal motion of accumulated particles – either inward or outward – can be predicted by computing the effective mobility $\Gamma_{eff}$ as function of the salt concentration (Figure S4). For salt concentrations equal or lower than 1 mM, $\Gamma_{eff}$ is always negative for any particles size. This indicates that diffusioosmotic induced flows prevail over particle diffusiophoresis in the x-direction. As a result, it can be anticipated that under low ionic strength conditions all particles will migrate inwards, as confirmed by the experimental observations in Fig. 2a. Under moderate ionic strength conditions, the salt concentration varies between 0.1 to 10 mM, and in this range $\Gamma_{eff}$ is always negative for sub-micron particles. Again, the predicted inward migration of particles is confirmed by the experimental observations in Fig. 2b.

Remarkably, in the salt concentration range for moderate ionic strength (0.1-10 mM), the calculated effective mobility of 1 µm particles is negative at lower concentrations and positive at higher concentrations. Consequently, it is expected that the particles which are accumulated near the walls in the lower concentration region, migrate inward. Conversely, the particles which are accumulated near the walls in the higher concentration regions, migrate outward. This interpretation, which is also confirmed by the numerical model discussed in the next section, is consistent with the experimental data in Fig. 2b. Indeed, the fluorescence intensity profile for 1 µm particles under moderate ionic strength conditions is the only profile displaying four accumulation peaks, two in the inner (lower salt concentration) region and two in the outer (higher salt concentration) regions. Importantly, the formation of four peaks moving along opposite directions cannot occur if the particle and wall zeta potentials and thus the diffusioosmosis, diffusiophoresis and effective mobilities were independent of the local salt concentration, as assumed in previous studies. Such finding demonstrates the importance of accounting for the effect of salt concentration on particle and wall zeta potentials and mobilities to interpret the experimental observations in our system.

Fig. 2c illustrates the intensity profile plots for the investigated particle size range under high ionic strength conditions (1-100 mM). For sub-micron particles, the profiles display four accumulations peaks – two in the inner region of the channel and two in the outer regions at the edges of the colloidal bands – with the exception of the 20 nm particles, for which the two inner peaks are not formed and a weak particle drift toward the center of the channel is observed instead. This observation is consistent with the calculated values of effective mobilities of these particles (Figure S4), which go from negative to positive at increasing salt concentrations within the range 1-100 mM. As observed for the moderate ionic strength case, the intensity of either diverging or converging peaks increases with the particle size because of the higher diffusiophoresis mobility of the larger particles. Moreover, the intensity of the peaks migrating inward is slightly lower under high ionic strength conditions than under moderate ionic strength conditions. Indeed, due to the change in the sign of the effective mobilities under high ionic strength conditions, a fraction of the colloids accumulated at the walls is pushed outward, resulting in a lower amount of colloids focusing in the inner region of the channel.
For 1 µm colloids, the accumulation peaks are absent from the cen-
ter of the device (Fig. 2c). Instead, two intense peaks can be seen to
diverge outward, towards high salt concentration regions (Fig. 2c). This
behavior is in stark contrast to the inward transverse displacement dis-
played by all sub-micron particles (≤ 500 nm) tested under the same
ion concentration field. The observed particle dynamics aligns with our
interpretation of a salt concentration-dependent focusing mechanism
since for 1 µm particles the effective mobility is positive for salt concen-
trations above 3.4 mM, namely almost the whole range of concentration
from 1 to 100 mM. Strikingly, the diverging particle peaks exhibit signif-
icantly pronounced fluorescent intensities with a normalized maximum
peak intensity value of 4.55, which is much larger than the intensity
peak values achieved for any other particle size under all examined con-
ditions. Such an intense focusing effect is the result of the high values of
the diffusiophoresis mobility of the 1 µm particles in the 1-100 mM salt
concentration range (Figure S3). Specifically, in this concentration range
the diffusiophoresis mobility of the 1 µm particles reaches a maximum
of 960 µm²s⁻¹, that is more than twice the mobility of any sub-micron
particles at any examined salt concentration.

To conclude, it is apparent that a high electrolyte concentration field
induces a change in the trajectory of 1 µm particle peaks when compared
to smaller particle sizes (Fig. 2c,d). The difference in particle dynamics
implies that this effect can be exploited for separation applications, as
exemplified in the micrographs in Fig. 2c illustrating the contrasting
motion of 0.5 and 1 µm particle peaks under high ionic strength condi-
tions. Before discussing the implementation of this particle separation
strategy, we will present the results of the numerical study that was
conducted to confirm the interpretation of the experimental analysis of
particle dynamics under high ionic strength conditions.

2.1.2. *Numerical analysis*

The dynamics of the colloidal particles was simulated through a fi-
nite element model developed in COMSOL Multiphysics (Supplementary
Text). The numerical hydrodynamic velocity field *u*, salt concentration
*c*, and particle concentration *n*, were calculated in a 3D domain consist-
ing of a straight rectangular channel. For the domain shape, we adopted
the channel sizes of the revised double-junction device, used in the sep-
aration experiments described in the next sections. In this new device,
the average velocity is the same for all inner and side channels, thus
there is no hydrodynamic broadening of the streams, which occurs in-
stead in the version of the device used for the experiments in Fig. 2. To
simulate the dynamics of the different types of particles examined in the
experiments, the particle diffusiophoresis mobilities were calculated as a
function of the local salt concentration as detailed in the Supplementary
Text. Similarly, a salt concentration-dependent diffusioosmosis mobility
was used in the simulation as detailed in the Supplementary Text.

Fig. 3b shows the simulated transverse profile of the normalized
particle concentration *n*/*n*<sub>0</sub> for 0.5 µm red fluorescent colloids at a nor-
malized distance from the downstream junction of *z*/*w*<sub>m</sub> = 25 (i.e.,
*z* = 5 mm) under high ionic strength conditions (1-100 mM). Consis-
tently with the experimental observations in Fig. 2c, the simulated pro-
file displays four accumulations peaks, two in the inner region and two
in the outer regions of the channel. Note that a close quantitative match
between experimental and numerical profiles is not expected since the
experimental profiles correspond to the convolution of the particle flu-
orescence intensity with the microscope point-spread function, whereas
the numerical profiles are calculated from the simulated particle con-
centration field by averaging the concentration over the channel depth
(*y* direction). A very good quantitative agreement between numerical
predictions and experimental observations can be seen in the inset of
Fig. 3b for the normalized inward displacement of the inner peaks, de-
fined as δ<sub>p</sub>(*z*) = (Δ<sub>p</sub>(0) − Δ<sub>p</sub>(*z*))/2 *w*<sub>m</sub>. This is consistent with the fact
that the effect of the microscope point-spread function on δ<sub>p</sub>(*z*) mea-
surements should be negligible.

Fig. 3c shows the simulated particle concentration field on the plane
perpendicular to the flow direction at z/w<sub>m</sub> = 25. Due to symmetry with

respect to the *x* and *y* axes, the concentration field is visualized only on
the top right quadrant of the channel cross-section, corresponding to the
red-shaded region in the schematic in Fig. 3a. The competing effects of
diffusoiosmosis and diffusiophoresis at the channel walls are apparent in
the in-plane total particle velocity field *u*<sub>p</sub>, shown by the white arrows
in Fig. 3c. As expected, since the particle effective mobility is negative
(positive) in the low (high) salt concentration regions, the total particle
velocity near the wall is directed inward (outward) in the inner (outer)
region of the channel. Consequently, a fraction of the particles accumu-
lated near the wall migrate inward and the reminder outward, leading
to the formation of two converging and two diverging peaks in the sim-
ulated particle concentration profile (Fig. 3b), in agreement with the
experimental observations (Fig. 2c).

On the other hand, for 1 µm particles under high ionic strength con-
ditions the effective mobility is positive, and the total particle velocity
is directed outward, almost anywhere near the walls (Fig. 3e). Conse-
quently, all particles accumulated at the wall migrate outward, resulting
in the formation of only two intense diverging peaks in the outer regions
of the channel, which are visible both in the simulated particle concen-
tration profile in Fig. 3d and in the experimental fluorescence intensity
profile in Fig. 2c. Furthermore, in the simulations – as observed in
the experiments – the 1 µm colloids are totally excluded from the central
region of the channel |*x*|/*w*<sub>m</sub> < 0.25. Notably, the high value of diffusio-
phoresis mobility of 1 µm particles at the examined salt concentrations
leads to a strong accumulation of colloids near the wall, where the par-
ticle concentration is predicted to exceed 30 times that of the solution
injected into the device (Fig. 3e).

2.2. Separation of particles by surface chemistry

The capability of continuously separating 0.5 µm from 1 µm carboxy-
late polystyrene particles by diffusiophoresis is remarkable, but also
quite surprising. Indeed, in these particle size range the diffusiophore-
sis mobility weakly depends on particle diameter, which suggests that
the separation mechanism must be chemical in nature. On the other
hand, the particles are made of the same polymer modified with the
same functional group, hence no significant difference in the particle
chemistry is expected. In fact, at a salt concentration of c<sub>L</sub> = 1 mM, the
two particle species have a similar apparent zeta potential, namely ζ<sub>p</sub> =
-47.2 ± 0.4 mV for 0.5 µm and ζ<sub>p</sub> = -68.7 ± 1.1 mV for 1 µm colloids,
corresponding to a relative difference of about 30%.

The solution to this conundrum lies in the plots of particle appar-
ent zeta potential against salt concentration (Fig. 4), which are notice-
ably different for these two types of particles. Specifically, for 0.5 µm
red particles the magnitude of the apparent zeta potential decreases
monotonically with the logarithm of the electrolyte concentration (i.e.
∂l/∂ζ|/∂c < 0), whereas for 1 µm particles the apparent zeta potential has
an extremum and below this point its magnitude increases with the salt
concentration (i.e. ∂l/∂ζ|/∂c > 0). The fall off in the magnitude of ap-
parent zeta potential of polystyrene colloids at low concentrations of an
indifferent monovalent electrolyte has been investigated in several stud-
ies [48–55]. Apparently, this observation contradicts the predictions of
the classical Gouy–Chapman model of the electrical double layer for
which a monotonic decrease with increasing salt concentration is ex-
pected due to the compression of the electric double layer. A similar
trend has been observed also for other materials, such as silica [56] and
other minerals [22].

As discussed in the extensive review by Hidalgo-Alvarez et al. [23],
under certain experimental conditions the Henry’s formula is no longer
valid and the apparent zeta potential is lower than the real zeta poten-
tial. Consequently, it has been shown that the weakening of the apparent
zeta potential, measured by electrophoretic light scattering, at the lower
ionic strengths reflects the reduction in electrophoretic mobility caused
by the surface electrical conductivity of the polystyrene particles [22].
This effect becomes apparent at the lower salt concentrations (i.e. lower
conductivities of the surrounding medium K₀) when the surface conduc-
<figure><img src="image_7.png" /><figcaption>**Fig. 3.** Numerical simulation results. (a) Schematic of the channel in the region near the downstream junction where particle dynamics were simulated ($w_m = 300$ µm, $h = 45$ µm). (b,c) Simulated normalized particle concentration profile (b) and particle distribution (c) on the cross-section slice highlighted in red in panel (a) at $z/w_m = 25$ (i.e., $z = 5$ mm) for 0.5 µm red particles at high ionic strength condition (1-100 mM). Inset in panel (b) shows the simulated (solid circles) and experimental (open triangles) normalized inward displacements of the inner peaks, $\delta_p = (\Delta_p(0) - \Delta_p(z))/2w_m$, as a function of the normalized distance from the downstream junction, $z/w_m$. (d,e) Simulated normalized particle concentration profile (d) and particle distribution (e) on the same cross-section slice at $z/w_m = 25$ (i.e., $z = 5$ mm) for 1 µm red particles at high ionic strength condition. In panel (c) and (e), the white arrows represent the streamlines of the total particle velocity $\mathbf{u}_p$ and the solid colored lines are the salt concentration isolines, which are slightly bent due to the Poiseuille-like velocity profile, thus leading to the generation of a vertical component of the salt concentration gradient. (For interpretation of the colors in the figure, the reader is referred to the web version of this article.)</figcaption></figure>

tance of the particles $K_s$ is comparable to the product of the medium conductivity and particle radius $a$ – namely, the Dukhin number $K_s/K_0a$ is not negligible. Combined with the compression of the electric double layer at the higher ionic strengths, the magnitude of the electrophoretic mobility and, thus, of the apparent zeta potential calculated according to Henry’s formula, may exhibit a point of maximum. Experimental observations indicate that the effects of surface conductance on particle electrophoretic mobility are more prominent for larger particles [53] and higher surface charges [49]. This justifies why the 1 µm particles with twice the size and four times the surface concentration of carboxyl groups compared to the red 0.5 µm particles (Table S1), display an extremum in the apparent zeta potential plot. Conversely, for all other red sub-micron particles, the effect of surface conductance is negligible and the zeta potential is instead a monotonic function of the salt concentration.

In a private communication, the technical support team of the particle supplier (Thermo Fisher Scientific) confirmed that slight variations in the actual diameter and surface charge concentration are expected between the examined carboxylate-modified polystyrene particles, as indicated in the certificate of analysis of the products. Additionally,

the charge concentration per particle is somewhat correlated with the particle diameter, with larger diameter beads exhibiting higher charge content per bead. This is because even slight variations in the amount of styrene monomer and incubation time in the emulsion polymerization process for particle synthesis may affect the actual particle diameter. Likewise, minimal changes in the amount of carboxyl groups added to the solution and the incubation time of the second polymerization process – required to create a dense, highly charged, porous layer of polymers containing carboxyl groups on the surface of the beads – may affect the actual carboxyl concentration of the particles.

In the next sections, we demonstrate the effective separation of similarly-sized carboxylate polystyrene particles based on their opposite apparent zeta potential sensitivity to the local salt concentration.

### 2.2.1. Separation of red 0.5 µm and 1 µm particles

For the separation experiments, we introduced a new variation of the double Ψ-junction device that enables the separation and extraction of particles converging towards the center of the device. Fig. 5a illustrates a schematic of the updated device with two key modifications. First, two side outlets and one central outlet are incorporated at the end of the microfluidic chip. The central outlet is designed to be quite narrow.
<figure><img src="image_8.png" /><figcaption>**Fig. 4.** Apparent zeta potential $\zeta_p$ as a function of LiCl salt concentration for different particle types. Top: 0.5 µm fluorescent red. Middle: 1 µm fluorescent red. Bottom: 0.5 µm fluorescent yellow-green particles. Markers are experimental data and dashed solid lines are the fits to Eq. (S4) in Supplementary Text for the 0.5 µm red particles and to Eq. (S5) in Supplementary Text for the 1 µm red and 0.5 µm yellow-green particles. Error bars, which are often smaller than the marker size, are calculated as the standard deviation of three repeated measurements of a sample.</figcaption></figure>

row to prevent the extraction of undesired streams. The design of the outlet channels ensures that under a no salinity gradient condition ($\nabla c = 0$), the injected colloidal streams exit solely through the side channel outlets. On the other hand, when there is a salinity gradient ($\nabla c \neq 0$), the particles from the peaks that converge towards the inner region of the device, can be extracted and recovered from the central outlet stream. Furthermore, the length of the channel downstream of the second junction was increased to allow the separation process to occur over longer distances. Finally, the width of the inner and outer channels of the two junctions were adjusted to prevent hydrodynamic focusing or broadening [18,57] (see Supplementary Text for channel sizes).

To carry out the separation experiment, a salt concentration ratio of $c_H/c_L = 100$ was imposed under high ionic strength conditions (1-100 mM). The flow configuration remained identical to previous experiments, as depicted in Fig. 5a, but the colloidal solution injected into the side channels of the downstream junction consisted in a binary mixture of 0.5 µm diameter (0.02% v/v) and 1 µm diameter (0.002% v/v) red fluorescent carboxylate polystyrene particles. The flow rate in each inlet of the device was 10 µL/min. To evaluate the separation process, the colloidal mixture injected into the device, referred to as the inlet stream, and the solution extracted from central outlet were analyzed.

Note that since both particle species were stained with the same fluorophore dye, it was not possible to perform an on-chip analysis of the separation process via epi-fluorescence imaging. Therefore, an off-line epi-fluorescence imaging procedure was adopted instead (see *Materials and Methods* section for details).

Fig. 5b shows an exemplar off-chip epi-fluorescence image of the dried colloidal sample extracted from the inlet (left) and central outlet (right) solutions. Note that the strong refractive index contrast between the colloidal particles and the surrounding medium (air) resulted in image distortion and particle lens effect, explaining why the 1 µm particles appear much larger than the 0.5 µm particles. Analyzing the inlet mixture sample revealed a total particle count of 11,629 where 90.5% of the population is represented by 0.5 µm colloids and the remaining 9.5% being 1 µm particles. Conversely, a total of 4,221 particles were detected in the central outlet droplet, all of which were 0.5 µm colloids. This corresponds to a 100% removal of 1 µm particle from the central outlet stream and a 40% recovery rate of 0.5 µm particle, namely 40% of the smaller particles injected into the device are recovered in the central outlet stream. The successful separation of the smaller particles from the mixture was also validated via dynamic light scattering analysis of the inlet and central outlet solutions (see Supplementary Text).

### 2.2.2. Separation of 0.5 µm red and yellow-green 0.5 µm particles

In the previous experiment, the particle separation is achieved because the opposite sensitivities of particle apparent zeta potential to salt concentration result in opposite effective mobilities (i.e. $\Gamma_{eff} < 0$ for sub-micron particles and $\Gamma_{eff} > 0$ for 1 µm particles) at almost any concentration in the range from $c_L$ to $c_H$ under higher ionic strength conditions (1-100 mM). The separation is not possible at lower and intermediate ionic strength conditions (i.e., 0.01-1 mM and 0.1-10 mM), since the effective mobility of 1 µm particles is also mostly negative at these salt concentrations. Nevertheless, it can be hypothesized that two particle species can still be separated even if they exhibit a negative effective mobility in the lowest salt concentration stream ($c_L$), namely they have rather similar diffusiophoresis mobilities, and hence similar size and apparent zeta potential in this stream. Indeed, as the electrolyte streams with low ($c_L$) and high ($c_H$) salt concentrations mix downstream of the junction, the particles are exposed to a surrounding solution with increasing salinity levels. If the rise in local salt concentration affects the apparent zeta potential of the two particle types in different ways, then their effective mobilities may also evolve differently depending on the particle surface physico-chemical properties. Specifically, if the local salt concentration becomes high enough to reverse the sign of the effective mobility of one particle species but not the other, the particles can be separated. Such a strategy would enable the fine separation of particles with very similar size and apparent zeta potential at the lowest salt concentration $c_L$, but different surface physico-chemical properties that affect their apparent zeta potential sensitivity to local ionic strength.

<figure><img src="image_9.png" /><figcaption>**Fig. 5.** Separation of a binary suspension of red fluorescent 0.5 µm and 1 µm carboxylate polystyrene particles. (a) Schematic of a long double Ψ-junction device showcasing the separation and subsequent extraction of 0.5 µm from 1 µm particles under high ionic strength conditions. A low salt concentration stream of $c_L = 1$ mM was injected in all channels of the upstream junction with the side channels containing a binary 1:10 (v/v) mixture of 1 µm and 0.5 µm carboxylate polystyrene particles. High salt concentration ($c_H = 100$ mM) streams were introduced in the side channels of the downstream junction. A particle concentration of 0.02% (v/v) and 0.002% (v/v) were used for the 0.5 µm and 1 µm colloids, respectively. (b) Off-chip epi-fluorescence images of dried samples of the inlet (left) and central outlet (right) streams. Scale bar represents 2.5 µm. The channel width $w_m$ is 200 µm.</figcaption></figure>
<figure><img src="image_10.png" /><figcaption>**Fig. 6.** Separation of a binary 1:1 (v/v) mixture of red-fluorescent and yellow-green fluorescent 0.5 µm carboxylate polystyrene particles. A low salt concentration ($c_L$ = 1 mM) was injected in all channels of the upstream junction with the side channels containing the binary colloid mixture. High salt concentration ($c_H$ = 100 mM) streams were injected in the side channels of the downstream junction. A particle concentration of 0.002%(v/v) was used for both yellow-green and red colloids. (a,b) Schematic and epi-fluorescence micrographs illustrating the distribution of red (a) and yellow-green (b) 0.5 µm particles at short ($z/w_m$ = 45) distance (blue rectangle) and long ($z/w_m$ = 175) distance (green rectangle) from the downstream junction. (c) Normalized fluorescence intensity profiles for both red and yellow-green particles at $z/w_m$ = 45 (left) and $z/w_m$ = 175 (right). (d) Overlaid epi-fluorescence micrographs of red and yellow-green 0.5 µm particles at $z/w_m$ = 45 (left) and 175 (right). Scale bar represents 50 µm. (For interpretation of the colors in the figure, the reader is referred to the web version of this article.)</figcaption></figure>

To demonstrate this separation strategy, an experiment was conducted in a double Ψ-junction device with the revised geometry previously described. The flow configuration was as in Fig. 5a with $c_L$ = 1 mM and $c_H/c_L$ = 100. In this instance, two populations of 0.5 µm carboxylate polystyrene particles, one fluorescently stained in red and one in yellow-green, were mixed in 1:1 (v/v) ratio in a solution at 0.002% v/v concentration and injected in the side channels of the upstream junction. The flow rate in each inlet of the device was 3.65 µL/min. At a salt concentration of $c_L$ = 1 mM, the 0.5 µm red and yellow-green particles have similar apparent zeta potential, namely $\zeta_p$ = -47.2 ± 0.4 mV for red and $\zeta_p$ = -58.3 ± 1.1 mV for yellow-green colloids, corresponding to a relative difference of just 20%. As a result, the effective mobility is negative for both particle types at this salt concentration. Importantly, the two particle species, although made of the same material, have a different surface chemical composition whereby the surface concentration of carboxyl groups of the yellow-green particles is almost nine times the one of the red particles (Table S1). Consequently, the effects of particle surface conductance are not negligible for the yellow-green particles and the magnitude of the apparent zeta potential, and thus of the electrophoretic mobility, increases with the salt concentration until it reaches a maximum around 10 mM (Fig. 4).

Fig. 6 shows the individual and combined particle dynamics of both sets of colloids in the mixture under high ionic strength conditions. Epi-fluorescence micrographs of either red (Fig. 6a) or yellow-green

(Fig. 6b) particles were taken at short (i.e. $z/w_m$ = 45, namely $z$ = 9 mm) and long (i.e. $z/w_m$ = 175, namely $z$ = 35 mm) distances from the downstream junction. At a short distance, the normalized fluorescence intensity profiles along the transverse direction $x$ (Fig. 6c) exhibit a similar trend to those in Fig. 2c for sub-micron colloids under high ionic strength conditions at a distance of $z$ = 9 mm from the downstream junction. Since for both particle types the effective mobility change signs within the salt concentration range 1-100 mM, two converging and two diverging accumulation peaks can be observed in the intensity profiles for both red and yellow-green particles. The slight difference in the intensities and positions of the four peaks between the two profiles is due to the different diffusiophoresis mobilities of the two particle species. At such a distance from the junction, the regions of the channel occupied by the red and yellow-green particles overlap and separation is not possible.

On the other hand, a stark difference between the intensity profiles of the two particle types is apparent at a long distance from the junction. At this location, the two peaks of yellow-green colloids, originally located in the inner region of the channel, almost vanished. Conversely, the two red particle peaks in the center of the channel survived, retaining a similar intensity to the one observed closer to the junction. Consequently, the near-complete disappearance of focused yellow-green particles in the inner region of the channel enables the separation between the two particle species. As illustrated by the overlaid red and yellow-green mi-
crographs in Fig. 6d, the red particle can be extracted from the binary mixture of red and yellow-green particles and recovered from central outlet stream.

To justify the observed dynamics, a numerical simulation was performed to calculate the salt concentration profile along the transverse direction at the channel wall and at either short ($z/w_m = 45$) or long ($z/w_m = 175$) distances from the downstream junction (Supplementary Text). The profiles were then used to calculate the effective mobility as a function of the transverse direction $x$ for both red and yellow-green particles. As shown in Figure S9a-b, the effective mobility of the red particles is negative in the inner region of the channel $x/w_m < 0.25$ both at short and long distance from the junction. On the other hand, the effective mobility of yellow-green particles in the same region changes from negative values at $z/w_m = 45$ to positive values at $z/w_m = 175$. This is because at large distances from the junction the electrolyte streams are mixed and the salt concentration at the channel walls ranges approximately between 2 and 3.5 mM. At these concentrations, the magnitude of the apparent zeta potential of the yellow-green particles increases ($\partial|\zeta|/\partial c > 0$) and their diffusiophoresis mobility is high enough to overcome the diffusioosmosis mobility, causing the particles to leave the center of the channel and migrate outwards. This is not the case for the red particles, for which $\partial|\zeta|/\partial c < 0$ and the diffusiophoresis mobility depends very weakly on the salt concentration (Figure S3). As a result, the dominating effect of diffusioosmosis confines the red particles in the inner region of the channel.

### 3. Discussion

Our findings demonstrate that the effect of salt concentration on the zeta potentials of the channel walls and colloidal particles can affect significantly the particle dynamics in our microfluidic device under the examined experimental conditions. A constant zeta potential model ($\partial\zeta/\partial c = 0$), which is commonly used in diffusiophoresis studies, cannot explain characteristic features of the observed particle dynamics, such as the formation of four accumulation peaks in the particle concentration profiles along the transverse direction of the channel (Fig. 2) and the reversal of the direction of motion of the accumulation peaks downstream of the junction (Fig. 6). At the low ionic strength conditions (0.01-1 mM), particle manipulation capability is severely restricted due to the weakening of diffusiophoresis effect caused by the thickening of the electric double layer. This result aligns with prior research, wherein, for a constant salt concentration ratio, lower electrolyte concentrations led to lower diffusiophoresis mobilities [58,59].

Generally, the accumulation of particles at the channel walls is more intense for larger particles. For 1 µm particles under high ionic strength conditions, we predicted a peak of particle concentration 30 times larger than the concentration of the colloidal solution injected into the device – an effect that could be exploited for the preconcentration of samples in microfluidic analytical systems. Particle focusing is only weakly affected by the particle size since the diffusiophoresis mobility depends weakly on this parameter. Under high ionic strength conditions, the average magnitude of the accumulation peaks in the transverse intensity profile for the 500 nm particles (ca. 1.5) is about four time higher than the peak's magnitude for the 100 nm particles (ca. 0.35) (Fig. 2c). This result suggests that the device could be adopted for the continuous removal of 0.1 µm particles from a mixture of 0.1 µm and 0.5 µm colloids, but the separation process would be incomplete since a fraction of the smaller particles will remain mixed with the larger particles.

Remarkably, the diffusiophoresis-driven dynamics of the particles are significantly affected by the surface concentration of carboxyl groups even if the particles have similar sizes and similar values of apparent zeta potential, namely electrophoretic mobility, in the solution in which they are originally dispersed (i.e. the low salt concentration stream). At first, this may sound like an oxymoron since zeta potential and diameter are the only properties of a rigid particle that affect its diffusiophoresis mobility. However, for larger ($\ge 0.5$ µm) particles, a higher surface con-

centration of ionizable groups translates, at the lower ionic strengths, in a non-negligible surface conductance effect that slows down the electrophoretic motion of the particle [52]. Consequently, for particles with a higher surface concentration of carboxyl groups, the magnitude of the apparent zeta potential (measured via electrophoretic light scattering and Henry's formula) increases with the local salt concentration ($\partial|\zeta|/\partial c > 0$) until it reaches a point of maximum between 1 and 10 mM. Conversely, the particles with a lower surface concentration of carboxyl groups exhibit a magnitude of the apparent zeta potential that decreases monotonically with the salt concentration ($\partial|\zeta|/\partial c < 0$). As the electrolyte streams mix downstream of the junction, the particle apparent zeta potential and, thus, diffusiophoresis mobility evolve differently depending on the particle's carboxyl group surface concentration.

Importantly, in our device the direction of particle migration along the transverse direction depends on the balance between the convection flows induced by diffusioosmosis at the channel walls, pushing the particle inwards, and the particle diffusiophoresis motion, pushing the particle outwards. Therefore, although the diffusiophoresis mobility of the examined particles is always positive, as they are all negatively charged, the colloids can move in opposite directions (either inwards or outwards) and, thus they can be separated, depending on whether their local diffusiophoresis mobility is greater or lower than the local diffusioosmosis mobility. In other words, diffusioosmosis at the channel walls plays a critical role in the separation mechanism.

In previous studies on passive and continuous separation of particles by diffusiophoresis the role of diffusioosmosis was negligible, and only particles with oppositely charged surface groups, and thus opposite diffusiophoresis mobilities, could be separated easily. In an externally-activated system, like the one recently introduced by Bekir and coworkers [60], diffusioosmotic flows are instead instrumental to the particle manipulation mechanism and particles can be separated based on their porosity, bulk chemistry or type of surface groups; however, this approach applies only to sedimenting particles and, like other active manipulation technique, it requires the use of an external energy source and auxiliary equipment. In our device, polystyrene particles with similar or identical sizes and same surface group chemistry, exhibiting only a slight difference (up to 30%) in the apparent zeta potential in the solution in which they are dispersed, can be continuously separated with high efficiency solely based on the concentration of the surface carboxyl groups. Specifically, for the separation experiments with 0.5 µm and 1 µm particles, 100% of the particles with the higher surface charge concentration (i.e., the 1 µm particles) were removed from the central outlet stream, whereas 40% of the particles with the lower surface charge concentration (i.e., 0.5 µm particles) were recovered from the central outlet stream. This result is unprecedented as no other microfluidic technique, whether active or passive, enables continuous particle separation based solely on the concentration of a surface group.

The proposed mechanism opens up new opportunities for the continuous separation of particles based not only on the surface concentration of ionizable groups but also on other important surface physico-chemical properties that influence the sensitivity of the particle electrophoretic mobility and apparent zeta potential to the local electrolyte concentration. For instance, it is reported that the roughness of polystyrene microbeads can affect their electrokinetic properties and, thus, apparent zeta potential depending on the ionic strength of the solution [50,61]. Hence, the mechanism reported in this study could be exploited for the separation of rough particles, for which $\partial|\zeta|/\partial c > 0$, from smooth particles, for which $\partial|\zeta|/\partial c < 0$ [54]. Similarly, particles coated with a polyelectrolyte coating, for which $\partial|\zeta|/\partial c \simeq 0$, could be separated from uncoated particles for which $\partial|\zeta|/\partial c < 0$ [38]. Furthermore, particle surface chemistry could be distinguished based on their different affinity to ions and other solutes that may affect their apparent zeta potential to different extent under varying ionic strength conditions [54]. More generally, the effects of 3D charge distribution, surface ion and flow permeabilities (i.e. porosity) and surface hetero-
geneity may alter the sensitivity of the particle electrophoretic mobility to the local salt concentration [62].

In conclusion, this microfluidic strategy could potentially be used for the continuous separation of colloids, such as engineered particles, environmental contaminants and biocolloids (e.g., liposomes, extracell-ular vesicles and bacterial cells) distinguished solely by differences in these surface physical and chemical properties, which is of great rele-vance especially for the purification of synthetic and biological samples. By relying on a simple experimental set-up with no external energy sources and by adopting easy-to-operate microchips, our microfluidic technique may facilitate fundamental studies of the physics, chemistry and biology of these particles, and also underpin the development of new microfluidic technological tools for chemical and biochemical anal-ysis, diagnostics, environmental monitoring, drug screening, and drug delivery applications.

# 4. Materials and methods

## 4.1. Materials

Polydimethylsiloxane (PDMS) RTV-615a and curing agent RTV-615b used for the fabrication of microfluidic channels were purchased from Techsil, UK. Pre-cleaned Corning™ glass slides used as the substrate to make PDMS microfluidic chips were purchased from Thermo Fisher scientific. 1H,1H,2H,2H-Perfluorooctyl-trichlorosilane was purchased from Merck and used for substrate silanisation. All aqueous solutions were prepared using deionized water (18.2 MΩ cm) produced from an ultrapure milli-Q grade purification system (Millipore, USA). Lithium chloride salt (LiCl, 99%) was purchased from Acros Organics. Red flu-orescent (580/605), carboxylate polystyrene beads (Invitrogen™ Part Number F8887, lot number 2294999) were purchased from Thermo Fisher Scientific at various nominal sizes. The 200 nm red fluores-cent (580/605), carboxylate polystyrene beads were purchased sepa-rately from Thermo Fisher Scientific (Invitrogen™ Part Number F8810, lot number 1934417A). Also the 500 nm yellow-green fluorescent (505/515) carboxylate polystyrene beads were purchased separately from Thermo Fisher Scientific (Invitrogen™ Part Number F8813, lot number 2247969).

## 4.2. Sample preparation

For all microfluidic experiments, the colloidal particle stock solu-tions (2% solids) were diluted in either $c_L = 0.01$ mM, 0.1 mM or 1 mM LiCl solution. The particle concentration was chosen to work in the dilute regime (i.e., negligible particle interaction) and to prevent both clustering and excessive surface contamination. The exact salt and parti-cle concentrations of the dispersions used are defined in their respective figure captions.

## 4.3. Fabrication and operation of the microfluidic devices

Microfluidic devices were made from PDMS channels bonded to a glass substrate. To make PDMS channels, standard photo-lithography and soft-lithography techniques were employed, as reported else-where [18]. For the results reported in Fig. 1 and 2, an inverted optical microscope (TE300, Nikon) equipped with a 10x objective lens (0.25 NA) was used to capture epi-fluorescence micrographs of the devices. A fluorescent lamp (CoolLED pE300) was used to excite the sample, which allowed the collection of fluorescent intensity data via a CCD camera (Ximea MQ013MG-ON). Collected data is in the form of 1264 x 1016 px, 16 bit TIFF images. For the results reported in other figures, a home-made inverted optical microscope was used to capture epi-fluorescence micrographs of the device. The microscope was assembled with Thor-labs components and featured an X-Cite 200 fluorescent lamp (Excelitas, Canada) and a CCD camera (Ximea MQ013MG-ON). A Nikon Plan fluor 10x objective lens (0.30 NA) was used for online imaging of particle

dynamics inside the microfluidic devices. For the experiment requir-ing offline epi-fluorescence imaging (Fig. 5), an oil immersion 100x (1.25 NA) was used instead. All epi-fluorescence micrographs of the mi-crofluidic devices were acquired by positioning the focal plane nearby the bottom (glass) wall and subsequently processed via ImageJ (contrast enhancement, LUT color change).

## 4.4. Offline epi-fluorescence micrograph analysis

A 30 µL drop of either the inlet or the central outlet solution was independently placed on a clean microscope slide. The droplet was then sandwiched by a coverslip and allowed to dry overnight. A Parafilm® layer with a punched circular all of ca. 5 mm in diameter was used as a spacer between the two glass substrates. Both the coverslip and the microscope slide were silanized via physical vapor deposition to make them hydrophobic and prevent the spreading of the drop on the glass surfaces. Different regions of the dried sample were then imaged under epi-fluorescence mode with hundreds of micrographs captured for each sample. ImageJ software was used to count the total number of particles in each frame and to determine the particle size distribution within the inlet and outlet solution.

## 4.5. Particle characterization

Size and zeta potential measurements were performed a minimum of three times at 25 °C using a ZetaSizer Ultra Red (Malvern Panalytical) equipped with a He-Ne laser (633 nm). For size measurements, non-invasive backscatter (173°angle) was used for all particle sizes. Error bars for particle size and zeta potential were calculated as standard devi-ations of at least three consecutive measurements of the sample loaded in the ZetaSizer. Details on the zeta potential measurements are pro-vided in Supplementary Text.

## CRediT authorship contribution statement

**Adnan Chakra:** Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Methodology, Investigation, Data curation. **Christina Puijk:** Writing – review & editing, Writing – original draft, Validation, Methodology, Investigation, Data curation. **Goran T. Vladisavljević:** Writing – review & editing, Writing – original draft, Supervision, Methodology, Funding acquisition. **Cécile Cottin-Bizonne:** Writing – review & editing, Writing – original draft, Supervision, Methodology. **Christophe Pirat:** Writing – review & editing, Writing – original draft, Supervision, Methodology. **Guido Bolognesi:** Writing – review & editing, Writing – original draft, Visualization, Supervision, Software, Methodology, Funding acquisition, Formal analysis, Data curation, 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.

## Acknowledgements

This research was supported by Engineering and Physical Sciences Research Council (EPSRC) grants EP/S013865/1 and EP/X01813X/1. For the purpose of open access, the authors have applied a Creative Commons Attribution (CC BY) license to any Author Accepted Manuscript version arising.

## Appendix A. Supplementary material

Supplementary material related to this article can be found online at https://doi.org/10.1016/j.jcis.2025.137577.
# Data availability

The data underlying this study are openly available on University College London repository [63].

Surface Chemistry-based Continuous Separation of Colloidal Particles via Diffusiophoresis and Diffusioosmosis (Original data) (Figshare)

# References

[1] S. Lin, Z. Yu, D. Chen, Z. Wang, J. Miao, Q. Li, D. Zhang, J. Song, D. Cui, Progress in microfluidics-based exosome separation and detection technologies for diagnostic applications, Small 16 (9) (2020) 1903916.

[2] D. Buschmann, V. Mussack, J.B. Byrd, Separation, characterization, and standardization of extracellular vesicles for drug delivery applications, Adv. Drug Deliv. Rev. 174 (2021) 348–368.

[3] S.M. Majedi, H.K. Lee, Recent advances in the separation and quantification of metallic nanoparticles and ions in the environment, TRAC, Trends Anal. Chem. 75 (2016) 183–196.

[4] P. Juliano, S. Temmel, M. Rout, P. Swiergon, R. Mawson, K. Knoerzer, Creaming enhancement in a liter scale ultrasonic reactor at selected transducer configurations and frequencies, Ultrason. Sonochem. 20 (1) (2013) 52–62.

[5] J.J. Milledge, S. Heaven, A review of the harvesting of micro-algae for biofuel production, Rev. Environ. Sci. Bio/Technol. 12 (2013) 165–178.

[6] W. Fraunhofer, G. Winter, The use of asymptotic flow field-flow fractionation in pharmaceutics and biopharmaceutics, Eur. J. Pharm. Biopharm. 58 (2) (2004) 369–383.

[7] S.P. Yeap, J. Lim, B.S. Ooi, A.L. Ahmad, Agglomeration, colloidal stability, and magnetic separation of magnetic nanoparticles: collective influences on environmental engineering applications, J. Nanopart. Res. 19 (2017) 1–15.

[8] R. Nasiri, A. Shamloo, S. Ahadian, L. Amirifar, J. Akbari, M.J. Goudie, K. Lee, N. Ashammakhi, M.R. Dokmeci, D. Di Carlo, et al., Microfluidic-based approaches in targeted cell/particle separation based on physical properties: fundamentals and applications, Small 16 (29) (2020) 2000171.

[9] P. Sajeesh, A.K. Sen, Particle separation and sorting in microfluidic devices: a review, Microfluid. Nanofluid. 17 (2014) 1–52.

[10] J. McGrath, M. Jimenez, H. Bridle, Deterministic lateral displacement for particle separation: a review, Lab Chip 14 (21) (2014) 4139–4158.

[11] D. Di Carlo, Inertial microfluidics, Lab Chip 9 (21) (2009) 3038–3046.

[12] B. Abécassis, C. Cottin-Bizonne, C. Ybert, A. Ajdari, L. Bocquet, Boosting migration of large particles by solute contrasts, Nat. Mater. 7 (10) (2008) 785–789.

[13] B. Abécassis, C. Cottin-Bizonne, C. Ybert, A. Ajdari, L. Bocquet, Osmotic manipulation of particles for microfluidic applications, New J. Phys. 11 (7) (2009) 075022.

[14] S. Shin, O. Shardt, P.B. Warren, H.A. Stone, Membraneless water filtration using co₂, Nat. Commun. 8 (1) (2017) 15181.

[15] K. Lee, J. Lee, D. Ha, M. Kim, T. Kim, Low-electric-potential-assisted diffusiophoresis for continuous separation of nanoparticles on a chip, Lab Chip 20 (15) (2020) 2735–2747.

[16] T.J. Shimokusu, V.G. Maybruck, J.T. Ault, S. Shin, Colloid separation by co₂-induced diffusiophoresis, Langmuir 36 (25) (2019) 7032–7038.

[17] M. Seo, S. Park, D. Lee, H. Lee, S.J. Kim, Continuous and spontaneous nanoparticle separation by diffusiophoresis, Lab Chip 20 (22) (2020) 4118–4127.

[18] A. Chakra, N. Singh, G.T. Vladisavljevic, F. Nadal, C. Cottin-Bizonne, C. Pirat, G. Bolognesi, Continuous manipulation and characterization of colloidal beads and liposomes via diffusiophoresis in single- and double-junction microchannels, ACS Nano 17 (15) (2023) 14644–14657.

[19] B.J. Kirby, E.F. Hasselbrink Jr, Zeta potential of microfluidic substrates: 1. Theory, experimental techniques, and effects on separations, Electrophoresis 25 (2) (2004) 187–202.

[20] B.J. Kirby, E.F. Hasselbrink Jr, Zeta potential of microfluidic substrates: 2. Data for polymers, Electrophoresis 25 (2) (2004) 203–213.

[21] R.J. Hunter, Foundations of Colloid Science, 2nd edition, Oxford University Press, Oxford, 2001.

[22] R.J. Hunter, The significance of stagnant layer conduction in electrokinetics, Adv. Colloid Interface Sci. 100 (2003) 153–167.

[23] R. Hidalgo-Alvarez, A. Martin, A. Fernandez, D. Bastos, F. Martinez, F. De Las Nieves, Electrokinetic properties, colloidal stability and aggregation kinetics of polymer colloids, Adv. Colloid Interface Sci. 67 (1996) 1–118.

[24] R.W. O'Brien, L.R. White, Electrophoretic mobility of a spherical colloidal particle, J. Chem. Soc., Faraday Trans. 2: Mol. Chem. Phys. 74 (1978) 1607–1626.

[25] S. Lee, J. Lee, J.T. Ault, The role of variable zeta potential on diffusiophoretic and diffusioosmotic transport, Colloids Surf. A, Physicochem. Eng. Asp. 659 (2023) 130775.

[26] J.T. Ault, P.B. Warren, S. Shin, H.A. Stone, Diffusiophoresis in one-dimensional solute gradients, Soft Matter 13 (47) (2017) 9015–9023.

[27] S. Shin, J.T. Ault, J. Feng, P.B. Warren, H.A. Stone, Low-cost zeta potentiometry using solute gradients, Adv. Mater. 29 (30) (2017) 1701516.

[28] S. Shin, E. Um, B. Sabass, J.T. Ault, M. Rahimi, P.B. Warren, H.A. Stone, Size-dependent control of colloid transport via solute gradients in dead-end channels, Proc. Natl. Acad. Sci. 113 (2) (2016) 257–261.

[29] J. Palacci, B. Abécassis, C. Cottin-Bizonne, C. Ybert, L. Bocquet, Colloidal motility and pattern formation under rectified diffusiophoresis, Phys. Rev. Lett. 104 (13) (2010) 138302.

[30] N. Singh, G.T. Vladisavljevic, F. Nadal, C. Cottin-Bizonne, C. Pirat, G. Bolognesi, Enhanced accumulation of colloidal particles in microgrooved channels via diffusiophoresis and steady-state electrolyte flows, Langmuir 38 (46) (2022) 14053–14062.

[31] N. Singh, G.T. Vladisavljević, F. Nadal, C. Cottin-Bizonne, C. Pirat, G. Bolognesi, Reversible trapping of colloids in microgrooved channels via diffusiophoresis under steady-state solute gradients, Phys. Rev. Lett. 125 (24) (2020) 248002.

[32] N. Singh, A. Chakra, G.T. Vladisavljević, C. Cottin-Bizonne, C. Pirat, G. Bolognesi, Composite norland optical adhesive (noa)/silicon flow focusing devices for colloidal particle manipulation and synthesis, Colloids Surf. A 652 (2022) 129808.

[33] M.K. Rasmussen, J.N. Pedersen, R. Marie, Size and surface charge characterization of nanoparticles with a salt gradient, Nat. Commun. 11 (1) (2020) 2337.

[34] S. Shin, J.T. Ault, K. Toda-Peters, A.Q. Shen, Particle trapping in merging flow junctions by fluid-solute-colloid-boundary interactions, Phys. Rev. Fluids 5 (2) (2020) 024304.

[35] J.T. Ault, S. Shin, H.A. Stone, Diffusiophoresis in narrow channel flows, J. Fluid Mech. 854 (2018) 420–448.

[36] A. Visan, R.G. Lammertink, Reaction induced diffusio-phoresis of ordinary catalytic particles, React. Chem. Eng. 4 (8) (2019) 1439–1446.

[37] B. Akdeniz, J.A. Wood, R.G. Lammertink, Diffusiophoresis and diffusio-osmosis into a dead-end channel: role of the concentration-dependence of zeta potential, Langmuir 39 (6) (2023) 2322–2332.

[38] B. Akdeniz, J.A. Wood, R.G. Lammertink, Diffusiophoretic behavior of polyelectrolyte-coated particles, Langmuir 40 (11) (2024) 5934–5944.

[39] L.R. Lechlitner, O. Annunziata, Macromolecule diffusiophoresis induced by concentration gradients of aqueous osmolytes, Langmuir 34 (32) (2018) 9525–9531.

[40] S.M. Friedrich, J.M. Burke, K.J. Liu, C.F. Ivory, T.-H. Wang, Molecular rheotaxis directs dna migration and concentration against a pressure-driven flow, Nat. Commun. 8 (1) (2017) 1213.

[41] A. Kodama, Y. Sakuma, M. Imai, T. Kawakatsu, N. Puff, M.I. Angelova, Migration of phospholipid vesicles can be selectively driven by concentration gradients of metal chloride solutions, Langmuir 33 (40) (2017) 10698–10706.

[42] S.V. Hartman, B. Božič, J. Derganc, Migration of blood cells and phospholipid vesicles induced by concentration gradients in microcavities, New Biotechnol. 47 (2018) 60–66.

[43] S. Shin, V.S. Doan, J. Feng, Osmotic delivery and release of lipid-encapsulated molecules via sequential solution exchange, Phys. Rev. Appl. 12 (2) (2019) 024014.

[44] S. Shim, S. Khodaparast, C.-Y. Lai, J. Yan, J.T. Ault, B. Rallabandi, O. Shardt, H.A. Stone, Co 2-driven diffusiophoresis for maintaining a bacteria-free surface, Soft Matter 17 (2021) 2568–2576.

[45] V.S. Doan, P. Saingam, T. Yan, S. Shin, A trace amount of surfactants enables diffusiophoretic swimming of bacteria, ACS Nano 14 (10) (2020) 14219–14227.

[46] R.E. Migacz, G. Durey, J.T. Ault, Convection rolls and three-dimensional particle dynamics in merging solute streams, Phys. Rev. Fluids 8 (2023) 114201.

[47] H. Liu, A.A. Pahlavan, Diffusioosmotic reversal of colloidal focusing direction in a microfluidic t-junction, Phys. Rev. Lett. 134 (9) (2025) 098201.

[48] C. Zukoski IV, D. Saville, An experimental test of electrokinetic theory using measurements of electrophoretic mobility and electrical conductivity, J. Colloid Interface Sci. 107 (2) (1985) 322–333.

[49] A.F. Barbero, R.M. García, M.C. Vilchez, R. Hidalgo-Alvarez, Effect of surface charge density on the electrosurface properties of positively charged polystyrene beads, Colloids Surf. A, Physicochem. Eng. Asp. 92 (1–2) (1994) 121–126.

[50] J.E. Seebergh, J.C. Berg, Evidence of a hairy layer at the surface of polystyrene latex particles, Colloids Surf. A, Physicochem. Eng. Asp. 100 (1995) 139–153.

[51] M. Minor, A.J. van der Linde, J. Lyklema, Streaming potentials and conductivities of latex plugs in indifferent electrolytes, J. Colloid Interface Sci. 203 (1) (1998) 177–188.

[52] J. Lyklema, M. Minor, On surface conduction and its role in electrokinetics, Colloids Surf. A, Physicochem. Eng. Asp. 140 (1–3) (1998) 33–41.

[53] I. Ermolina, H. Morgan, The electrokinetic properties of latex particles: comparison of electrophoresis and dielectrophoresis, J. Colloid Interface Sci. 285 (1) (2005) 419–428.

[54] S. Lu, K. Zhu, W. Song, G. Song, D. Chen, T. Hayat, N.S. Alharbi, C. Chen, Y. Sun, Impact of water chemistry on surface charge and aggregation of polystyrene microspheres suspensions, Sci. Total Environ. 630 (2018) 951–959.

[55] M.V. Manila, N.I. Lebovka, S. Barany, Effects of sort and concentration of salts on the electrosurface properties of aqueous suspensions containing hydrophobic and hydrophilic particles: validity of the hofmeister series, J. Mol. Liq. 276 (2019) 875–884.

[56] P. Leroy, N. Devau, A. Revil, M. Bizi, Influence of surface conductivity on the apparent zeta potential of amorphous silica nanoparticles, J. Colloid Interface Sci. 410 (2013) 81–93.

[57] G.-B. Lee, C.-C. Chang, S.-B. Huang, R.-J. Yang, The hydrodynamic focusing effect inside rectangular microchannels, J. Micromech. Microeng. 16 (5) (2006) 1024.

[58] A. Gupta, S. Shim, H.A. Stone, Diffusiophoresis: from dilute to concentrated electrolytes, Soft Matter 16 (30) (2020) 6975–6984.

[59] D.C. Prieve, S.M. Malone, A.S. Khair, R.F. Stout, M.Y. Kanj, Diffusiophoresis of charged colloidal particles in the limit of very high salinity, Proc. Natl. Acad. Sci. 116 (37) (2019) 18257–18262.
[60] M. Bekir, M. Sperling, D.V. Muñoz, C. Braksch, A. Böker, N. Lomadze, M.N. Popescu, S. Santer, Versatile microfluidics separation of colloids by combining external flow with light-induced chemical activity, Adv. Mater. 35 (25) (2023) 2300358.

[61] J.F. Duval, J.P.S. Farinha, J.P. Pinheiro, Impact of electrostatics on the chemodynamics of highly charged metal–polymer nanoparticle complexes, Langmuir 29 (45) (2013) 13821–13835.

[62] P.P. Gopmandal, J.F. Duval, Electrostatics and electrophoresis of engineered nanoparticles and particulate environmental contaminants: beyond zeta potential-based formulation, Curr. Opin. Colloid Interface Sci. 60 (2022) 101605.

[63] A. Chakra, C. Puijk, G. Vladisavljevic, C. Cottin-Bizonne, C. Pirat, G. Bolognesi, Surface Chemistry-Based Continuous Separation of Colloidal Particles via Diffusio-phoresis and Diffusioosmosis, April 2025, https://doi.org/10.5522/04/28731329 (FigShare).