Hidden Comet-Tails of Marine Snow Impede Ocean-based Carbon Sequestration

In order to collect fresh marine snow aggregates, an expedition in the Gulf of Maine was planned. The marine snow aggregates were collected in a freely hanging sediment traps (2m diameter) Ben2015 in the Gulf of Maine ($42.5^{\circ}$ N $69.5^{\circ}$ W), on the research vessel RV Endeavor [see Figure 1C]. In multiple deployments of these traps at depths of 80m for a duration of 24 hours [see supplementary], we acquired marine snow as a sediment.

Fresh marine snow aggregates were collected on board R/V Endeavor during the RIPPLE expedition in the Gulf of Maine (42.5^∘N, 69.5^∘W) using freely hanging sediment traps (2m diameter) in multiple deployments at depths of 80m for a duration of 24 hours [see Supplementary]. Particles accumulated in a sediment traps were brought to the surface. The samples were collected and divided using a quantitative splits [see supplementary], and the marine snow particle were kept at the in-situ temperature to maintain biotic component of the marine snow alive and active. The particles were loaded immediately in scale-free tracking microscopy wheels and imaged instantly. For a high-density flux of particles, some marine snow particles can accumulate and thus loose their individual identity in sediment trap sampling, and become part of the bulk sediment. We gently re-suspended those particles and focused on the response of the organic debris to the hydrodynamic stresses generated by gravitational sinking SR2001 . We also ensured a dilute limit in which inter-particle hydrodynamic interactions could be neglected. The ship frame of reference contributes rocking and rolling disturbances to the setup which we minimize by mounting the Gravity Machine on a two axis gimbal [Figure 1 D].

Micro-scale sedimentation dynamics of falling marine snow particles was measured in the Gravity Machine Krishnamurthy_2020 , as soon as the particles are brought to the research vessel [Fig. 1 E]. We directly measured the settling velocity by tracking individual particle in the gravity machine while simultaneously performing high resolution imaging of marine snow and the micro-hydrodynamic flow around it. Plastic bead particles ranging from 700nm to 2 microns are addeded to the fluid for high-resolution particle image velocimetry (PIV). We developed an analysis pipeline that automatically measures the size and velocity statistics of the particles and calculate and analyse the flow fields, allowing us to get a one-to one map between various measurable quantities – structure, flow morphology and sedimentation velocity.

Limited volumetric imaging has previously been performed on marine snow particles in the past [cite]. To better understand the three-dimensional structure of a marine snow particles, we perform the first quantitative phase imaging (Holotomograoghy) in 3D and obtain isolate materials based on refractive index (Fig. 3A). This method allowed us to observe the 3D density and heterogeneity of samples without fixation or stains, thus preserving the cell density and porosity of the aggregates Park2018 . The heterogeneous structure was clearly depicted, highlighting segments of diatom frustules embedded in the marine snow particle as ballast (Fig. 3A, Supplementary Video 3). Secondly we imaged particles using brightfield and confocal microscopy (Fig. 3B) to observe the presence of biological materials within the sample. Exciting the particle with DAPI, FITC, and AO we observe emission of autofluorescence detecting live cells and associated chloroplasts. Lastly, we imaged with a color camera and brightfield imaging after staining particles with Alcian blue to visualize Transparent Exopolymer Particles (TEP) as a representation of polysaccharides present in the marine snow particles (Fig. 3C). This is commonly used for marine snow particles to reveal polysaccharides which might be surrounding the particle but not visible. In combination, these three imaging datasets created a more complete picture of the composition of marine snow particles. We are able to observe the heterogeneity including the presence of biotic material, ranging from whole cells (Fig. 3B) to fractions of whole cells, both rigid in diatom frustrules (Fig. 1D) and soft in mucus (Fig. 1EF).

A predictive understanding of marine snow sedimentation necessitates in-situ measurements of a one-to-one map between the structure of marine snow and the sinking velocity SANDERS2014200 . Thus, we embarked on measuring detailed dynamics of all collected particles while on-board the ship. We track individual marine snow particles in the GM, measuring their sinking speed, and carrying out detailed microscopy at the resolution of 0.828 $\mu$m per pixel at the rate of 5 frames per second. This presents a high resolution zoo of aggregate shapes and sizes [Fig.2 A ], where gravitational torques due to shape polarity has already aligned the principle axis of the aggregate along gravity Witten_2020 , resulting in a nearly stable orientation over the measurement window of $\simeq 5$ min. In addition, the hydrodynamic levitation directly measures the sinking speed associated with each particle. Plotting sinking speeds as a function of equivalent spherical radius calculated by thresh-holding method 10.3389/fmars.2020.00564 [see Supplementary], shows significant spread, presenting the lack of a deterministic trend [Fig2. B]. We studied a visible spectrum of particle ‘radius’ ranging from $50-350\,\mu$m, with mean radius $187.35\pm 8\,\mu$m [Fig.2 C], and present a one-to-one map between detailed structure of marine snow [Fig.1 A] and sedimentation velocity [Fig.2 D], with velocities ranging between $5-200$ m/day. In our observations, we occasionally encountered unsteady singular events like merging, slow depletion due to hydrodynamic stresses, and grazing by ciliates and copepod; all of which adds further richness to marine snow sedimentation and likely makes it a highly dynamic process at long-time scales.

In-situ observations of marine snow (Fig.1) McDonnell_2012 ; Alldredge1988 ; Picheral2010 ; Trudnowska2021 along with Martin’s curve Martin_1987 , has allowed meaningful estimates of carbon flux in the ocean. These calculations, however, rely on a deterministic relationship between particle size and its sinking speed Giering2022 , which has thus far been elusive [Fig. 2 B], presenting a long-standing puzzle in the sedimentation of marine snow IVERSEN2020102445 . This suggests the presence of unaccounted degrees of freedom in the system, likely coming from incorrect size estimates Giering2022 and the density fluctuations across particles MCCAVE1975491 . We seek further cues of any hidden degrees of freedom in the flow field around individual aggregates.

The ship environment presents a challenging set-up for extracting clean flow-field from consecutive particle laden images, because of the high-frequency jitters in the equipment, in addition to the canonical rock and roll dynamics. A 2-axis gimbal helped reduce the low frequency structured noise, and the high frequency random noise was removed in post-processing pipeline [see Supplementary]. This allowed for the first micro-scale PIV (Fig. 3 A) and corresponding sedimentation velocity (Fig. 2 D) of marine snow in a field setting, to the best of our knowledge. The measured flow around these sinking aggregates conspicuously displayed the transparent mucus around them. Note that the aggregate in Fig. 3 B is the same as Fig.1 E, with its viscoelastic degrees of freedom visible. Alcian blue staining (Fig. 1 H) confirms that this mucus halo consisted of Transparent Exo-Polymers, which is known to have a biological origin in algal blooms and plays a key role in particle agglomeration PASSOW2002287 ; Burd2009 . This presents a multi-phase fluid-structure interaction problem.

The detailed PIV enabled visualization of the comet like morphology of marine snow which is universal across all particle shape and sizes. We found that the amount of mucus that an aggregate is dressed with is independent of the size of the visible aggregate (Fig. 3 C). This invisible degree of freedom significantly changes the effective size of the aggregate, sets a different fluid-mechanical boundary condition, and reduces the effective density. This is evident in the inverse relationship between the relative volume of mucus to particle and the settling velocity (Fig. 3 D). The invisible size spectrum is dramatically different from the visible spectrum, with a mean $415\pm 21\,\mu$m, which is more than twice the mean size of the visible part of marine snow (Fig. 2 C).

Based on our field observations and analysis of freshly collected marine snow aggregates in the Gulf of Maine, we constructed a minimal model for the Stokesian sinking of marine snow with mucus halo by analytically treating the halos as an deformable ellipsoid McNown1950 with semi-major and semi-minor axes $b$ and $a$, respectively, and density $\rho_{m}$. The visible particulate aggregate with effective radius $l$ has a density $\rho_{p}$ greater than $\rho_{m}$ [Fig. 4 A]. Here we treat marine snow as a two-phase aggregate with visible particulate aggregate embedded in the invisible mucus halo, sedimenting under its own weight. Hydrodynamic self-stress generated due to sedimentation would perturb the shape of mucus - further deforming and hence influencing the steady state sinking velocity of these particles. We construct the minimal model that accounts for this feedback between deformation and sedimentation and elucidate the microscopic origins of marine snow sedimentation dynamics.

We always found that the particulate matter is present at the bottom of the mucus halo, thus marine snow with mucus halo is effectively a bottom heavy sedimenting particle Witten2017 ; nissanka_ma_burton_2023 . In the ambit of linear response, the shape degree of freedom $\delta\mathbf{b}\equiv(b/b_{0}-1)\hat{z}$ is assumed to evolve viscoelastically through the Kelvin-Voigt (KV) model Christensen1984 and the translational degree of freedom $\mathbf{X}$ is governed by the Stokesian mobility relation Happel1983 ; KIM1991 with a shape dependent mobility $\stackunder[1.2pt]{$\stackunder[1.2pt]{$\mathbb{M}$}{\rule{3.44444pt}{0.32289pt}}$}{\rule{3.44444pt}{0.32289pt}}(\mathbf{\delta b})$ McNown1950 ; Witten_2020 , giving rise to the coupled equations

for shape and sinking dynamics respectively. In (10) $\mathbf{\sigma}=(\mathbf{\nabla v}+\mathbf{\nabla v}^{T})/2$ is the symmetric part of the velocity gradient generated by a force monopole of strength $\mathbf{F}$, which is assumed to be located at the origin of visible particulate aggregate, due to its relatively dominant contribution to weight as compared to mucus Guo2021 . $\mathbf{F}$ induces translational dynamics of the center of gravity $\mathbf{X}$ of marine snow through the mobility relation (2). In equation $\eqref{KV}$ the second term on the left captures the visco-elastic relaxation, and the term on the right presents a one-way hydrodynamic coupling between the KV dimer located at the origin of mucus halo and sedimentation induced flow $\mathbf{v}$, to leading orders in velocity gradient. The phenomenological parameter $\alpha$ can, in general, depend on the shape of the visco-elastic halo, and determining it requires solving the detailed fluid mechanical problem doi:10.1146/annurev-fluid-010719-060107 . For the sake of simplicity in the present analysis, we fix $\alpha=\mu$ on dimensional grounds. When the extensional axis is aligned with the gravity axis, thanks to the polarity of the marine snow, the Stokesian hydrodynamic stress induced by $\mathbf{F}$ along $\mathbf{b}$, to leading order in $l/a_{0}$ becomes [see Supplementary text]

We have defined $\tilde{\rho}\equiv(\rho_{p}-\rho_{m})/(\rho_{sw}-\rho_{m})$, which lumps the sea water density $\rho_{sw}$, mucus density $\rho_{m}$ and aggregate density $\rho_{p}$ into a single non-dimensional density parameter; with $V_{p}$ and $V$ being the volume of the particulate aggregate and the net volume of the marine snow respectively. We consider a volume conserving mucus and an isotropic initial condition with non-zero mucus volume, $b_{0}=a_{0}>l$. Combining (10) and (13) and non-dimensionalizing (10) and (2) using length scale $L=a_{0}$ and sedimentation time scale $T=9\mu/2g(\rho_{sw}-\rho_{m})a_{0}$ for $\rho_{m}\neq\rho_{sw}$ gives the dynamical equations for longitudinal deformation $\delta b$ and vertical depth $z$ scaled by $a_{0}$,

In (10) $\mathcal{D}\equiv 9E/[2g(\rho_{sw}-\rho_{m})a_{0}]$ is the ratio of elastic to hydrodynamic stress response, the magnitude of which is set by the biology of mucus secretion in phytoplankton PASSOW2002287 ; Meng2016 ; Bidle2015 . The scalar mobility of the spheroid with its symmetry axis aligned with gravity, $\mathbb{X}^{-1}(e)\equiv{3}\left[(1+e^{2})\ln\left({1+e}/{1-e}\right)-2e\right]/{8e^{3}}$ captures shape dependent sinking as a function of eccentricity $e=\sqrt{1-(1+\delta b)^{-3}}$. Equation (5) gives the condition for non-zero sinking of the marine snow $\tilde{\rho}\geq V/V_{p}$ implying that marine snow with larger mucus halos falls slower, potentially reducing the net carbon flux in the ocean PASSOW2002287 .

We solve (14) and (5) in the steady state approximation of the mucus comet tail $\dot{\delta b}=0$. A stable fixed point is guaranteed in (14) and the steady state tail length has a closed analytical expression [see Supplementary text] which is plotted as a function of $\mathcal{D}$, $V_{p}/V$ and $\tilde{\rho}$ [Fig. 3 B]. Asymptotic analysis of the steady state yields two scaling regimes for very small and very large deformations

where the viscosity sets the time scale to achieve the steady state; however, (6) is independent of $\mu$ and $\mu^{\prime}$. Figure 4 C shows the steady state sinking velocity (5) as a function of $\mathcal{D}$, $V_{p}/V$ and $\tilde{\rho}$. Comparison between theory and field data allows us to get the density distribution of the visible particulate matter [Fig. 4 D], which further enables the sedimentation based measurement of the Elastic modulus of mucus [see Supplementary] with the mean value of $0.028$ Pascal [Fig. 4 E]. Viscoelastic rheology of xanthan gum in salt solutions provides useful insights into hydrodynamic nature of marine mucus, while in-situ measurements remain limited Mrokowska2022 ; Jenkinson1986 . Here we present a sedimentation based measurement of the storage modulus of fresh marine snow mucus in field setting PASSOW2002287 .

Our field experiments and theoretical framework shows that sinking speed of two-phase particle is inversely proportional to the relative volume of mucus in marine snow [Fig. 3 D], in accord with equation (5). This mucus induced impedance in marine snow reduces the sedimentation flux and increases the residence time of mucus rich aggregates in our data-set. The estimate of residence time shows that presence of mucus almost doubled the mean residence time of marine snow in the upper 100m of the ocean (1.92 days) as compared to that without mucus (0.9 day) [see Fig. 4 F and Supplementary], assuming a steady sinking state.

Gravity machine directly gives the virtual vertical distance traversed as a function of time $z(t)$. The effective vertical position as a function of time, shows fluctuation in vertical velocity due to the ship motion, but this disturbance only adds a residual error in a linear fit, thanks to the gimbal. This gives us the vertical settling speed. To correlate it with the visible particle size we threshold the images after conversion to 8-bit and measure the projected area and from this get the effective radius of a circle with an equivalent area.

The collected images and tracks were initially processed in a customized ImageJ macros. The vibrations of the ship resulted in misalignment of aggregates in adjacent frames. To remove this noise we automated the image registration process using a Matlab script. A command-line based PIV was conducted on the resulting images, on Matlab PIVLab. The PIV data and GM tracking data were then coherently analysed for mucus and particulate matter quantification using a custom Matlab function. All the image processing and analysis were automated, the codes for which are made available.

To account for the deformation of the mucus halo, we minimally approximate the mucus blob as a viscoelastic spring subjected to the stress field due to sedimenting particulate aggregate attached to the halo. The sedimentation self-stress of a force monopole located at the origin, along gravity axis $-\hat{z}$ is

Here, the strength of the monopole $F^{k}$ incorporates the effective buoyancy of particulate matter and mucus combined

Particulate matter, initially embedded in the bulk of mucus, being heavier than the surrounding mucus falls to the boundary of the mucus domain. We assume that the sedimentation time-scales $T=9\mu/2g(\rho_{p}-\rho_{m})l$ associated with this fall is much smaller than the mucus deformation time-scale $\tau=\mu^{\prime}/E$, where $\mu^{\prime}$ and $E$ are the mucus viscosity and the Young’s modulus respectively; thus it is assumed that the aggregate is present at the boundary of the mucus at all times. We treat the mucus relative extension $\delta\mathbf{b}/b_{0}\equiv(b/b_{0}-1)\hat{z}$ as a visco-elastic spring evolving via the Kelvin-Voigt model

When the extensional axis is aligned with gravity axis, thanks to the polarity of the marine snow, combining (2) and (9) gives the self-stress

where $\tilde{\rho}={(\rho_{p}-\rho_{m})}/{(\rho_{sw}-\rho_{m})}$. Expanding the denominator in (11) as a power series in $l/b_{0}$ gives

For non-zero mucus volume $l/b$ is always less than 1, thus we retain only the leading term in $l/b_{0}$, which gives the sedimentation self-stress

Note that we have imposed volume conservation and specifed initial condition $b_{0}=a_{0}>l$ i.e. initial particle shape is isotropic and there is a non-zero mucus volume. Combining (10) and (13) and non-dimensionalizing using length scale $L=a_{0}$ and sedimentation time scale $T=9\mu/2g(\rho_{sw}-\rho_{m})a_{0}$ gives the equation for deformation of the viscoelastic spring

where $\mathcal{D}\equiv 9E/[2g(\rho_{p}-\rho_{m})a_{0}]$ is the ratio of elastic to gravitational response. At long times (14) yields two asymptotic scaling regimes for very small and very large deformations

Note that the viscosity sets the time scale to achieve the steady state, however, steady state is independent of the viscosity $\mu$ and $\mu^{\prime}$. We now turn to the distortion of the mucus in the degenerate transverse direction. The volume conservation of the mucus $V_{m}$, in the prolate spheroid approximation gives $a$, which does not have an independent dynamics

which gives dynamic eccentricity of the mucus halo $e$ as a function of tail extension $\delta b$

In the fluid-mechanical regime where viscous forces dominate over the inertial forces, the sinking speed for a sphere of radius $l$, density $\rho$ in an ambient fluid of viscosity $\mu$ and density $\rho_{sw}$ is given by the celebrated Stokes law

Here, $\mathbf{g}$ is the acceleration due to gravity. In our minimal model we assume that the mucus halo to be ellipsoidal with semi-major and semi-minor axes $b$ and $a$ respectively and density $\rho_{m}$. The visible particulate aggregate with effective radius $l$ has a density $\rho_{p}$ greater than $\rho_{m}$.

In the fluid-mechanical regime where viscous forces dominate over the inertial forces, the sinking speed spheroid with semi-minor axis $a$ and semi-major axis $b$, density $\rho$ in an ambient fluid of viscosity $\mu$ and density $\rho_{sw}$ is given by the mobility relation

using the Einstein summation convention, where $\mathbf{d}$ is the unit orientation vector along the symmetry axis of the particle, and $X_{A}^{-1}$ and $Y_{A}^{-1}$ are the mobility functions that depends on the eccentricity, $e=\sqrt{1-(a/b)^{2}}$, which for prolate spheroids take the form KIM1991 :

These account for the shape dependent sinking of the aggregate. Since, the visible aggregates are generally heavier than the mucus halo, an effective particle (particle + mucus) can be treated as a bottom heavy particle that aligns with the gravity axis $\mathbf{g}$ in a steady state ($\mathbf{d}\times\mathbf{g}=0$). Therefore for the present analysis only $X_{A}^{-1}$ will contribute. Note that the external force $F^{j}$ is the buoyant weight of the particle, given by

where, $V=4\pi a^{2}b/3$ is the volume of the spheroid, $\mathbf{g}$ is the acceleration due to gravity. Defining the effective density of the marine snow with particulate matter and mucus combined, $\rho_{eff}=(\rho_{p}\,V_{p}\,+\,\rho_{m}V_{m})/V$, where $V_{p}$, $V_{m}$ and $V$ is the volume of the particle, mucus and the total volume respectively (note that $V=V_{p}+V_{m}$).

Non-dimensionalizing using the characteristic length scale $L=a_{0}$ and characteristic time scale $T=9\mu/2g(\rho_{sw}-\rho_{m})a_{0}$ gives

where $\tilde{z}\equiv z/a_{0}$. Substituting the form of mobility function $X_{A}^{-1}$ for prolate spheroid gives the scaling relation for the non-dimensional sinking speed $\tilde{U}_{z}$,

where the scaling function is

Note that the eccentricity of the spheroid $e$ is a function of $a/b$; the first half of the scaling function is purely geometrical while the second half incorporates the physical parameters (relevant densities). In the above scaling, we have not accounted for the dependence of drag on the shape of the emergent particle, that could be elongated.