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A new mechanism of sediment attachment to oil in turbulent flows: Projectile particles Lin Zhao, Michel C Boufadel, Joseph Katz, Gal Haspel, Kenneth Lee, Thomas King, and Brian Robinson Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/acs.est.7b02032 • Publication Date (Web): 06 Sep 2017 Downloaded from http://pubs.acs.org on September 11, 2017

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Environmental Science & Technology

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A new mechanism of sediment attachment to oil in turbulent flows:

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Projectile particles

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Lin Zhao1, Michel C. Boufadel1*, Joseph Katz2, Gal Haspel3, Kenneth Lee4, Thomas King4, Brian Robinson4

8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

1: Center for Natural Resources Development and Protection, Department of Civil and Environmental Engineering, New Jersey Institute of Technology, Newark NJ. [email protected]; http://nrdp.njit.edu 2: Department of Mechanical Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA 3: Federated Department of Biological Sciences, New Jersey Institute of Technology and Rutgers, Newark NJ. 4: Bedford Institute of Oceanography, Department of Fisheries and Oceans, Dartmouth, Canada

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Abstract

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The interaction of oil and sediment in the environment determines, to a larger extent, the

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trajectory and fate of oil. Using confocal microscope imaging techniques to obtain detailed 3D

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structures of oil particle aggregates (OPA) formed in turbulent flows, we elucidated a new

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mechanism of particles attachment, whereby the particles behave as projectiles penetrating the

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oil droplets to depths varying from ~2 to 10 µm due to the hydrodynamic forces in the water.

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This mechanism results in higher attachment of particles on oil in comparison with adsorption, as

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commonly assumed. The projectile hypothesis also explains the fragmentation of oil droplets

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with time, which occurred after long hours of mixing leading to the formation of massive OPA

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clusters. Various lines of inquiries strongly suggested that protruding particles get torn from oil

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droplets and carry oil with them, causing the torn particles to be amphiphillic so that they

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contribute to the formation of massive OPAs of smaller oil droplets (~5-10 µm). Low particle

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concentration resulted in large irregular shaped oil blobs after time, of which the deformation

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without fragmentation could due to partial coverage of the oil droplet surface. The findings

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herein revealed a new pathway for the oil fate in environments containing non-negligible

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sediment concentrations.

42 43 44 45

Keywords: oil particle aggregation; oil spill; oil trapping rate; OPA formation; nearshore

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environment

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Oil - Green

Particle - Red

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INTRODUCTION

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Oil from natural seeps1 and/or accidental spills could interact with sediments in the environment

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to cause the formation of oil-particle-aggregates (OPA),2 which could affect the fate and

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transport of spilled oil3 and enhances oil dissolution and biodegradation.4 Oil droplets stabilized

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by fine particles coated on the droplet surface form Pickering emulsion,5 that prevents adhesion

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and coalescence. The buoyancy of the OPA is lower than that of an oil droplet alone due to the

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larger density of the particles. This facilitates the transport of OPA by deeper currents than those

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experienced by an oil droplet.6-8 We used confocal imaging techniques to examine the detailed

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3D structures of OPAs formed in turbulent flows, with the goal of revealing the theory and

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mechanisms of oil-particle interactions in a turbulent system, ultimately leading to elucidation of

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the fundamentals of oil-particle interactions.

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Solid particles as emulsion stabilization agents have long been used for many industrial

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applications such as personal care products, in the food industry, and in oil recovery and mining

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process.9 The existing theory on the mechanism of oil-particle aggregation has pointed to free

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energy change analysis, as derived by Rapacchietta and Neumann10 for a solid sphere with an

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infinitely flat oil-water interface. This was extended to emulsion-droplets coated by close-

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packed monodisperse spherical particles by Menon, et al.11 and Levine, et al.12 Typically, an

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initial state of free droplet and particles, and a final state of droplet coated with a close-packed

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monolayer of particles were assumed. For a plane liquid interface, the free energy change is

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∆E =

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the oil/water interfacial tension,; θs is the oil-water static contact angle in the presence of

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particles; and the plus or minus sign within the brackets represent the energy needed to remove

π 4

D p2σ ow (1 ± cos θ s ) , where Dp represents the equivalent diameter of the particle; σow, is 2


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the particle from or place it onto the interface.9 Based on this theory, oil droplet-particle

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aggregation depends solely on the oil-water interfacial forces and the three-phase contact angle.

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Other analysis of the influence of capillary and van der Waals forces between particles, line

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tension and monolayer curvature energies on the emulsion stability were also studied

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theoretically.13,14 However, these theories were established with the assumption that the

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adsorption of particles from the continuous bulk phase takes place based only on surface physic-

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chemical forces. The impact of the hydrodynamics on the oil-particle interaction in a turbulent

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system was omitted or neglected, and is thus the focus of our investigation.

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In this study, we show the 3D structures of particle arrangements inside oil droplets following

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encounters of the two in turbulent flow, and demonstrate a projectile-like mechanism that

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governs the particle penetration into the droplet. Such a mechanism allows for more irregular

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shape particles attaching to the droplet surface, which could explain the increased particle

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packing behavior on the droplet surface with particle concentration reported by Zhao, et al.15 The

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projectile mechanism could also explain the decreased sediment uptake by a weathered oil.16

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Contrary to the stable OPA under quiescent condition, we demonstrate a continuous decrease in

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the size of the droplet over time in presence of turbulence and high particle concentration. This

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finding has significant environmental implications, as the small droplets have large interfacial

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areas, thus enhancing oil dissolution and biodegradation. A large interfacial area enables

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additional particles attach to the droplet, promoting oil sedimentation. Massive OPA networks

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(or clusters) were formed after long hours.

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MATERIALS AND METHODS



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The three phases we used to form OPA were Alaska North Slope (ANS) crude oil, artificial

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seawater as the continuous medium, and Kaolinite particles. The oil properties were measured at

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15°C-19°C and had a density of 878 kg/m3, dynamic viscosity of 18.9 cp, using Anton Parr

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SVM3000 Stabinger Viscometer, and oil-water interfacial tension of 15.5 mN/m by Krüss K20

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force tensiometer. The artificial seawater was made using ultrapure deionized water with pre-

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calculated weight of ocean sea salt to obtain a salinity of ~34 ppt. Kaolinite was recognized as

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one of the most efficient mineral for sedimenting oil.17 The Kaolinite (Sigma-Aldrich) we used

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was in the shape of plate particles (Figure S1), with a median equivalent diameter dp50 of ~7 µm

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(the size represents an equivalent spherical diameter based on the volume, the dp50 was obtained

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at the 50% point of diameter in the cumulative volume fraction as shown in Figure S2b and Sec.1

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of the Supporting Information). The length of the particles reached up to 20 µm and the average

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width was ~2 µm. The particle was moderately hydrophilic with a contact angle of ~27° and the

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density was ~2630 kg/m3.18,19 The organic carbon content was zero, confirmed by the lack of

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fluorescent emission in the confocal microscope.

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A layout of the experimental design is presented in Figure S3 (Supporting Information). The

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experiment started with the generation of groups of oil droplets by adding 60 mg oil to a baffled

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flask20 containing 120 mL seawater. The flask was shaken on an orbital shaker for 1 hr. While it

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was shaking, a design amount of particle stock solution was added into the flask, and different

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shaking times for oil-particle interactions were selected, varying from 1 min to 24 hr. To study

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the effects of particle content on OPA formation, two particle concentrations were selected: 1500

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mg/L and 100 mg/L (the total particle number concentration was ~9.8×109 #/L and ~6.5×108 #/L;

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the particle size distribution is shown in Figure S2 and Sec.1 of the Supporting Information),

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corresponding to an oil-to-particle mass ratio of 1:3 and 5:1, respectively (the oil concentration 6 ACS Paragon Plus Environment

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was 500 mg/L of oil). The adopted particle concentration range is observed in the natural

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environment.15 After the preset shaking time, the flask was left static overnight to allow phase

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separation. Depending on the amount of particles attached to the oil, the oil droplet becomes

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either negatively buoyant OPA which settled in the bottom or floats on the water surface as

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buoyant OPA or free oil. For all the experiments, the mixing speed of 200 rpm was adopted. The

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mixing energy in the baffled flask was carefully characterized using a particle image velocimetry

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(PIV).20 The energy spectra obtained at the experiment conditions showed a region with “–5/3”

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slope which confirmed the existence of the inertial subrange and the presence of turbulent flow

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in the vessel. The mean velocity u at the speed of 200 rpm was 8.81 cm/s and the root mean

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square of turbulent velocity fluctuations u ' was 5.62 cm/s. The energy dissipation rate ε was

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0.67 W/kg, the Kolmogorov length scale η was 63.8 µm, and the integral length scale τ was

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measured at 1.27 mm.20 Such mixing energy represents a typical breaking wave condition.21

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The final sample of the negatively buoyant OPAs was carefully taken from the bottom layer and

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transferred onto the microscope slide for analysis using a confocal laser scanning microscope

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(Leica DM6000). In order to maintain the OPA structure, a coverslip-seal chamber gasket with

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20 mm in diameter and a 150 µm deep well (volume of ~50 μL) was attached to the slide to hold

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the sample without disrupting the morphology of the specimen. A confocal microscope allows

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one to scan a thin cross-section of the specimen by excluding most of the light from the

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specimen that is not from the microscope’s focal plane; thus, make it possible to build a three-

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dimensional (3D) reconstructions of a volume of the specimen from a series of scanned slices.22

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In this study, simultaneous excitation wavelengths of 488 and 638 nm were used. The signal

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emitted in the range of 519-605 nm was recorded in the green channel to represents the

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fluorescent oil, whereas wavelengths of 607-672 nm in the red channel represent the particles in 7 ACS Paragon Plus Environment


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the reflectance mode. The 40x oil immersion objective lens was used and multiple scans were

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acquired in focal planes 0.35 µm apart to reveal 3D structures of the OPA.

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All the OPA images (2D and 3D) were obtained using the commercial software LAS X provided

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by Leica Microsystems. For the 3D images, the clipping function resided in LAS X was adopted

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to reveal the inside structures of the OPA (see Figure S4 and Sec. 2 of the Supporting

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Information for details of clipping).

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RESULTS

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For a high particle concentration (Cp=1500 mg/L), representing the swash zone,15 the bottom

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layer in the flask became brownish within a minute of oil-particle interaction, indicating rapid

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formation of negatively buoyant OPAs (the particles are white). Under the confocal microscope

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(Figure 1 and Figure S5 of the Supporting Information), individual droplets with size in the range

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of 15-50 µm were abundant (see the droplet size distribution in Figure S6), and were enveloped

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by particles. The droplets were generally spherical, with a slightly distorted surface due to the

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presence of particles. By clipping (i.e., cutting open; see Figure S4 and Sec. 2 of the Supporting

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Information) the droplet at different angles through microscopy, the particle arrangement inside

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the droplet was revealed; many particles penetrated the droplet to different depths (Figures 1a-g

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and Figures S5a-k). The depth was generally in the range of ~2-3 µm (Figure 1a-d, Figure S5a,

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S5e, and S5h-k), but depths >4 µm were also observed, with the deepest penetration close to ~10

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µm (Figure 1e-f, Figure S5c-d, and S5f-g). Most of the deep penetration seems to occur when the

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particle width is small, i.e. ~1 μm for the particles in Figure 1e-f and Figure S5c-d, with the

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exception of Figure S5f-g where particle width of ~3 μm results in a penetration of ~5 μm. Often,

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some particles or tiny OPAs (~1-3 µm) partially deposited within the droplet (Figure 1g),


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indicating the occurrence of collision which results in the embedment of particles (or tiny OPAs)

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inside droplets. We also observed that some particles are attached on the droplet surface without

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penetration (Figure 1a and 1g, Figure S5a-e). Most of these posturing particles are flattened (or

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tilted in certain angle) on the droplet surface (Figure S5a-d). Nevertheless, we believe the

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arrangement of the particle in relation to the oil droplet is related to the state (e.g. hydrodynamics

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and properties) of particles and droplets during the encounter. The particle penetration occurs

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within a very short time (within 1 min based on the experiments, and within milliseconds based

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on the prediction which is discussed later), after which, there were no apparent changes in the

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penetration depth even after 24 hours of oil-particle interaction (e.g. Figure 3, Figure S8, and Sec.

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3 in the Supporting Information). This suggests that there were no permanent forces driving the

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particles deeper into the droplet over time. In most cases, the penetration was perpendicular to

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the droplet surface via the narrow side of the particle (Figure 1e-g and Figure S5a, S5c-g and

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S5i-k), which is contradictory to the theory of adsorption which relies on maximizing the contact

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surface (whereby the particle would be flattened on the droplet).23

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One plausible theory for the penetration process is a “projectile” mechanism whereby the particle

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collides with the oil droplet at relatively large speed resulting from turbulence. We constructed a

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simple model to help interpreting the observation: Assume a simplified case of a thin smooth flat

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particle (~7 µm) arriving at the surface of a droplet (~20 µm). As both the particle and the

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droplet are below the Kolmogorov scale η of the system (~63.8 µm, based on the energy

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dissipation rate ε in the flask ~0.7 W/kg, see Materials and Methods), the velocity can be

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estimated by ~ ε 1 / 2 D p /ν 1 / 2 .24 The collision velocity of the particle and the droplet could reach

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~2 cm/s (mostly due to the relatively large velocity of the droplet, i.e. ~1.6 cm/s for 20 μm

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droplet). Gravity forces of the droplet or particle are negligible with respect to inertial forces in 9 ACS Paragon Plus Environment


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this system as the Froude number, Fr = u p ( ρ / ∆ρ gD p ) >>1. Using the flat plate theory,25 and

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ignoring nonsteady drag (e.g. added mass and Basset history forces), the motion of the particle

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with respect to the droplet is given by m p

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stress within the oil droplet. Under such circumstances, the drag experienced by the flat particle

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is purely friction drag,25 FD = b∫ τ w ( x)dx , where b is the width of the plate, h is the penetration

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1/2

du p dt

= − FD , where FD is the drag force due to shear

h

0

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depth, τ w is the local wall shear stress, given by τ w ( x ) = 0.332 ρu 2p / Re x , Re x = u p x /ν is the

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Reynolds number where x is the instantaneous penetration depth, and ν is the oil kinematic

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viscosity. Based on the literature, in micro-scale flow at the fluid-solid interface, the slip

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boundary condition has shown to be very important to affect the flow state; as a consequence, the

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tangential shear stress (the friction drag) at the solid boundary must be considered in most of the

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micro-scale flow simulations.

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condition.

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The penetration depth for different particle width and initial velocity was estimated (Figure 2a);

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the increase in the penetration depth with the particle initial velocity was nonlinear; the

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penetration depth increases rapidly at very small (relative) velocity, then more gradually when

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the velocity increases. The depth was also influenced by the plate width in a linear way,

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consistent with increased friction due an increase in the surface area. The flat plate theory

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reproduced well the spectrum of penetration depth from the experiments. For example, for the

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relative speed of 2.0 cm/s, one notes in Figure 2a that a penetration depth of 10 µm corresponds

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to a width of 1 µm, which is observed in Figure 1f. For a large particle width (e.g. 5-10 µm), the

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penetration depth by the theory is ~2.4-3.8 µm, consistent with the observations (Figure 1c-d, g,

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Thus, using the friction drag should be valid in the current


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Figure S5b, h). For a small relative speed of 0.5 cm/s, the penetration depth by the theory is

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~1.5-7 µm, which is still within the depth range observed from the experiments. An in-depth

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investigation on the particle penetration in droplets is presented in the Discussion Section.

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Individual droplet OPAs with an average penetration depth of ~2-4 µm were observed in the 10-

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min oil-particle interaction duration (Figure S8 and Sec. 3 in the Supporting Information). The

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internal motion inside the droplet was apparently not strong enough to affect the positioning of

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the particles when comparing the 1 min, 10 min, and longer interaction (3D OPAs are not

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reported herein) results. It seems that similar to the effect of surface-active contaminants, the

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particles rendered the droplet interface rigid, thus dampening out the internal motion.29

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As time proceeded, the size of droplets enveloped by the particles decreased (see the droplet size

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distribution in Figure S6). The droplet size distribution (DSD) after 10 minutes of interaction

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slightly shifted to the smaller sizes compared to the distribution of 1 min interaction, having a

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median diameter of 18 μm compared to 22 μm of 1 min interaction. After 3 hours, an clear

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reduction in the droplet size was observed, as the majority of the droplets were less than ~10 µm,

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with a median diameter of 3.5 µm. In addition, the droplets were loosely bound together to form

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multi-droplet OPAs or a cluster-OPA (Figure 3a-c), while single-droplet OPAs were barely

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found in the samples. An even more massive OPA clusters of hundreds or even thousands of

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small droplets with particles were observed after 24 hours oil-particle interactions (Figure 3d),

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with a further reduction of droplet size to basically less than ~5 µm (Figure S6) and a median

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diameter of 2.6 µm. The OPA clusters persisted even after 48-hr of oil-particle interaction,

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displaying only a slightly decreased droplet size from that at 24 hours..

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This demonstrates that turbulence causes fragmentation of OPAs, while it is generally known

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that under quiescent condition, formed OPAs are very stable and persist for long durations 11 ACS Paragon Plus Environment


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(months) without changes of shapes and phase separation.30-32 The decrease in the droplet size

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resulted in an increase of the interfacial area, enabling additional particles to adhere onto the

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droplet, promoting therefore a high oil trapping rate in the settling OPAs (Figure S9 and Sec. 4 in

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the Supporting Information), with ~95% of the total oil in the negatively buoyant OPAs at 24-hr,

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in comparison to 28% at 1-min, 55% at 10-min, and 71% at 2-hr.

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By analogy with the effects of surfactants, Levine, et al.12 postulated that a complete coverage of

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a monolayer of particles on the droplet surface would lower the oil-water interfacial tension

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(IFT). Binks33 believed that solid particles could function in many ways like surfactants and

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summarized the major difference between solid particles and surfactants as emulsifier: i)

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particles have typically a particular affinity, while surfactants are amphiphilic; ii) particles

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adsorb strongly and irreversibly to the oil-water interface, while surfactant molecules adsorb and

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desorb on a relatively fast timescale. However, recent studies reported that no interfacial tension

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reduction was observed at the oil/water interface in the presence of particles, instead more

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energy was required to fragment droplets when only particles presented on the interface.34 Mei,

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et al.35 showed that the apparent interfacial tension of particle-covered droplets first decreased at

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low surface coverage by particles, and then increased as the particle concentration at the droplet

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surface increased, to almost double the interfacial tension of a pure droplet at very high particle

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concentration. They postulated that the increase of interfacial tension is due to the formation of a

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particle network which suppresses the droplet deformation. Yet, our results showed that the

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cluster formation of OPAs did not entirely stop the droplet fragmentation rather slowed it down

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in comparison with shorter interaction time, i.e. the droplet size was reduced only ~1 μm from 3

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hr to 24 hr interaction (see also Figure S6 for DSD). While studies have elucidated how particles

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stabilize emulsion droplets,14,30 the role of particles on droplet stability during oil-particle 12 ACS Paragon Plus Environment

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interaction is still an open question,36 and is needed to provide answers to major questions of

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natural cleaning up of spilled oil. This study indicated that the presence of particles caused the

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fragmentation of droplets in turbulent flows.

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Our hypothesis is that the attached particles on the droplet are exposed to a dynamic pressure as

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the droplet moves about in turbulence (Figure 2b). The particles (with various penetration

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depths) may wiggles and locally weaken the interfacial energy, would eventually cause the

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particle to be torn from the droplet, and to carry (or scoop) with it a certain oil volume, which

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explains the reduction of the droplet size with time. Once a particle is torn from the droplet

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(Figure 2b), it would invariably have some oil attached onto it, and thus it becomes amphiphilic,

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which allows it to behave as a bridge to binding particles and oil droplets.37 This appears to be

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prerequisite for the formation of massive clusters with time (Figure 3), where the oil that covered

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the particle surface acts as cement between particles.

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To confirm the droplet fragmentation by particles, two control cases were performed: 1) In the

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absence of particles, the oil droplet size distribution (DSD) reached equilibrium (steady state)

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after 1-hr of agitation in the same setup (Figures S11-S12 and Sec. 5 in the Supporting

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Information). The median droplet diameter d50 was ~75±7µm for any period of agitation that is

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within 1-25 hr; (2) When a biocide was added to the oil-particle system, the bio-control showed

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no difference in droplet sizes and OPA structures with the base case (Figure S13 and Sec. 6 in

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the Supporting Information). Thus, biodegradation did not play a role in the fragmentation, and

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thus, the presence of particles in a turbulent flow caused the fragmentation of oil droplets.

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The low particle concentration (Cp=100 mg/L), representing the breaker zone (typically 500 to

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3,000 m from the beach) in the nearshore environment15 and the water column in the ocean,



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resulted in smaller amount of negatively buoyant OPAs than the high Cp=1500 mg/L (Figure

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S10). For 1 min and 10 min oil-particle interaction, the bottom layer in the flask appeared to be

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white color (the particle color is white), indicating the majority of the settled material was

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particles. The settled OPAs have similar structure as the ones found at the high concentration

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condition (Figure S14). After 3 and 24 hrs of oil-particle interaction (Figure 4), the OPA

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structure consisted generally of multiple large-sized irregular shaped oil volumes covered with

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particles. Such an OPA structure is different from that of the clustered formed under high

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concentration (Figure 3), and is very close to emulsions formed due to arrested coalescence.38

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Due to the small amount of particles in solution, most of the droplets were only partially covered

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with particles on the surface. As such droplets come into contact with one another, the

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coalescence could be initiated from the contact of particle-free patches; it is possible that

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particles in the contact region were pushed away towards the periphery to form a dimple

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surrounded by a ring of particles,39,40 due to the lower energy requirement of displacing particles

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laterally at the droplet interface than pushing them inside.41 Once the droplets coalesced, if

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sufficient particles were present on the droplet surface, the cohesive structures of the particles

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resist the Laplace pressure gradient that drives the droplets together,40 resulting in the non-

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spherical droplet structure. The same theory may apply to the observations by Waterman and

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Garcia42, who obtained large irregular-shaped OPA using a different mixing technique, which

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invariably resulted from repeated sequences of oil entrainment, resurfacing, and re-coalescence.

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DISCUSSION

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The high concentration results indicated that some particles penetrate the droplets perpendicular

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to the droplet surface. We interpreted the penetration depth using the flat plate theory. Two


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issues would need to be addressed: 1) The positioning of these particles at 90°with the droplet

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surface and 2) the apparent success of the flat plate theory in interpreting the penetration depth.

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The motion of anisotropic particles in turbulence is complicated,43 involving not only the

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complexity of turbulence and multiphase flows, but also the forces and torques that depend on

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the particle rotation and orientation. Thus, particle orientation could result in the particle contact

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with the droplet at different angles. Jeffery44 first theoretically studied the motion of ellipsoidal

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particles with no-inertia (density is matched with the liquid) immersed in a very viscous fluid,

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and found that prolate spheroidal particles (slightly similar to ours) tend to rotate around the

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direction perpendicular to the plane in which the motion of the fluid takes place. After that, many

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studies have investigated the motion of anisotropic particles in turbulent flows, and the general

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findings was that prolate particles in turbulent flow align perpendicular to the velocity gradient in

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the flow; near a boundary (e.g. a wall in a turbulent channel flow), where the velocity gradients

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are strong, the prolate particles have tendencies to be aligned parallel to the wall.45,46 This

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alignment could be unstable, especially for higher inertia particles and can be maintained for

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rather short times before the particles turn perpendicular to the wall.47 Such a behavior was

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confirmed for Stokes number (the ratio of particle relaxation time to the fluid timescale) St>1.48

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Though the particles we used have higher density than the surrounding fluids, they have St≈~0.1

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on the average due to their small sizes, which suggests that they would align parallel to the wall

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of the droplets. Nevertheless, it is obvious that a fraction of them penetrated at near 90 degrees

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into the droplets (e.g. Figure 1, Figure S5). Based on Figures 1 and S5, that fraction is between

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20% and 40% of the total particles attached to the droplets. It is thus possible that the local shear

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rate and the eddy frequency near the droplets varied in a way to cause the local Stokes number to

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approach 1.0 causing the particles to be at 90 degrees with the droplet surface.48 Thus, St could 15 ACS Paragon Plus Environment


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go beyond 1 locally and the particle inertial plays a role in its orientation causing the particles

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aligned to the interface-normal direction. In addition, the particle concentration (1500 mg/L) was

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high in our system, where particle interactions, i.e. particle-particle collision, are inevitable. Such

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collision may exert extra force on the particle motion, which would cause the rotation deviate

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from the preference alignment.46,49

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The flat plate boundary model based on friction in the oil was capable of reproducing the

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observed depth given the macroscopic turbulent conditions. This suggests that the interfacial

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force that would resist penetration was small (it was neglected in the model). When the particle

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is between the two immiscible fluids, a three phase contact line is formed (Figure 2c). Under

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static condition (i.e. the solid boundary is not moving in relation to the liquid), the state of the

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contact line is expressed through the balance of the tangential projections of the forces along the

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solid boundary acting on the contact line in terms of interfacial tension σ between medias and a

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static contact angle θs.14,50

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σ po − σ pw = σ ow cos θ s , where the subscript p, o and w represents particle, oil, and water. When

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the particle moves relative to the oil-water interface, the contact line moves, and would result in

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a distortion of the shape of the interface, leading to a dynamic contact angle θd, deviating from

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the static contact angle.51 The interface distortion is directly related to the capillary number:52

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Ca = µoU s / σ ow , where µo is the oil viscosity, Us is the relative velocity of contact line to the

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solid. The capillary number, describing the relative strength of viscous dissipation at the contact

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line to the energy required to distort the interface,52 was

A New Mechanism of Sediment Attachment to Oil ... - ACS Publications

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