3D particle transport in multichannel microfluidic networks with rough surfaces

Abstract

The transport of particles and fluids through multichannel microfluidic networks is influenced by details of the channels. Because channels have micro-scale textures and macro-scale geometries, this transport can differ from the case of ideally smooth channels. Surfaces of real channels have irregular boundary conditions to which streamlines adapt and with which particle interact. In low-Reynolds number flows, particles may experience inertial forces that result in trans-streamline movement and the reorganization of particle distributions. Such transport is intrinsically 3D and an accurate measurement must capture movement in all directions. To measure the effects of non-ideal surface textures on particle transport through complex networks, we developed an extended field-of-view 3D macroscope for high-resolution tracking across large volumes ([Formula: see text]) and investigated a model multichannel microfluidic network. A topographical profile of the microfluidic surfaces provided lattice Boltzmann simulations with a detailed feature map to precisely reconstruct the experimental environment. Particle distributions from simulations closely reproduced those observed experimentally and both measurements were sensitive to the effects of surface roughness. Under the conditions studied, inertial focusing organized large particles into an annular distribution that limited their transport throughout the network while small particles were transported uniformly to all regions.

Figure 1

(a) Layout of the fracture network in the flow-cell. All channels were etched to a depth of $\sim 200\mathrm{\mu }\text{m}$, but have different widths. The initial segment of the flow cell was $1000\mathrm{\mu }\text{m}$ wide. At the location labeled split #1, the channels were $500\mathrm{\mu }\text{m}$, $1000\mathrm{\mu }\text{m}$, and $750\mathrm{\mu }\text{m}$ wide (left to right). The final channels, in the split #2 region, were $250\mathrm{\mu }\text{m}$, $500\mathrm{\mu }\text{m}$, $1000\mathrm{\mu }\text{m}$, $500\mathrm{\mu }\text{m}$, and $750\mathrm{\mu }\text{m}$ wide (left to right). (b) Fully assembled flow-cell with inlet and outlet ports. The top surface in this photograph was the illuminated side and the bottom was the surface through which the flow-cell was imaged. The etched channels and inlet/outlet ports were components of the top plate while the bottom plate was a clean and smooth glass slide. (c) Schematic of the astigmatic macroscope used for 3D particle tracking. Fluorescent particles in the flow-cell are excited with a 470 nm LED fitted with a 477/60 nm emission filter. A microscope objective ($1.25\times$ or $2\times$ Plan Apo, Olympus) serves as the first element of a tandem lens pair with a 135 mm camera lens (Canon) serving as the second element of the pair and the corrective optics. A 488 nm dichroic beamsplitter in the infinity space between the pair is used to isolate the emission from the excitation. Astigmatism is introduced with a 400 mm focal length cylindrical lens before the camera. (d) $10\mathrm{\mu }\text{m}$ diameter (top) and $45\mathrm{\mu }\text{m}$ diameter (bottom) particle distributions measured at the position labeled initial in (a). Both distributions were measured at a volumetric flow rate of 25 $\mathrm{\mu }\text{L}/\text{min}$. The smaller particles are uniformly distributed within the channel at this point while the larger particles have formed an annulus.

Figure 2

Cross sections of the particle distributions for $10\mathrm{\mu }\text{m}$ beads at a volumetric flow rate of 25 $\mathrm{\mu }\text{L}/\text{min}$. (a) Experimentally measured cross sections (top) and LBM simulations (bottom) after the first set of channel splits. (b) Experiment/simulation cross section pair after the second set of channel splits. The channel profiles within the region that the cross-section was measured (1 mm slice) are plotted as multiple overlapping semi-transparent black lines to indicate the local boundaries. Particle velocities are indicated by color. In both regions, the distribution edges follow the smooth top surface and irregular bottom surfaces of the flow-cell and were uniformly distributed within the channels. Consistent with Poiseuille (pressure-induced) flow, the highest particle velocities occurred in the center of the channels. The velocities decreased as the outer two channels split and the same volume of fluid expanded to fill the larger cross-sectional areas, unlike the center channel that did not split and had the same profile in both regions.

Figure 3

Cross sections of the particle distributions for $45\mathrm{\mu }\text{m}$ beads measured at a volumetric flow rate of 75 $\mathrm{\mu }\text{L}/\text{min}$. The upper plot of (a) shows the experimentally measured cross sections after the first set of channel splits and the lower plot shows the results from simulation. Similarly, the upper and lower plots in (b) show the experimental and simulation results, respectively, after the second set of channel splits. The distributions of $45\mathrm{\mu }\text{m}$ particles within the channels are not uniform: an annulus with no particles flowing through the centers of the channels. None of the $45\mathrm{\mu }\text{m}$ particles were transported into the smallest (bottom left) channel.

Figure 4

Ratios of particles distributed into each channel. (a) The relative numbers of particles distributed into each of the three channels after the first branching section of the flow-cell. The upper pair depicts the distributions for the $10\mathrm{\mu }\text{m}$ particles and the lower pair depicts the distributions for the $45\mathrm{\mu }\text{m}$ particles. Experimentally observed distributions are indicated in blue and the corresponding LBM simulations in orange. The central channel corresponds to the non-hatched segment while the outer channels are depicted with hatched bars. Uncertainty bars for the ratios correspond to $3\sigma$ of a multinomial distribution based on the number of particles in the ratio calculation. (b) The relative numbers of particles distributed into each of the five channels after the second branching section of the flow-cell. The outer-most channels are depicted with spot filling. Because none of the $45\mathrm{\mu }\text{m}$ particles entered the left-most channel, this segment does not appear in the lower pair. In all but the case of $45\mathrm{\mu }\text{m}$ particles after the second branching, the experimental and simulation results showed similar distributions.

Figure 5

Inertial focusing of $45\mathrm{\mu }\text{m}$ particles from the feed tube. Orthogonal projections of the flow-cell inlet region at a volumetric flow rate of 25 $\mathrm{\mu }\text{L}/\text{min}$ are shown in (a) with a 1.25$\times$ objective for extended depth imaging. Color scales of each plot indicate distance along the flattened axis of each projection. The size and approximate position of the feed tube is indicated in red (hatched boxes and dashed circle). The distribution of the particles exiting the feed tube was an annulus smaller than the diameter of the feed tube. Expansion into the inlet region and compression into the rectangular cross-section of the initial channel is depicted in this figure. LBM simulations of the inertial focusing as the particles travel through the feed tube, (b), indicate the $10\mathrm{\mu }\text{m}$ particles did not migrate significantly while the $45\mathrm{\mu }\text{m}$ particles found an equilibrium at the same radial distance as the experimentally observed annulus. Tracks of several tracer particles starting at various radial distances from the center of the feed tube are shown. The length of feed tube of the experiment was $100\text{mm}$.