Particle trapping in merging flow junctions by fluid-solute-colloid-boundary interactions

Merging of different streams in channel junctions represents a common mixing process that occurs in systems ranging from soda fountains and bathtub faucets to chemical plants and microfluidic devices. Here, we report a spontaneous trapping of colloidal particles in a merging flow junction when the merging streams have a salinity contrast. We show that the particle trapping is a consequence of nonequilibrium interactions between the particles, solutes, channel, and the freestream flow. A delicate balance of transport processes results in a stable near-wall vortex that traps the particles. We use three-dimensional particle visualization and numerical simulations to provide a rigorous understanding of the observed phenomenon. Such a trapping mechanism is unique from the well-known inertial trapping enabled by vortex breakdown [Proc. Natl. Acad. Sci. USA 111, 4770 (2014)], or the solute-mediated trapping enabled by diffusiophoresis [Phys. Rev. X 7, 041038 (2017)], as the current trapping is facilitated by both the solute and the inertial effects, suggesting a new mechanism for particle trapping in flow networks.

Figure 1

Particle trapping induced by merging of different saline solutions at a T-junction. (a) Schematic of a symmetric T-junction with merging flows of solute concentrations $c_1$ and $c_2$. (b) A photograph of a glass microfluidic T-junction device made by selective laser-induced etching. (c) Image sequence of fluorescent colloidal particles (carboxylate-modified polystyrene latex, $1\mu \mathrm{m}$ in diameter) accumulating near the junction by merging of two colloidal suspensions with different solute concentrations (NaCl, $c_1=10\mathrm{mM}$, $c_2=0.01\mathrm{mM}$). Inlet mean flow speed is $U=0.34\mathrm{mm}/\mathrm{s}$. The channel has a square cross section with width $w=0.7\mathrm{mm}$ throughout the entire channel. See also Movie 1 in the Supplemental Material [22]. (d) Particle trapping versus the inlet mean flow speed. The images are taken at 5 min after the flow has started.

Figure 2

Particle trapping is a consequence of interactions between diffusiophoresis, diffusioosmosis, and inlet fluid flow. (a) Solute distribution $c$ in a 2D T-junction. Near the interface between two streams, a solute gradient is established that induces diffusioosmosis directed toward the less saline stream (positive $x$ direction). Because diffusioosmosis is a slip flow, the combination of diffusioosmosis and inlet fluid flow results in a vortical flow near the wall. (b) Close-up simulation results near the wall [red box in (a)] showing fluid streamlines, $c$, $-{\partial }_{y}c$, and particle trajectories. (c) Solute concentration adjacent to the wall ($y\to 0$) normalized by the bulk solute concentration of more saline stream ($c_1$) near the interface of the two solutions for various inlet mean flow speeds. $x$ is rescaled by the channel width $w$, $x^{*}=x/w$. (d) A snapshot of the T-junction observed from the front ($x\text{−}y$ plane). A small region of the trapped particles is denoted by a red box. (e) A reconstructed image of the particles in the red box in (c) by overlaying image sequence to visualize the particle trajectories. (f) Normalized solute dispersion length ${\ell }_{\text{s}}^{*}={\ell }_{\text{s}}/w$, normalized particle cluster length ${\ell }_{\text{p}}^{*}={\ell }_{\text{p}}/w$, and (g) normalized particle cluster location $x_{\text{p}}^{*}=x_{\text{p}}/w$ versus the inlet mean flow speed $U$. ${\ell }_{\text{s}}^{*}$ and ${\ell }_{\text{p}}^{*}$ for various wall diffusioosmotic conditions are presented by altering the solution pH. Open blue circle represents ${\ell }_{\text{s}}^{*}$, open triangle, diamond, and square represent ${\ell }_{\text{p}}^{*}$ at various pH conditions, and closed triangle, diamond, and square represent $x_{\text{p}}^{*}$ at various pH conditions. (h) ${\ell }_{\text{s}}^{*}$ and ${\ell }_{\text{p}}^{*}$ replotted with ${\mathrm{Pe}}^{*}=Uw/{\mathcal{M}}_{\text{w}}$.

Figure 3

Colloidal vortices. (a) A full 3D simulation of the colloidal vortex at $U=0.34\mathrm{mm}/\mathrm{s}$. Close-up images of the vortex from the red box are elongated by a factor of 10 times in the $y$ direction for a better visualization. (b) Particle trajectories cropped from the red box in Fig. 2. The image is also elongated 10 times in the $y$ direction for comparison. (c) Particle trajectories in $x\text{−}z$ planes for various flow rates. Simulated particle trajectories are also presented for comparison. See also Movie 2 in the Supplemental Material [22]. (d), (e) Particle trajectories for the merging flows having colloidal particles only in either (d) the less saline (0.01 mM) or (e) the more saline (10 mM) solution. Only the particles coming from the less saline side are trapped. See also Movie 3 in the Supplemental Material [22].

Figure 4

Solute transport determines the morphology of the particle cluster. (a), (b) 3D simulations of the particle $n$ and the solute $c$ distributions at (a) $U=0.34\mathrm{mm}/\mathrm{s}$ and (b) $10\mathrm{mm}/\mathrm{s}$ adjacent to the channel wall. (c), (d) Close-up images of the solute gradient in the $z$ direction (${\partial }_{z}c$), flow velocity in the $z$ direction ($u_z$), and the particle velocity in the $z$ direction ($u_z+{\mathcal{M}}_{\mathrm{p}}{\partial }_z\ln c$) from the red boxes in (a, b). Particle trajectories are overlaid on the particle velocity panels. Yellow dots represent the particle stagnation points. (e), (f) $u_z$ taken along the $z$ axis that intersects the maximum particle concentration regions [$x^{*}=0.45$ in (e); $x^{*}=0.16$ in (f)]. Blue curves indicate $u_z$ in the absence of diffusioosmosis (${\mathcal{M}}_{\mathrm{w}}=0\mu {\mathrm{m}}^2/\mathrm{s}$). Red curves indicate $u_z$ in the presence of diffusioosmosis (${\mathcal{M}}_{\mathrm{w}}=1600\mu {\mathrm{m}}^2/\mathrm{s}$). Gray curves indicate $u_z$ in between the two diffusioosmosis conditions with an interval of $200\mu {\mathrm{m}}^2/\mathrm{s}$. $z$ is rescaled by the channel width $w$, $z^{*}=z/w$. All the data are taken at $y=5\mu \mathrm{m}$.

Figure 5

Diffusioosmosis enhances diffusiophoresis. (a), (b) 2D simulations of (a) the solute gradient in the $y$ direction ${\partial }_{y}c$ and (b) their distribution near the interface at $y=50\mu \mathrm{m}$. The gradient is plotted with an interval of $200\mu {\mathrm{m}}^2/\mathrm{s}$. (c) Close-up images of the particle concentration $n$ from the red box in (a) for various wall diffusioosmotic mobilities ${\mathcal{M}}_{\mathrm{w}}$. (d) Particle distributions in $x\text{−}z$ plane for various pH values. The images are taken at 5 min after the flow has started. Yellow arrows in (c), (d) indicate the locations of the center of the particle cluster $x_{\text{p}}$. $U=0.34\mathrm{mm}/\mathrm{s}$ for all cases.

Figure 6

Particle trapping also occurs in other merging flow geometries. Particle trapping in a staggered T-junction where two inlets are offset. The channel has a square cross section, but with different widths for the inlets and the outlet; 0.7 mm for the inlets and 1.2 mm for the outlet. (a) Experimental and (b) full 3D numerical simulation results for various inlet mean flow speeds. See also Movie 4 in the Supplemental Material [22].