Active sinking particles: sessile suspension feeders significantly alter the flow and transport to sinking aggregates

2.1. Experimental system

To study the multi-scale process of microscale near-field flows and macroscale sinking dynamics we leveraged SVTM [28] that uses controlled rotation of a circular ‘hydrodynamic treadmill’ to automatically keep small objects centred in the microscope field-of-view while allowing free movement with no bounds along the axis of gravity (figure 2a,b). SVTM allowed us to concurrently measure aggregate trajectories over metres (figure 2c), and capture images through video-microscopy at rates of $100\hspace{0.17em}\mathrm{frames}\hspace{0.17em}{\mathrm{s}}^{-1}$ (figure 2d,e, electronic supplementary material, movie S1). The optical resolution of the imaging system was approximately 1 μm, thus enabling resolution of flows and dynamics at the scale of single cells colonizing the aggregate (figure 2e). We observed sinking spherical millimetre scale aggregates that were either bare or had one to several attached V. convallaria, a common species of sessile ciliates. Vorticella species are found abundantly on sinking aggregates in marine, freshwater and man-made ecosystems [15,16]. We then measured flow around active sinking particles using both particle image velocimetry (PIV) and particle path-line traces on short video segments.

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2.2. Model sinking aggregates

We created simple model aggregates that share many of the properties of natural aggregates. In nature, macroaggregates are composed of aggregated biological and other debris and range in size from 0.5 mm to several centimetres [1,2,5]. Aggregates are typically smaller in estuaries and other areas of high shear (less than 2 mm) [2]. In all aquatic environments, aggregates are amorphous and fragile, have varied shapes and are typically highly porous [1,2,5,6]. Aggregate sinking rates range from less than 1 m d⁻¹ to hundreds of m d⁻¹, with larger particles sinking faster [2,5].

We created approximately spherical particles from 0.3% agarose gel by dripping hot agar into a layer of oil as described in Cronenberg & Van den Heuvel [29]. We used vegetable oil rather than kerosene and also made particles of various sizes by directly touching drops to the oil surface while still attached to the syringe needle tip. This density of gel resulted in spheres that sank at velocities within the range observed for similarly sized marine snow [5]. We next incubated these gel particles overnight in cultures of V. convallaria, which were cultured as described in Vacchiano et al. [30]. We determined the number of V. convallaria cells per aggregate by counting them in the microscopy images obtained during SVTM.

2.3. Flow measurement

We measured flow around active sinking particles using PIV on short video segments. The water surrounding the spheres was seeded with 2 μm polystyrene spheres (Polysciences 19814). PIV analysis was performed using PIVlab [31]. The aggregates were masked manually; we then used a multi-pass PIV algorithm with decreasing size of the interrogation windows from $128\times 128\hspace{0.17em}\mathrm{pixels}$ to a final window size of $64\times 64\hspace{0.17em}\mathrm{pixels}$ with 50% overlap. Flow fields were then time-averaged over the length of the video (typically, between 1 and 2 s).

We selected a subset of our particles to analyse that were either bare of V. convallaria, or that had V. convallaria in focus and with feeding currents primarily directed in the focal plane. We also chose to analyse only video segments where the focal plane coincided with the centre of the aggregate in the depth dimension. These choices minimized out-of-plane flow, so that most of the flows of interest could be measured. As a result of these choices, we analysed flow fields for 12 video segments across seven different aggregates (details in electronic supplementary material, section S1.1). Aggregates ranged in diameter from 0.70 to 1.2 mm (mean of 0.97 mm), had sinking speeds of 0.2–5 mm s⁻¹ (mean of 3 mm s⁻¹), and Reynolds numbers of 0.2–0.5 (mean of 0.3). Details of each aggregate are in electronic supplementary material, section S1.1, and PIV results for all measured flow fields are available in a Dryad data repository [32], and the analysis code in a GitHub repository [33].

For obtaining particle path lines, the images were first registered using the Registration plugin in ImageJ [34] to stabilize small movements relative to the camera. The path lines were then obtained using the FlowTrace plugin for ImageJ [35] by taking the maximum intensity projection of images over a 1 s interval.

2.4. Widths of encounter region and plume

Using our measured flow fields, we estimated the width of the plume left behind by the aggregate as well as the width of the encounter region below the aggregate by following streamlines. The encounter region below a sinking aggregate is the volume of fluid where particles will, eventually, come into contact with the aggregate as it falls through the water column; the size and shape of this region is important for determining particle aggregation rates [10]. The plume is a volume of higher solute concentration left behind the aggregate as it sinks; bacteria and zooplankton may use the plume to find and colonize (or consume) sinking aggregates [6,7,36–38]. Following streamlines is a reasonable first approach, because the Péclet number (Pe) for these processes is much greater than one, indicating that flow dominates over diffusion in most situations. In the plume, concentrations of small molecules like oxygen and organic solutes, as well as of motile and non-motile bacteria can be increased or decreased by the presence of the aggregate. Diffusion constants for these can range from 10⁻⁹ (for oxygen and organic solutes) to 10⁻¹⁴ m² s⁻¹ (for large non-motile bacteria), with motile bacteria falling in between [6,39,40]. Therefore, plume Péclet numbers for our aggregates are approximately 150–10⁷. The Sherwood number, defined as the ratio of total mass transport to mass transport from diffusion alone is also an important indicator of the relative importance of advection and diffusion around a sinking aggregate. For bare sinking spheres of similar Reynolds number to ours, the Sherwood number is 5 for $\mathrm{Pe}\hspace{0.17em}\mathcal{O}({10}^2)$ and 10 for $\mathrm{Pe}\hspace{0.17em}\mathcal{O}({10}^4)$, again indicating that advection dominates over diffusion at this scale [6].

When considering the encounter region below the sphere, advection is even more dominant, and the Péclet number even higher. For instance, considering the encounter rate with a 100 μm sphere, the Stokes–Einstein relation gives D = 2 × 10⁻¹⁵ m² s⁻¹ with a resulting Péclet number of 10⁸ [41].

When finding the plume width, we started streamlines in a ring around the aggregate at a distance of 140 μm from the aggregate surface and integrated forward in time in the measured flow field (figure 4). Streamlines that approached within 16 pixels (35 μm) of the aggregate surface were terminated, as the flow field measurement is noisy in this region. The width of the plume at each height above the aggregate is the distance between the outer-most streamlines (yellow line in figure 4). Here, choosing a distance of 140 μm from the aggregate surface can be considered choosing an approximate diffusion constant for the substance of interest: from a scaling perspective, the substance will diffuse approximately 140 μm in the time it takes the aggregate to sink its own diameter. This yields D ∼ 10⁻⁹ m² s⁻¹, appropriate for oxygen or small organic solutes.

Similarly, we estimated the width of the encounter region below the aggregate, following the ideas in Humphries [10]. Particles within this region of fluid would come into contact with the aggregate as it falls through the water column. Similar to our plume calculation, we determined streamlines that began in a ring around the aggregate at a distance of 140 μm from the aggregate surface. To find the encounter region, we then integrated backward in time in the measured flow field. The width of the encounter region is the distance between outer-most streamlines (equivalent to 2 × λ in Humphries [10], fig. 2). Choosing a beginning location of 140 μm from the aggregate surface effectively gives the encounter region for particles in the water column that are 140 μm or larger.

We compared our measured plume and encounter region widths with the known results for Stokes flow and Oseen’s modification to Stokes flow ([42] eqns. (4.9.12) and (4.10.3)), where the Oseen flow was calculated for Reynolds numbers that matched parameters for each individual aggregate (see electronic supplementary material, table S1). Stokes flow is accurate for zero Reynolds number, while Oseen flow makes adjustments for Reynolds numbers close to one [42].

For more direct comparison with work such as Humphries and with theoretical coagulation kernels [9,10], we extended our experimentally measured streamlines beyond the field-of-view of our experiments to a final vertical distance above and below the sphere of 20 times the particle radius (20a) using Oseen flow around a sinking sphere. We began the theoretical streamlines at the location of our experimentally measured streamlines when they were a vertical distance of 2a above or below the middle of the sphere (above for plume measurements and below for encounter region). The width of the plume at 20a was, then, the distance between the outer-most theoretical streamlines. These long-distance widths were only calculated for particles where the distance 2a was in the field-of-view (N = 9 for encounter volume and N = 10 for plume). Following Humphries [10], we also calculated long-distance widths of encounter regions and plumes using Oseen flow only (no input from experimental measurements) to compare experimental widths with theoretical widths for aggregates with the same size and sinking speed, but no attached V. convallaria.

Because of the low sample size, our flow field, and resulting plume and encounter region results, are a subset of what is possible with attached organisms, and probably do not show the full range of possible outcomes. Other results, such as the increased variation in encounter rate with increasing number of organisms and the rotation rate results, were found to be statistically significant, even with our low sample size, and can be considered representative results that would probably be reproducible in future experiments.

3.1. Conceptual framework

Active sinking particles lie on the continuum spanned, on the one hand, by passive sinking particles that have no biological activity, and, on the other, by active swimmers under the influence of gravity (figure 1). This continuum can be parametrized by a non-dimensional ratio of forces due to activity and buoyancy. The active forces scale as nF where n is the number of active entities (Vorticella in our case) whose influence on the fluid is approximated as point forces (Stokeslets) of strength F [43]. The buoyant force due to gravity scales as ΔρVg where Δρ is the density mismatch between the particle and ambient fluid, g is the acceleration due to gravity and V is the aggregate volume. The dimensionless ratio of active and buoyant forces is given by: $\mathcal{A}=nF/\mathrm{\Delta }\rho Vg$. Using this parametrization, passive sinking particles have $\mathcal{A}=0$, active swimmers are typically characterized by $\mathcal{A}\gtrsim 1$, while active sinking particles have $0<\mathcal{A}\lesssim 1$ (figure 1d). The value of $\mathcal{A}$ for some representative aggregates are shown in table 1.

3.2. Vorticella convallaria modify near-field flow and reshape boundary layers

We found that attached V. convallaria substantially changed the flows near sinking aggregates in ways that were variable and depended sensitively on the location and orientation of the attached organisms (representative examples in figure 3; all measured flow fields in electronic supplementary material, figure S1; N = 12). A typical bare aggregate had relatively smooth flow (figure 3a,b) and both perpendicular and parallel flow near the particle that was similar to the predictions of flow at zero Reynolds number around a sphere of the same size (figure 3c, electronic supplementary material, movie S2). As expected, tangential flow was fastest at the equator, and radial flow was fastest at the poles (figure 3c).

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On the other hand, figure 3 also shows two aggregates, each with three V. convallaria attached at random locations across the sphere, where the flow was modified by the V. convallaria. In figure 3d–f, the modifications to the flow were somewhat subtle: streamlines were pulled toward the V. convallaria, disrupting the background flow (figure 3d–f, electronic supplementary material, movie S3). The V. convallaria in the bottom left, which was pulling fluid towards the particle, increased the radial flow and caused the tangential flow to be reduced on one side of the organism and enhanced on the other side (figure 3f). The cell near the north pole changed the local flow from primarily radial to primarily tangential (figure 3f). Since the V. convallaria altered the flow velocities and gradients near the sphere, they will cause the transport boundary layer to be thicker in some regions of the sphere (where velocities were reduced), and to be thinner in others (where velocities were increased). These changes were more substantial and widespread than smaller scale changes induced by irregularities on the surface of a bare aggregate (figure 3c). In figure 3g–i, the modifications to the flow by the V. convallaria were more dramatic: organisms on this aggregate caused large-scale eddies, which changed the flow structure, completely altering tangential and radial flow velocities near the sphere (figure 3g–i, electronic supplementary material, movie S3). In some regions, the flow direction was even reversed from what it would have been for a bare sinking aggregate (figure 3i). Again, the boundary layer near this sphere was substantially reshaped in ways that would change both total mass transport to the sphere and which regions of the sphere have the highest rates of mass transfer. These effects on the flow field were even more dramatic for larger numbers of V. convallaria (greater than three) (electronic supplementary material, movie S4), though we had fewer examples of such aggregates in our experiments. Such diversity of flow structures caused by V. convallaria feeding flow is similar to that observed and predicted previously for Vorticella, and similar organisms, attached to surfaces and in ambient flow [20,39,43,48]. In still water next to a wall, the Vorticella feeding current consists of a toroidal eddy when the cell body is perpendicular to the surface, but flow that does not recirculate at other orientations [39,48]. In flowing water, there is recirculation when the organism pushes against the ambient flow [43].

Other experimentally measured flow fields are shown in electronic supplementary material, figure S1, and original PIV flow field data for all included flow fields are available in a Dryad data repository [32].

To understand the relative effects of activity and sinking on mass transport from the aggregates, we can compare their relative contributions with the velocity within the mass transport boundary-layer. Advective effects of the flow dominate diffusive effects for the range of aggregate sizes, sinking speeds and even for transport of small molecules such as oxygen from the aggregate (Material and methods). This implies that the non-dimensional Péclet number (Pe = Ua/D), which quantifies the relative importance of these effects, is much greater than 1 (Material and methods). Here, U is velocity scale of the flow, a is the aggregate radius and D is the diffusivity of the molecule of interest. At such high Péclet number, the mass transport boundary layer is a thin region near the aggregate whose thickness is approximately aPe^−1/3 [49]. The hydrodynamic effect of V. convallaria on the fluid can be modelled as a point-force of magnitude F at a height h above the boundary [43]. The velocity scale due to Vorticella within this boundary layer is then F/μh. On the other hand, the velocity scale within the boundary layer due to sinking is $\mathcal{O}(U{\mathrm{Pe}}^{-1/3})$. Comparing these two scales in the vicinity of a Vorticella cell we obtain a critical sinking speed that separates the ‘activity-controlled’ and ‘sinking-controlled’ mass transport regimes,

For sinking speeds above this scale, sinking is expected to dominate mass transport. Note that this picture is local, and the overall effect of the mass transport will depend on the number of Vorticella, as well as their orientation relative to the sinking direction of the aggregate. For instance, when Vorticella are oriented parallel to the local flow they can cause local flow reversals that completely disrupt the boundary layer structure and cause it to lift off the aggregate surface (see, for instance, figure 3g,h). Based on the measured parameters for V. convallaria ($F=200\hspace{0.17em}\mathrm{pN}$, h ∼ 100 μm; [39]), aggregate size a = 0.5 mm, and considering the transport of biologically relevant small molecules like oxygen (D = 10⁻⁹ m² s⁻¹), we obtain U_critical = 63 mm s⁻¹. This number is much higher than the sinking speeds in our experiments (which, in turn, are representative of sinking speeds of real aggregates), indicating that activity probably dominates mass transport locally (see table 2).

3.3. Vorticella modify encounter region and plume width

We find that attached V. convallaria significantly modify both the region of encounter below sinking aggregates and the shape of the plume left behind (figure 4). Our aggregates show that bare spheres have encounter regions and plumes fairly close to those predicted by Stokes and Oseen flow (figure 4a), while those with V. convallaria have plumes and encounter regions with significant asymmetry and that can be both narrower and wider than those of bare spheres (figure 4b–e). Changes are particularly dramatic when the Vorticella cause recirculation in the flow (figure 4c–e). When extrapolated to distances far from the sphere (more details in Material and methods), we find that the width of the region encountered by the sphere and the width of the plume left behind are significantly changed by attached organisms, and that these changes lead to both thicker and thinner plumes and wider and narrower encounter regions (figure 4f,g). Each of our measurements are at a single time point and measure a two-dimensional cross-section of a three-dimensional flow. It is, therefore, possible, for instance, that in some cases attached V. convallaria cause the plume to be thinner in one dimension while thicker in another. Also, these changes are likely to be dynamic in time, leading to e.g. a sometimes wider encounter region and sometimes narrower as time passes and V. convallaria orientations and positions on the aggregate change.

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We also used our long-distance encounter-width measurements (figure 4g) to predict how attached organisms change particle coagulation kernels. Particle encounter dynamics are included in aggregation models through the coagulation kernel that expresses encounter rate (in volume/time) [9]. The two most commonly used kernels are the rectilinear kernel,

and the curvilinear kernel, where r_i is the radius of the larger particle (here the sinking agar sphere), r_j is the radius of the smaller particle (here assumed to be 140 μm for simplicity—see Material and methods for further details), and u_i and u_j are the sinking speeds of the two particles [9]. The rectilinear kernel does not include any distortion of the flow due to the presence of particles, the curvilinear kernel is more accurate and is based on the assumptions of Stokes flow [9]. If we assume our long-distance encounter widths (figure 4f) are axisymmetric, our experimental kernels would have the form, where λ is half of the encounter width shown in figure 4f [10]. Using this formulation, we find that attached organisms lead to encounter kernels that are always smaller than the rectilinear kernels, and approximately 2× to 10× the curvilinear kernels (figure 4h).

It has previously been shown that including the finite size and sinking speed of particles (as opposed to assuming Stokes flow and zero Reynolds number) has a similar effect of increasing the size of encounter kernels [10]. We, therefore, also compared our experimental encounter kernels with those calculated theoretically from Oseen flow, by following the Oseen encounter regions (e.g. dashed orange lines in figure 4a–c), to long distances. Then,

where λ_O is half of this theoretical long-distance encounter width [10].

We found that aggregates with attached V. convallaria had larger encounter kernels, compared with the Oseen kernel, than those without (figure 4i), and that this was more pronounced for aggregates with a larger number of attached V. convallaria, though this trend was not significant with our small sample size (linear regression model: R² = 0.42; p = 0.057), and with a larger sample size, we predict we might also observe encounter kernels smaller than bare spheres. Perhaps more important, the variation in encounter kernel size compared with theoretical bare spheres increased with increasing number of attached organisms (figure 4i; Levene’s test indicated unequal variances; F = 8.5, p = 0.018).

3.4. Vorticella convallaria cause sustained rotation of aggregates

Our novel experimental system enabled us to observe aggregates as they sank freely in the ambient fluid without the constraining influence of tethers or other attachments, required in earlier experimental systems [27]. We observed that freely sinking aggregates displayed sustained rotational motion correlated to the presence of V. convallaria (figure 5a, electronic supplementary material, movie S5). To explore this quantitatively, we developed a custom image-processing pipeline (electronic supplementary material, section S1.2), and used tracked surface fiduciary markers naturally occurring on the aggregates to estimate rotation rates and three-dimensional rotation axes from the two-dimensional images generated by SVTM. We find that aggregates without V. convallaria show little to no rotation (figure 5a). On the other hand, aggregates colonized by one or more V. convallaria show sustained rotations that are visible by eye even over a 30 s interval (figure 5b). To explore if the number of organisms was the main driver of this rotation, we isolated the effects of aggregate size on the observed rotation rates by rescaling the rotation rate by the scaling factor $\hspace{0.17em}\tilde{\mathit{\Omega }}=F_{\mathrm{vorticella}}/8\pi \mu a^2$, where F_vorticella is the force-scale exerted on the fluid by a single V. convallaria cell (approx.$\hspace{0.17em}200\hspace{0.17em}\mathrm{pN}$ [43]), μ is the ambient fluid viscosity and a is the aggregate radius. This scaling factor corresponds to the theoretical rotation rate for a spherical aggregate with a single V. convallaria oriented tangential to the aggregate surface. Upon rescaling, we find that the mean dimensionless rotation rates are higher for aggregates with V. convallaria than for aggregates without (figure 5d; mean dimensionless rotation rate with no Vorticella: 0.32 ± 0.27, 1–3 Vorticella: 0.53 ± 0.27, and greater than 3 Vorticella: 0.82 ± 0.50, the differences in mean rotation rates were found to be statistically significant based on the Kruskal–Wallis test χ²(3) = 257, p < 10⁻⁶, N = 13 distinct aggregates). That the dimensionless rotation rate is $\mathcal{O}(1)$ further indicates that V. convallaria are indeed the driving factors behind the rotation (figure 5d, inset). We further confirmed that measured changes in rotation rates were best explained by V. convallaria numbers and not due to other experimental conditions (electronic supplementary material, figure S2). Interestingly, we found that not only does the mean rotation rate rise with V. convallaria number, but the fluctuations about the mean do as well, with the distribution of higher V. convallaria numbers becoming heavy-tailed (figure 5d and inset). These results can be explained by the previously observed stochastic reorientation of V. convallaria body angle relative to the surface of attachment: V. convallaria reorient with a period of minutes, which could lead to a time-varying torque from each organism [43]. If these motions are uncoordinated among the various attached individuals, both the mean rates of rotation and largest rates of rotation increase with Vorticella number for small numbers of Vorticella, as we observe. Models, experiments with much larger numbers of Vorticella, or experiments in which Vorticella body angle was explicitly tracked, could reveal if there is any coordination among the organism (either actively, or passively through coupled flows).

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We also find that V. convallaria induce rotations about specific axes that lie close to the axis of gravity, as evident in the distribution of the rotation axis over a unit sphere (figure 5c). The distribution is relatively uniform for the no Vorticella case, but with increased number of V. convallaria, the distribution peaks along the axis of gravity (θ = 0). We interpret this result as occurring due to gravity breaking symmetry in orientation space, wherein aggregates have a stable sedimentation orientation along the polar axis (θ) due to possible density distribution or shape effects, including the drag due to Vorticella, providing a stabilizing torque. Thus, the stochastic active torques due to V. convallaria cause the aggregate to sample orientation space along the azimuthal direction (ϕ), as evidenced in our measurements.