Hydrodynamic resistance of a yeast clog

Bioclogging, the clogging of pores with living particles, is a complex process that involves various coupled mechanisms such as hydrodynamics and particle properties. The lack of sensitive methods to simultaneously measure the hydraulic resistance of a clog and the position of particles at high enough resolutions limits our understanding of this tight fluid-structure interplay. In this article, we explored bioclogging at the microscale level, where flow rates are typically extremely low ($<100\mathrm{nl}{\min }^{-1}$). We developed a highly sensitive method to precisely measure small flow rates ($<6.7\%$ error) with a low response time ($<0.2\mathrm{s}$) while retaining the capability to image the structure of a fluorescently labeled yeast clog at high resolution. This method employed a microfluidic device with two identical channels: a first one for a yeast suspension and a second one for a colored culture medium. These channels merged into a single wide outlet channel, where the interface of the colored medium and the medium coming from the yeast clog could be monitored. As a yeast clog formed in the first channel, the displacement of the interface between the two media was imaged and compared to a pre-calibrated image database, quantifying the flow through the clog. We carried out two kinds of experiments to explore the fluid-clog interaction: filtration under constant operating pressure and filtration under oscillating operating pressure (backflush cycles). We found that in both scenarios, the resistance increased with clog length. On the one hand, experiments at constant imposed pressure showed that the clog's permeability decreased with increased operating pressure, with no detectable changes in cell density as assessed through fluorescence imaging. On the other hand, backflush cycles resulted in an approximately four times higher permeability, associated with a significant nonmonotonic decrease in cell density with the operating pressure. Leveraging on our unique dual measurement of fluid flow and clog microstructure, our study offered enhanced insights into the intricate relationships between clog microstructure, permeability, and construction history. A better understanding of the fluid-structure interplay allowed us to develop a novel physical modeling of the flow in a soft and confined porous medium that challenged the empirical power-law description used in bioclogging theory by accurately replicating the measured permeability-pressure variations.

Figure 1

Micrography of the microsystem ($5\times$ magnification). The yeast suspension is pushed in the left-hand microchannel at pressure $P_0+\mathrm{\Delta }{P}_1$, with $P_0$ the atmospheric pressure. The constriction retains the yeast particles, so a clog is constructed on the left-hand microchannel. Colored culture medium flows in the right-hand microchannel at pressure $P_0+\mathrm{\Delta }{P}_2$. An interface between clear and colored liquids appears downstream of the merging region, where the pressure equals $P_0+P_p$. The location of this interface is used to measure the flow rate ratio between the two microchannels [42]. Each microchannel has a width $W=140\mu \mathrm{m}$. The constriction has a width $w=6\mu \mathrm{m}$ and a length $L=10\mu \mathrm{m}$, and the merging region has a width equal to $315\mu \mathrm{m}$.

Figure 2

Raw fluorescence pictures and detected particles. The raw fluorescence image is displayed in black and white. A red dot represents the position of a detected cell. For visualization, only the first $140\mu \mathrm{m}$ of the clog are represented. This clog has been constructed at constant pressure, with an operating pressure of 40 kPa.

Figure 3

Examples of pictures extracted from the data bank. The pressure drop ratio is indicated in each picture. The corresponding $Q_1/Q_2$ ratios are, from left to right: 43.05, 3.35, 1.0, 0.30, 0.025.

Figure 4

Equivalent electrical circuit of the microfluidic system in absence of clog. $Q_1$ and $Q_2$ are the flow rate in the left-hand and right-hand microchannels, respectively. $Q$ is the flow rate in the merged microchannel. $R_i$ is the hydrodynamic resistance of an inlet microchannel plus a constriction and $R_o$ is the hydrodynamic resistance of the unique outlet microchannel. $P_p$ is the pressure at the merging point and $P=0$ is the atmospheric pressure.

Figure 5

(left) Cross-correlation coefficient versus flow rate ratio of the pictures from the data bank. (top-right) Experimental picture. (bottom-right) Picture from the data bank corresponding to the cross-correlation peak.

Figure 6

Top row: Simultaneous observation of the clog growth and of the flow rate reduction. From (A) to (F): different images taken during a typical experiment. In the top part of each picture, the clog area is computed from clog segmentation (red lines). The inset of picture A represents a zoom on the clog. The clog length (defined as the minimal distance between the pore and the top border of the clog) of image F is displayed with a dark red line. Bottom row: clog length ($L_c$), flow rate ($Q_1$), and clog hydrodynamic resistance ($R_c$) evolution as a function of time after the beginning of clogging. Experience realized with $\mathrm{\Delta }{P}_1=\mathrm{\Delta }{P}_2=70$ kPa.

Figure 7

Presentation of the backflush experiments. One backflush starts at time $t_{B_i}$ (A), at the moment when the flux is rapidly reverted, by setting the pressure $\mathrm{\Delta }{P}_1$ at $-6.9$ kPa (B) for 20 s (C). The pressure is finally reset to its initial value of 100 kPa, and the clog rapidly returns to its initial position (D–F). Experience realized with $\mathrm{\Delta }{P}_1=100$ kPa and $\mathrm{\Delta }{P}_2=300$ kPa.

Figure 8

Hydrodynamic resistance of different clogs ($R_c$) constructed under different conditions, computed as a function of clog length ($L_c$). Results obtained during constant pressure experiments (left) and backflush cycles (right). For constant pressure experiments, different operating pressures are used, see the legend. A vertical dashed line is placed at $70\mu \mathrm{m}$. Only a representative fraction of all the experiments are presented, as explained in the text. The operating pressure is kept at 100 kPa during the reconstruction phase of the clog for backflush experiments. The hydrodynamic resistance of backflushed clogs and the clog length are measured at the end of the backflush cycle, and a solid line represents a linear fit of all experimental data. With backflushes, experiments 4 and 6 were conducted in $6.35\mu \mathrm{m}$ deep chips; the others were conducted in $6.1\mu \mathrm{m}$ deep chips. The data from the constant pressure experiment conducted at 100 kPa are reported in gray for easier comparison (with extrapolated data from a linear fit presented with a gray straight line).

Figure 9

Permeability at constant pressure (triangles pointing upwards for experiments on a $6.1\mu \mathrm{m}$ deep chip and downwards for experiments on a $6.35\mu \mathrm{m}$ chip), and during backflush cycles (green hexagram), with uncertainty bars representing the confidence interval at $99\%$, computed during the linear fit. Linear representation at the top and log-log representation at the bottom. Dashed-dotted red line: fit from power law, Eq. (8). Dashed blue line: fit from the model developed in this article [Eq. (12)]. In the top panel, the figure presents the dataset obtained in the range $[0.3\times {10}^{-14}–1.5\times {10}^{-14}]{\mathrm{m}}^2$, excluding the permeability after backflushes. The inset presents the evolution of the clog offset hydrodynamic resistance ($R_{c_0}$) as a function of $\mathrm{\Delta }{P}^{★}$.

Figure 10

Cell density as a function of $\mathrm{\Delta }{P}^{★}$, for the two different kinds of experiments: constant pressure in black and backflush cycles green. Experiments conducted on a $6.1\mu \mathrm{m}$ chip are noted with upwards pointing triangles and those conducted on a $6.35\mu \mathrm{m}$ chip are noted with downwards pointing triangles. Error bars represent errors of 5% of the mean value.

Figure 11

Representation of the two different kinds of pore openings in the yeast clog: small pores, located between pairs of cells and the wall (red), and large defects (blue).

Figure 12

Permeability predicted by the fitted model, presented in Sec. 4. The operating pressure varies in the range $[{10}^2-{10}^7]$ Pa, and the permeability is simulated over the full range of operating pressure. The shaded area represents the pressure range explored during experiments.