Localized fluidization burrowing mechanics of Ensis directus

There are many examples of animals that live in particulate substrates and have adapted unique locomotion schemes. The sandfish lizard (Scincus scincus) wiggles its body from side to side in order to effectively swim through sand (Maladen et al., 2009). Smaller organisms, such as nematodes (Caenorhabditis elegans), have been observed to move quite efficiently via an undulatory motion in saturated granular media (Jung, 2010a; Wallace, 1968). Clam worms (Nereis virens) have been observed to burrow in gelatin, a material with properties similar to those of elastic muds, by propagating a crack (Dorgan et al., 2005). Throughout this paper, we use the terms ‘soil’ and ‘substrate’ to refer to the media in which burrowing organisms live, regardless of whether they are granular or cohesive. We specify that these substrates are composed of small particles (from clay to coarse sand) with the term ‘particulate’.

Numerous soft-bodied organisms that live in particulate substrates saturated with a pore fluid use a two-anchor system to burrow: one section of the animal expands to form an anchor while another section contracts and extends to progress forward in the burrow; once extension is exhausted, the roles of each section are reversed (Dorgan et al., 2005; Fager, 1964; Holland and Dean, 1977; Jung, 2010b; Shin et al., 2002; Stanley, 1969; Trueman, 1966a; Trueman, 1966b; Trueman, 1967; Trueman, 1975). In this paper, we show that the Atlantic razor clam (Ensis directus Conrad 1843), which burrows via the two-anchor method, uses motions of its valves to create a pocket of fluidized substrate around its body to reduce drag forces and burrowing energy expenditure.

Trueman measured ∼10 N as the maximum pulling force that E. directus can exert to pull its valves into soil (Trueman, 1967). Using a blunt body with a size and shape similar to that of E. directus, pressed into the animal's habitat soil on a mud flat in Gloucester, MA, we measured that 10 N of force should enable E. directus to submerge to approximately 1–2 cm. In reality, razor clams can dig to 70 cm (Holland and Dean, 1977). Because drag force scales linearly with depth for a body moving through a granular medium (Robertson and Campanella, 1983), muscle force measurements indicate that E. directus is approximately 75 times too weak to reach full burrow depth in static soil. Thus, the animal must manipulate the surrounding environment to reduce drag.

Ensis directus is enclosed by two, long, slender valves that hinge along an axis oriented longitudinally to the animal. A foot, which is a dexterous, soft organ, resides at the bottom of the valves. Ensis directus burrows by using a series of valve and foot motions to draw itself into the substrate (Fig. 1). We estimate an upper bound of the mechanical energy per depth for the animal to advance its valves downwards by adapting pedal strength, valve displacement, hinge stiffness and mantle cavity pressure measurements from Trueman (Trueman, 1967) and summing the expended mechanical energy and attained displacements for each burrowing motion: valve uplift (0.05 J, 0.5 cm), valve contraction (0.07 J, 20 deg) and valve penetration (0.20 J, –2.0 cm), for a total of 0.21 J cm^–1. Re-expansion of the valves is accomplished through elastic rebound of the hinge ligament and thus requires no additional energy input by the animal. To put the magnitude of the energetics in perspective, E. directus can travel over 0.5 km through soil on the energy stored in a AA battery (Energizer, 2009).

Ensis directus specimens used for our research were collected from natural stocks in Orleans and Gloucester, MA, under the appropriate research permits issued by the Massachusetts Department of Fish and Game. Once specimens were harvested and brought back to the laboratory, they were held in a chilled, saltwater commercial lobster tank (50-gallon lobster tank, Stark Products, College Point, NY, USA).

The device shown in Fig. 2 was used to measure drag force on the valves of E. directus static soil. The device was constructed from a pair of E. directus valves bonded to an aluminum rod with a urethane casting compound (McMaster-Carr #8690K1, Princeton, NJ, USA). The valves were positioned in their natural orientation and the cross-sectional area of the rod was less than the frontal area of the valves, as to minimize its effect on drag. A fish scale (Jennings Ultrasport 30, www.jscale.com) attached to a pushing handle was mounted to the top of the rod to measure insertion force. The device was operated by slowly pushing it into the soil (as to avoid inertial effects) and recording the force at each depth increment marked on the rod.

The adage ‘clear as mud’ is used to describe the difficulty of visually investigating burrowing animals in situ. To surmount this challenge and view the burrowing motions of E. directus, as well as deformations in the soil surrounding the animal, we developed the visualizer shown in Fig. 3A. The visualizer is essentially a backlit ant farm, or Hele-Shaw cell, which is commonly used in fluid mechanics experiments to measure flow in two dimensions (Kundu and Cohen, 2004). The front viewing pane is adjustable forward and aft via a lead screw and bellowed side walls, allowing tank and animal thickness to be matched. Specimens were oriented vertically in the visualizer with their valves orthogonal to the tank walls (Fig. 3B). This forced a plane strain condition while allowing for soil deformation in the principal directions of the animal's burrowing motions.

The substrate used in the visualizer is composed of 1 mm diameter, optically clear soda-lime glass beads (Potters Industries A-100, Malvern, PA, USA). This substrate was chosen because its particle size and density (ρ2.52 g cm^–3) are close to that of coarse silica sand (Terzaghi et al., 1996), one of the substrates in which razor clams live (Holland and Dean, 1977). Although smaller substrate particles are more common in E. directus habitat, we found through experimentation that soda-lime glass beads less than 1 mm in diameter did not provide adequate light transmission for visualization.

Heat dissipation was an important consideration in the visualizer design, as the halogen lamps generate sufficient heat to melt the polycarbonate walls of the tank (and kill the animals) within minutes if not actively cooled. Chilled and oxygenated water supplied from the commercial lobster tank used to hold specimens is circulated through the visualizer (Fig. 3C). This water is mixed with hot water flowing out of the visualizer and gravity fed into a pump. The pump sends water to a reservoir with a float valve that maintains fill level near the top of the visualizer. Two outlets leave the reservoir: one into the top of the visualizer and one directly back to the lobster tank. The flow rate through the visualizer is 10 gallons min^–1, which yields a downwards bulk flow velocity of ∼0.08 cm s^–1. This is 15 times slower than the uplift velocity of E. directus (Trueman, 1967) and was therefore assumed to not interfere with burrowing motions.

Because the flow resistance through the substrate within the visualizer is much greater than the resistance of the ‘short circuit’ line from the reservoir to the lobster tank, the portion of heated water that enters the supply stream at the pump is small compared with the chilled water from the lobster tank. As a result, we were able to maintain temperature in the visualizer to within 2°C of the lobster tank, which was set to 10°C.

Ensis directus specimens placed in the visualizer were filmed with a high-definition video camera (Sony HD Handycam, Tokyo, Japan) at 30 frames s^–1. During some tests, the animals were stimulated to dig by lightly touching their siphons. In most tests, E. directus burrowed naturally without any applied stimulus. Each test was composed of one complete burrowing cycle (Fig. 1). The data presented in this paper represent 23 burrowing cycles performed by three separate animals at a depth ranging from 0.5 to 1 body lengths.

Kinematics of E. directus were tracked using the following process: (1) frames of each digging cycle were converted to 720×480 pixel grayscale images (Fig. 4A); (2) each image was converted to black and white in MATLAB (The MathWorks, Natick, MA, USA), with a threshold chosen to accentuate the contrast between dark areas of the valves and light areas of the foot and substrate; (3) the images were filtered to remove all connected components consisting of fewer than 50 pixels, which removed dark areas that do not correspond to the valves; and (4) the remaining points were divided into four quadrants that approximate the top, bottom, left and right sides of the valves using a rectangular orthogonal regression algorithm (Arbenz, 2008). The size and position of this rectangle was then used to identify the width and depth of the clam in each video frame of each test (Fig. 4A).

To measure substrate deformations around burrowing E. directus, opaque particles were interspersed in the visualizer substrate at a concentration of 7% and were tracked using MatPIV particle image velocimetry (PIV) software (Sveen, 2004). Raw video from each of the 23 burrowing cycle tests was converted to grayscale and cropped to show only the substrate to one side of E. directus (Fig. 4A). This removed tracking artifacts generated by the motion of the valves and the shadow projected by the animal's body. The substrate to the side of E. directus that exhibited the greatest displacement was used for PIV analysis (causes for asymmetry are discussed in the Results). Each video frame was then converted to a 720×480 pixel image. Adjacent images were processed with MatPIV in three iterations with interrogation windows of 64×64, 32×32 and 16×16 pixels, all with 50% overlap.

Displacements between each video frame were summed to find the total horizontal and vertical displacement fields. At the point of valve contraction (Fig. 1D), immediately before valve penetration (Fig. 1E), the mean (±s.d.) horizontal displacement of the soil adjacent to the animal for all tests was found to be 9.2±4.9 times greater than the vertical displacement. As a result, horizontal soil displacement was considered to be the most important factor in the animal's manipulation of the substrate. To reduce PIV noise, horizontal displacement as a function of horizontal position was determined by averaging the rows of the horizontal displacement field (Fig. 4B).

With Eqn 3, temporal changes in void fraction around burrowing E. directus were calculated from PIV data (Fig. 4B). The only initial condition required was the initial void fraction, which was determined to be 0.38 by measuring the volume of the experimental setup and the volume of the pore fluid.

Fig. 5 shows valve kinematics during five consecutive burrowing cycles for one of the E. directus specimens tested. Each stage of the burrowing behavior, corresponding to Fig. 1C–F, can be seen. The digging progress per cycle is small but apparent. Each stage of the digging motion does not happen discretely; contraction (Fig. 1D) continues during penetration (Fig. 1E) and the valves tend to rise during expansion (Fig. 1F).

Fig. 6 shows the temporal changes in substrate displacement during one E. directus burrowing cycle. Valve uplift (Fig. 6B) and contraction (Fig. 6C) result in a local soil disturbance. The magnitude of the particle motion on either side of the animal was rarely symmetric. This result is expected if E. directus lies at a slight angle relative to vertical; the substrate on the uphill side of the animal will preferentially deform by sliding downwards, rather than the substrate on the downhill side of the animal deforming by sliding upwards (Terzaghi et al., 1996). This behavior is consistent with our observations. Soil deformations caused by the valve motions E. directus occurred on a time scale smaller than that required for the soil to collapse and fill around the animal. The natural failure wedge that occurs in this condition can be seen in Fig. 6D, with the matching overlaid failure angle, θ_f, which was calculated from the soil's friction angle. The relationship between friction and failure angle is explained in the Discussion.

Void fraction values calculated from PIV displacement data taken at the point of valve contraction (Fig. 1D) that immediately precedes valve penetration (Fig. 1E) show that these burrowing motions unpack and locally fluidize the substrate proximate to E. directus (Fig. 7). The void fraction at incipient fluidization for the substrate was assumed to be ≈0.41, which is consistent with the level measured by Wen and Yu for substrate particles of similar size, shape and density (Wen and Yu, 1966). Table 1 reports the horizontal displacement functions that were fit to the horizontal displacement PIV data to calculate changes in void fraction and the location of the fluidized zone. These functions were used to extrapolate data (gray dotted lines in Fig. 7) for the shadow regions between the animal's body and the cropped video frames (Fig. 4A).

As E. directus contracts its valves, it reduces the level of stress acting between the valves and the surrounding soil. At some stress level, the imbalance between horizontal and vertical stress causes the soil adjacent to the animal to fail. Continued valve contraction draws pore water towards the animal, which mixes with the failed soil to create a region of localized fluidization.

The stress state in soil at equilibrium and failure can be represented as Mohr's circles (Hibbeler, 2000) on a normal versus shear stress plot (Fig. 8). Failure occurs when the internal shear stress equals the shear strength. Graphically, this is represented when circle b in Fig. 8 is tangent to the failure envelope formed by the soil's friction angle, φ. The stress state shown in Fig. 8 relates to a cohesionless soil; for a cohesive soil, the same failure analysis can be used, but the failure envelope will be shifted vertically by half the soil's cohesive strength.

When E. directus first starts to contract its valves, it brings the soil to a state of active failure (Terzaghi et al., 1996). At this point the soil will tend to naturally landslide downward at a failure angle, θ_f, illustrated by inset b in Fig. 8. The failure angle is the transformation angle between the principal stress state and the stress state at the tangency point between the circle and failure envelope. This angle can also be seen in Fig. 8 by connecting the tangency point on the failure envelope, the horizontal failure effective stress, , and the principal stress axis, and is given by θ_f=(π/4)+(φ/2). Effective stresses, indicted with a prime, represent the actual stress between soil particles, neglecting hydrostatic pressure of the pore fluid.

We observed that valve uplift and contraction occur on a smaller time scale than that required to form a landslide failure wedge in the substrate around burrowing E. directus (Fig. 6B–D). This gives the animal time to move through the fluidized soil before it collapses. The calculated failure angle in the visualizer substrate, determined via the friction angle (measured as 25 deg for 1 mm soda-lime glass beads), aligns with the failure wedge angle observed in the PIV data (Fig. 6D).

Although bulk landslide movement of the soil does not occur when E. directus initiates valve contraction, the resulting imbalance in stresses brings the soil to a state of failure, creating a failure surface at angle θ_f. The existence of this failure surface is crucial because it creates a discontinuity in the substrate surrounding E. directus, where the soil particles within are free to move and the soil particles beyond remain stationary. As E. directus contracts its valves, it reduces its own body volume; this change in volume must be compensated by pore fluid drawn into the failure zone. Increasing the pore fluid while retaining the same number of particles within the failure surface results in a net increase in void fraction, creating a fluidized zone around E. directus.

This analysis yields time scales of 0.075 s for 1 mm soda-lime glass beads in water. These time scales are considerably less than the ∼0.2 s valve contraction time measured by Trueman (Trueman, 1967) and the contraction time of 1.46±0.58 s (mean ± s.d.) measured in our tests. Furthermore, 1 mm particles represent an upper bound for E. directus habitat; the time scale mismatch is even greater for smaller substrate particles. As such, soil particles surrounding E. directus can be considered inertia-less and are advected with the pore fluid during valve contraction.

The presence of a failure surface breaks the coupling between particles and pore fluid movement; particles within the failure wedge can freely move and fluidize, whereas particles outside remain static. Without the wedge, an initially uniform particle distribution would remain uniform as substrate particles follow the pore fluid flow, which is incompressible and governed by ∇·v=0. No divergence in the flow field implies no divergence between particles, and thus no unpacking.

Combining Eqns 5–8 enables us to compute the settling velocity, and thus the required bulk upward fluid flow velocity, at the incipient fluidization void fraction. The fluidization velocity at φ′=0.41 for 1 mm soda-lime glass beads is 1.35 cm s^–1. The uplift velocity of E. directus measured by Trueman is 1.25 cm s^–1 (Trueman, 1967). The peak uplift velocity during the uplift stroke (shown by segment C on Fig. 5A) measured in our experiments where there was a clearly distinguishable upward jerk before valve penetration was 1.30±0.89 cm s^–1 (mean ± s.d., N=18). This means that the uplift motion of E. directus induces a velocity in the pore fluid on the order of the velocity required to fluidize the substrate below the animal. Furthermore, 1 mm is near the upper bound of particle size in E. directus habitat; using the same uplift velocity, E. directus can easily fluidize smaller particles. For example, spherical 0.5 mm soda-lime glass beads will reach φ′=0.41 at an upward flow velocity of 0.5 cm s^–1.

To evaluate Eqn 12, the effective viscosity of the liquid and particle mixture, μ_eff, must be determined. Fig. 9A juxtaposes the pulling capabilities of E. directus in static substrates, determined through tests with the blunt body in Fig. 2, and drag forces calculated with Eqn 12 using the effective viscosity models in Table 2, which depend on void fraction at incipient fluidization.

As the void fraction at incipient fluidization in E. directus habitat was not known, we estimated φ′ to be 0.399, which is the average of the expressions in Eqn 5 with round particles. Variation in burrow radius corresponds to the zone in Fig. 7 where the mean plus one standard deviation in void fraction is above the incipient fluidization threshold (1<r/R_E<3). The fluidized void fraction was taken to be the largest mean value in Fig. 7, φ′=0.411. The radius used for the animal was R_E=1.6 cm. Maximum downwards velocity (10 cm s^–1) and pulling force of the animal (10 N) were measured by Trueman (Trueman, 1967). Although E. directus is too weak to move through static soil, the data shown in Fig. 9A demonstrate that moving through fluidized soil lowers drag forces to within the animal's strength capability.

Data adapted from Trueman's measurements of burrowing E. directus (Trueman, 1967) compared with the blunt body energetics calculated from force data shown in Fig. 9A show that moving through fluidized, rather than static, soil reduces the amount of energy E. directus has to expend to reach full burrow depth by an order of magnitude (Fig. 10). In an idealized fluidized medium, the drag force on a body does not depend on depth. Moving through a packed, static particulate medium, as in the case of the blunt body, requires pushing force that increases linearly with depth (Robertson and Campanella, 1983). As a result, burrowing energy, calculated by E=∫Fdz, scales linearly with depth for E. directus, rather than with depth squared for the blunt body.

The authors thank C. Becker, M. Bollini, D. Dorsch, J. Kao, K. Ray and D. Sargent for their experimental and analytical assistance.