Supplementary materials

Supplementary Table 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Supplementary Table 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Supplementary Fig. 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Supplementary Text A - Diffusivity for the particles . . . . . . . . . . . . . . . . . . . . . 4

Supplementary Text B - Light attenuation technique . . . . . . . . . . . . . . . . . . . . 5

Supplementary Fig. 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Supplementary Text C - Dissolution model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Supplementary References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1

Table 1: Experimental conditions imposed at the source. �: linear stratification experiment, in which the tank is filledwith salt water using the double bucket technique. Values at the LNB (u) are calculated using a model of turbulent jet(Carazzo et al., 2008) with conditions imposed at the source (0).

Exp. ∆T0 ∆S 0 ∆C0 ρ0 Q0 ∆Tu ∆S u ∆Cu Rρ(K) (psu) (g/g) (kg m−3) (m3 s−1) (K) (psu) (g/g)

1 0 10 0.1 1063.5 4.1 × 10−5 0 1.2 1 × 10−2 0.12 0 10 0.025 1013.6 4.1 × 10−5 0 1.2 2 × 10−3 0.73 0 10 0.025 1013.6 2.6 × 10−5 0 1.2 3 × 10−3 0.54 0 10 0.025 1013.6 2.6 × 10−5 0 1.2 3 × 10−3 0.55 0 10 0.08 1049.7 4.1 × 10−5 0 1.2 1 × 10−2 0.16� 0 10 0.025 1013.6 2.6 × 10−5 0 1.2 3 × 10−3 0.57 40 10 0.1 1051.5 2.6 × 10−5 1.7 2.3 2 × 10−2 0.28 15 20 0.1 1057.7 2.6 × 10−5 2.1 4.0 2 × 10−2 0.39 40 10 0.025 1004.9 2.6 × 10−5 5.8 4.5 2.4 × 10−3 3.210 50 10 0.01 993.2 2.6 × 10−5 5.7 4.5 9 × 10−4 8.611 50 10 0.02 1017.9 2.6 × 10−5 4.6 4.5 6 × 10−3 1.2

Table 2: Physical characteristics of event plumes. Hu: thickness of the cloud thickness; Hl: thickness of the underlyingcolumn of seawater; ∆Tmax: maximum temperature anomalies observed; ∆Cmax: maximum particle anomalies observed;T: residence time; nobs: number of layers observed. References: (1): Baker et al. (1987); (2): Lupton et al. (1989); (3):Massoth et al. (1994); (4): Baker et al. (1989); (5): Nojiri et al. (1989); (6): Coale et al. (1991); (7): Gamo et al. (1993);(8): Baker et al. (1995); (9): Massoth et al. (1995); (10): Baker et al. (1998); (11): Feely et al. (1998); (12): Kelley et al.(1998); (13): Massoth et al. (1998); (14): Lupton et al. (1998); (15): Baker et al. (1999); (16): Edmonds et al. (2003);(17): Murton et al. (2006); (18): Baker et al. (2011); �possible event plume; †thickness estimated by grouping individuallayers.

Event Location Diameter Hu Hl ∆Tmax ∆Cmax nobs References(km) (m) (m) (K) (g L−1)

EP86 SJdFR 20 700 300 0.28 5.51 × 10−4 1 (1; 2; 3)EP87A SJdFR 16 600 400 0.20 4.37 × 10−4 1-2 (4; 3)EP87B� NFB N/A 600 400 0.10 N/A 2 (5)EP89 SJdFR 5 250 100 0.06 1.02 × 10−4 2-3 (3; 6)EP90� MB 70 800 200 0.03 N/A 3 (7)EP93A NJdFR 6.5 500 400 0.23 4.37 × 10−5 3-4 (8; 9; 10)EP93B NJdFR 9 400 400 0.18 6.49 × 10−5 3 (8; 9; 10)EP93C NJdFR 13 600 500 0.16 5.96 × 10−5 1 (8; 9; 10)EP96A GR 14 1000 300 0.11 7.50 × 10−5 4-5 (11; 12; 13)EP96B1 GR 12 450 600 0.04 5.60 × 10−6 1-2 (12; 13; 14)EP96B2 GR 12 400 400 0.07 1.12 × 10−5 1 (12; 13; 14)EP98� SJdFR > 15 300 200 0.19 N/A 1-2 (15)EP01� GaR > 9 1200 800 0.06 6.49 × 10−5 3 (16)EP03� CR > 70 900 700 0.07 1.39 × 10−4 3 (17)EP08A-C NELSC 3.2 150† 600 1.00 N/A 3 (18)EP08D-G NELSC 2.8 200† 400 1.00 N/A 4 (18)

2

0

5

10

15

20

25

30

35

40

0 50 100 150 200 250 300

Time (s)

Heig

ht

(cm

)

Linear stratification Single interface

t = 100 s t = 100 s

980 1000 1020

0

5

10

15

20

25

30

35

1043 1043.5 1044

0

50

100

150

200

250

Heig

ht

(m

)

Density (kg m-3

)

Heig

ht

(cm

)

POSITIVELY

BUOYANT

NEGATIVELY

BUOYANT

0 0.2 0.4 0.6 0.8

0

5

10

15

20

25

30

Plume velocity (m s )

Heig

ht

(cm

)

5 10

Plume radius (cm)-1

C

B

0

Density (kg m-3

)

A

NEGATIVELY

BUOYANT

POSITIVELY

BUOYANT

Hydrothermal plume

Laboratory plume

LNB

LNB

Supplementary Figure 1: (A) Comparison of plume (solid line) and ambient (dashed line) densityprofiles in our experiments (top) and in nature (bottom). Calculations are made with a model ofturbulent jet (Carazzo et al., 2008). (B) Comparison of plume height as a function of time for twoexperiments made at N

2 = 0.38 s−2 with a linear stratification (red curve - exp. 6) and a singledensity interface (blue curve - exp. 4). The insets show two photographs of the experiments at t =100 s. (C) Theoretical predictions of plume velocity and radius for two experiments made at thesame source conditions but with a linear stratification (red curve) and a single density interface(blue curve). These comparisons confirm that both lab-scale and natural plumes are qualitativelysimilar, and that the two-layer and linear density stratification give identical quantitative results.

3

A. Diffusivity for the particles

Classical experiments involving hot particle-laden fluids have been carried out using smallparticles (3 − 20 µm) with a low Brownian diffusion coefficient (Green, 1987; Huppert et al.,1991; Chen, 1997; Hoyal et al., 1999), which is given by

κp =k0Ta

3πρ f νdp

, (A.1)

where k0 is the Boltzmann constant, Ta is the absolute temperature, dp is the particle diameter,ρ f is the interstitial fluid density, and ν is the kinematic viscosity. In our experiments, the solidfraction consists of non-Brownian particles (dp = 300 µm) but the hydrodynamic diffusivity,which refers to the bulk random-walk motion of groups of particles in response to gradients inflow velocity and concentration, can be estimated from well-established theoretical and experi-mental studies of particle diffusion (e.g., Leighton and Acrivos, 1987a; Davis, 1996; Da Cunhaand Hinch, 1996). For spherical particles this diffusivity is given by

κp = k γ̇ d2p�n

p, (A.2)

where �p is the particle concentration, γ̇ is the local shear strain rate, and k and n are constantcoefficients, which vary from one study to another (k = 0.0075 & n = 1 in Da Cunha and Hinch(1996), k = 0.33 & n = 2 in Davis and Leighton (1987); Acrivos et al. (1993), k = 0.5 & n = 2in Leighton and Acrivos (1987a)). Hydrodynamic diffusion can arise under both low-Reynoldsnumber (Leighton and Acrivos, 1987a,b; Schaflinger et al., 1990; Acrivos et al., 1993) and high-Reynolds number conditions (Solomatov et al., 1993; Solomatov and Stevenson, 1993; Rampalland Leighton, 1994; Huppert et al., 1995; Ziskind and Gutfinger, 2002). In our experiments,based on the rate of propagation of the water-rich layers we infer γ̇ ∼ 0.01 s−1 (Carazzo andJellinek, 2013), which leads to κp = 10−14 − 10−13 m2 s−1 for a range of k and n found in theliterature.

A minimum bound for κp in layered hydrothermal clouds is given by the Brownian diffusioncoefficient. For 0.5 − 50 µm particles, Eq. (A.1) gives κp = 8 × 10−15 − 8 × 10−13 m2 s−1. Fromour experiments and well-established theoretical and experimental studies of particle diffusion, amore appropriate diffusivity is a hydrodynamic value (Davis, 1996; Carazzo and Jellinek, 2013).However, because there is no adequate observational constraints on the local particle concen-tration (�p) and rate of shear across each PBL (γ̇) in layered hydrothermal clouds, which enterboth in a significant manner in Eq. (A.2), we cannot estimate the hydrodynamic diffusivity forthe natural case. Comparing the Brownian and hydrodynamic diffusion coefficient in our exper-iments, we argue that a plausible hydrodynamic value in the natural case may be 2 to 4 orders ofmagnitude larger than the Brownian value, which still satisfies the instability condition given inEq. (1) of the paper.

In spite of the uncertainties on κp, the criterion for the onset of particle diffusive convection islargely attained in both our experiments and hydrothermal clouds (Eq. 1 of the paper). Further-more, the effective value of κp has no influence on the quantitative predictions made with our sed-imentation model (Eqs. 4 & 5 of the paper) since the rate of change in particle content from thecloud is controlled by the diffusivity of the fastest diffusive substance (i.e., temperature), whosevalue is well known (κT = 10−7 m2 s−1 in our experiments, and κT = 3 × 10−6 − 7 × 10−5 m2 s−1

in the deep-ocean (Kelley, 1984)).

4

B. Light attenuation technique

Variations in transmitted light were measured with a video camera and two light sheets setup on both sides of the tank, following the same approach as Carazzo and Jellinek (2013). Theimages obtained in the RGB system were converted into grayscale images, and the intensity ofeach pixel was determined using ImageJ (Supplementary Fig. 2). The calibration law giving thelight attenuation (I/�) received by the camera at a given location along the cloud as a functionof the mean particle mass fraction (C) is of the form

log�

I

��= −a C, (B.1)

where I is the intensity of the transmitted light, � is the intensity of the incident light, and a isa constant parameter that depends on the absorption properties of the fluid and particles, and onthe distance traveled by the light through the particle-fluid mixture. This relationship is foundto capture the behavior of our experimental materials in a simplified 2D Hele-Shaw geometryin the limit of dilute suspension (5 × 10−4 < C < 5 × 10−2) such as a = 1.2 with R

2 = 0.953.Moreover, it is fully consistent with previous experimental results on particle sedimentation indilute suspensions (Bergougnoux et al., 2003; Chehata Gomez et al., 2008, 2009).

Estimating the value of a is not straightforward in our experimental configuration becausewe cannot easily impose C in the cloud (which differs from the particle content imposed at thesource of the vertical plume). However, rewriting Eq. (B.1) to express the ratio of the particleconcentration in the cloud to its initial value (C0) as a function of I gives

C(t)C0=

log�

I(t)I0

�

log�

I0�� + 1, (B.2)

where I0 is the intensity of the transmitted light immediately after the cloud emplacement (t = 0).Eq. (B.2) shows that the gray level averaged intensity of all the pixels of the region of interest att = 0 (i.e., when C = C0) can be used to estimate I0 (stage t2 in Supplementary Fig. 2), whereasthe averaged gray-scale intensities after the sedimentation is complete (i.e., when C = 0) can beused to estimate � (stage t4 in Supplementary Fig. 2). By means of this calibration, Eq. (B.2)can be used to infer the dimensionless particle concentration, C(t)/C0, from the amount of lightattenuation by particles, I(t). As discussed in Bergougnoux et al. (2003), the light attenuation ismainly due to light scattering by the surfaces of the particles because the index of refraction ofthe particles differs from that of the fluid. The effect of multiple scattering is considered to besmall (within the error bars in Fig. 4 of the paper) at the low concentration used in this study,which is consistent with our 2D experiments and previous published work (Bergougnoux et al.,2003; Chehata Gomez et al., 2008, 2009).

5

xsalt water

cloud cloud

fingers

t1 t2 t3 t4

cloud

cloud

salt w

ater

pixel intensity

z

xz

xz

pixel intensity

pixel intensity

xz

pixel intensity

xz

t1 t2

t3 t4

tank floor

A

B

salt w

ater

salt w

ater

salt w

ater

Supplementary Figure 2: Representation of the method used to measure the rate of change ofparticle content relative to the initial concentration (exp. 10). (A) After conversion into grayscale(horizontal and vertical field widths, 10 cm). (B) Corresponding surface plot obtained using Im-ageJ representing the intensity of each pixel in panel A (0 = black; 1 = white). Stage t1: priorto the experiment; Stage t2: immediately after the cloud emplacement. This stage correspondsto the initial condition (t = 0 min) prior to particle sedimentation (I = I0). The dashed line cor-responds to the cloud/salt water layer interface; Stage t3: during the vertical transfer of particlesfrom the cloud to the lower layer of salt water (t = 10 min). Stage t4: after the complete transferof particles from the cloud to the lower layer of salt water (t = 150 min). Some particles are heldin suspension in the lower layer by convection but all the particles left the cloud.

6

C. Dissolution model

The model assumes that dissolution is rate-limited by the diffusion of solute across relativelythin compositional boundary layers (CBL) around each particle (Kerr, 1994, 1995). The dissolu-tion rate of a given particle is given approximately by:

dm

dt= A K ∆c, (C.1)

where m is the mass of dissolving substance, A is the particle surface area, ∆c ∼ 1 is the effectiveconcentration difference (i.e., thermodynamic disequilibrium) driving dissolution, and K is aneffective mass transfer coefficient. This coefficient is a well-characterized function of the flowregime governing the CBL thickness, which depends on the particle Reynolds number (Rep)and the ratio of the diffusivities of momentum and solute (ν/κs) (Kerr, 1995; Nield and Bejan,2006), and a more complicated function of the local pH-Eh conditions in the CBL (Sato, 1960;Luther, 1987; Moses and Herman, 1991). The dissolution experiments of Feely et al. (1987) giveK = 8 × 10−10 kg m−2 s−1 for pyrite particles held in suspension in deep-ocean waters.

The area available for dissolution can be determined from the total grain size distribution(TGSD). Assuming that the particle-fluid mixture is dilute (Feely et al., 1992) and taking a spher-ical geometry for the particles, we write

A =

n�

i=1

Np(i) Ap(i) =n�

i=1

Np(i) πd2p(i), (C.2)

where n is the maximum particle size remaining in the cloud, Np(i) is the number of i-sizedparticles, Ap(i) is the surface area of a single i-sized particle. For each class of i-sized particles,the number of particles is given by the ratio,

Np(i) =V1(i)Vp(i)

=6 C1(i)ρpπd3

p(i)=

6 y1(i) C1

ρpπd3p(i)

(C.3)

where V1(i), C1(i), and y1(i) are the volume, concentration, and mass fraction of i-sized particlesin the cloud, respectively, and Vp(i) is the volume of a single i-sized particle. Replacing Np(i) byits expression gives a general expression for the surface area available for dissolution,

A =6 C1

ρp

n�

i=1

y1(i)dp(i)

. (C.4)

However, rigorous constraints on the TGSD in hydrothermal clouds are not available (e.g., Ger-man and Von Damm, 2004). Thus, we only consider pyrite particles with a grain size distributionnarrowly centered on a single value (dp) decreasing with time at a rate of 5.3×10−12 cm s−1 (Feelyet al., 1987). Bearing in mind this assumption, we write

A =6C1y1

ρpdp

, (C.5)

where C1 is in units of mass/volume and A is in units of surface area/volume. For pyrite, weassume that y1 = 0.1 based on recent field measurements within hydrothermal clouds (Toneret al., 2012) and we take ρp = 5, 000 kg m−3.

7

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