Fisher ABSTRACT Balanomorph barnacles use their cirral net as a sieve to strain food from sea water. Previous investigations have documented activity of the barnacle cirral net, but no study has examined the relationship between barnacle body mass and cirral net size. This study explores this relation¬ ship, employing a hydromechanical approach. I found that smaller barnacles have cirral nets with greater area relative to their body mass. An exami¬ nation of flow through the cirral net shows that this disproportionate area allows flow rates through the net, relative to body size, comparable to those of larger barnacles. In increasing current speeds, barnacles minimize drag of the extended cirral net primarily through vertically withdrawing their cirri. Barnacles do not turn their net edge on to the flow to dodge drag, as earlier reported. Fisher INTRODUCTION While many investigators have examined the feeding activity of the barnacle cirral net (Anderson, 1978, 1980; Barnes and Reese, 1959; Crisp and Southward, 1961; Southward 1955a, 1955b; Southward and Crisp, 1965; Stone and Barnes, 1973), no one has examined the relationship between cirral net area and barnacle body mass. Furthermore, little work has been directed toward investigating the hydromechanics of the cirral net (Johnson, 1982). In this study I attempt to quantify the relationship between cirral net and barnacle size, and to explain this relation through hydromechanics. This effort was quite amenable to laboratory study because of the detailed information available on cirral morphology (Crisp and Southward, 1961; Darwin, 1854). The cirral net of balanomorphs (acorn barnacles), the filter-like apparatus by which these barnacles sieve sea water for food, consists of six pairs of heavily setaed cirri (Appendix). The anterior three pairs of cirri are short and stout, and do not play a large role in sieving water or forming the cirral net (Crisp and Southward, 1961). The posterior three pairs of cirri are thin and elongate, and they form the main cirral net area. Each of these posterior cirri branches at its proximal end into two equally sized, heavily setaed rami. Consequently, a balanomorph cirral net resembles a twelve-fingered hand, forming a concave, arched structure when extended. This twelve-fingered hand achieves its maximal area during extension, as defined by Crisp and Southward (1961). In extension, the barnacle holds its cirri outside the shell for varying periods without rhythmic beating movements. One might assume cirral net area is directly proportional to barnacle mass. If this were true, however, the cirral net of the smaller mass Fisher barnacles would approach such tiny dimensions that it would appear impos¬ sible to sieve water through the minute apertures formed by setae between rami. Logically, smaller barnacles should have cirral nets with greater area relative to their body mass to facilitate flow rates, relative to body mass, equal to those of larger barnacles. A hydromechanical approach is needed to examine such an issue. I sought the answers to three questions: 1. Do smaller mass barnacles have cirral nets with greater area relative to body size? 2. If smaller barnacles have disproportionately larger cirral nets, is this to permit flow rates, relative to barnacle mass, equal to those of larger barnacles? 3. How do barnacles minimize drag in the extended cirral net position? METHODS I. The relation between cirral area and barnacle mass. I collected 20 barnacles from among the species Tetraclita rubescens (13 barnacles), Balanus glandula (5 barnacles), and Balanus nubilus (2 barnacles) on the periphery of the Great Tide Pool, Pacific Grove. After giving the animals a twenty-four hour recovery period, I placed eachbarnacle in a flow tank (Fig. 1), as described by Vogel and LaBarbera (1978). I increased sea water speed in the tank until cirral net extension occurred. I then photographed a posterior view of the extended cirri through amirror placed behind the barnacle at a 45° angle to flow. Portions of the flow tank's trough walls were covered to prevent any shading response caused by a reduction in the amount of light falling on the barnacle. Water temperature remained fairly constant at 14.2° + 0.3°C throughout this procedure. I measured cirral net Fisher area from sketches of enlarged film negatives, using an Apple II digitizer. Cirral net area was defined as frontal area, the maximum projection of the cirri on a plane normal to the flow. Upon completeing area measurements, I recorded the wet tissue mass of each barnacle without shell. II. The relation between cirral area and mainstream speed. Using B. nubilus, I measured cirral net area, maximal cirral height, and maximal net width at various mainstream speeds. Height and width, like area, were measured in a plane normal to flow. I later made morphological measurements of distance between setae extending from the rami, and determined a mean for the number of setae per cirrus. III. Drag on the cirral net. The fluid-mechanical force on the cirral net, drag, was examined using a model (Fig. 2). I mounted the model upside¬ down on a force transducer (Fig. 3), and manipulated the cirral net into various configurations. Velocities were adjusted so that the Reynolds number, a dimensionless index of fluid motion relative to an object, was the same as that for actual barnacles. Reynolds number values (Re = 1U/2/ where I is characteristic length, U fluid speed, and/ kinematic viscosity) ranged from approximately 5,000 to 40,000. Knowing that equality of Reynolds number implies equality of drag coefficient (Vogel, 1981), I examined in three separate experiments the effects of mainstream speed, spacing between rami. and orientation of the net relative to flow. I held all other variables constant during each of these tests. RESULTS The area of the cirral net / body mass is greater for smaller barnacles (Fig. 4). Area per mass increases rapidly with decreased barnacle mass such that smaller barnacles (20.40 g) have much greater cirral areas for their Fisher body size. Cirral net area changes, however, with mainstream speed. Net area for the test barnacle increases to a maximum at 26 cm/s andthen decreases at higher speeds (Fig. 5). Width and height, the components of area, follow similar trends (Fig. 6), although height decreases more markedly at higher speeds. No substantial change occurs in the angle at which the barnacle extends its net relative to a plane normal to the flow as mainstream speed increases; that is, no substantial bending of the net backward or sideways occurs. Drag on the cirral net is proportional to the square of mainstream speed (Fig. 7). This result agrees with the theoretical prediction (Vogel, 1981) that D - 2 CpPSU where D is drag, Cp the drag coefficient, o density of sea water, S area, and U speed. Constancy of drag coefficient as a function of Reynolds number (Fig. 8) supports this relationship. Drag does not differ significantly with ramal spacing (Table 1). Drag does vary with orientation of the cirral net relative to flow (Fig. 9). Forces reach a maximum with the cirral net in its normal position, perpendicular to the current (0°), and achieve a minimum with the net edge on to the flow (90°), Further calculations can estimate the relative volume flow rate--the volume of water passing through the barnacle's sieve per time--as a function of mainstream speed. For a singular circular aperture, reasonably far from other apertures and at a Reynolds number less than 3. 9 a3AP 3 where Q is volume flow rate, a the radius of the aperture, Ap the change in pressure across the aperture, andthe dynamic viscosity of sea water (Vogel, Fisher 1981). Although the aperture formed by 2 setae and 2 cirri is rectangular, I assume that this formula can still yield a reasonable estimate of relative volume flow rate for a setal aperture, differing at most by a constant. Thus, relative volume flow rate is 9 k dAp A where k is a constant and d is one-half the distance between setae. Distance between setae for an average B. nubilus is 0.0074 mm, and half this distance can be assumed d. A knowledge of the number of setal apertures extended into the mainstream at different speeds gives an estimate of the total relative volume flow rate for the entire cirral net. A graph of relative volume flow rate for B. nubilus appears in Fig. 10. Volume flow rate increases with speed, but the rate of increase reaches a maximum near 45 cm/s and gradually decreases at higher mainstream speeds. One can also formulate a theoretical relationship for relative volume flow rate per cirral area as a function of mass, at a fixed mainstream speed. I assume that a given increase in mass entails an increase in distance between setae proportional to mass. Although this assumption may not be entirely true (because smaller mass barnacles have larger nets per body size and this hints at larger distances between setae, relative to mass, for these barnacles), it provides a reasonable estimate. Since relative volume flow rate is k d'Ap M and area of the setal aperture is Aed? then for relative volume flow rate per setal aperture area akd, Fisher where k' is a constant. Scaling volume flow rate per setal aperture area to volume flow rate per cirral net area merely increases the constant, as long as the total number of setal apertures remains the same. Such is the case at constant velocity. This theoretical procedure yields the graph in Fig. 11. The rate at which water passes through the cirral net relative to the area ofthe sieve increases in proportion to the cube root of the mass. One may obtain relative volume flow rate for the cirral net per barnacle mass as a function of mass, if the ordinates of the graphs in Figs. 4 and Il are multiplied. This procedure yields a fairly constant volume flow rate per mass as a function of mass (Fig. 12). That is, the rate at which a balanomorph cirral net sieves water relative to barnacle size is roughly constant over barnacle sizes, above a mass of 0.75 g. DISCUSSION The disproportionately larger cirral nets seen in smaller mass barnacles maintain a fairly constant flow rate of water through the sieve relative to body mass. Intuitively this makes sense. If a small barnacle had a cirral net in the same proportion to its mass as that of a large barnacle, areas of setal apertures would be too small to allow a large enough flow rate for the barnacle to survive. The cirral net would almost act as a solid wall, with the cirri and setae all closely spaced. To compensate for this, the smaller barnacles have developed larger cirral nets, with correspondingly larger setal apertures, to permit flow rates per barnacle mass roughly equal to those of their larger barnacle counterparts. Equal flow rates per mass would enable smaller barnacles to sieve water equally well for their body size. This argument, nonetheless, has two problems. It neglects the slight Fisher upward increase of volume flow rate relative to barnacle size for the balanomorphs less than 0.75 g, and it neglects the factor of metabolism. H. Barnes and M. Barnes (1959) report a markedly weight dependent oxygen uptake in barnacles, small barnacles consuming more O, per mass than large barnacles. O, consumption is proportional to body mass"1/3. Fig. 12 can therefore be converted to relative volume flow rate per mass, relative to respiration rate, as a function of barnacle mass (Fig. 13). The high values at small mass seen in Fig. 12 decrease strikingly. Only a small upward tail remains. Nevertheless, a difficulty arises. The formerly constant large mass end of the curve is transformed to a positively sloping line. This may not be a problem. Barnes' metabolic analysis deals only with barnacles up to 0.20 g in size. At masses greater than 1.00 g, weight dependent O, uptake may disappear and metabolic rate may remain more constant with barnacle size. If barnacles greater than 1.00 g are assumed to have a fairly constant metabolic rate, then volume flow rate per mass, relative to respiration rate, is constant (Fig. 13). The only portion of the curve remaining to be explained is the now small upward tail at small mass, This upturn may be explained by boundary layer theory. Cirral nets for barnacles less than 0.50 g, despite their disproportionately larger area, are still quite small, approximately 7 to 40 mm’. Consequently, these organisms exist in a boundary layer-a velocity gradient in fluid where speed changes from zero at the surface to free stream velocity slightly higher (Vogel, 1981). Denny et al. (1984) estimate a boundary layer thickness of 0.5 om in wave-caused flows. Barnacles less than 0.50 g may see less than the mainstream speed assumed in calculating volume flow rate because their whole net is very close to their shell surface and the rock surface. If true, then the volume flow rate calculated for barnacles less than 0.50 g Fisher would be slightly higher than the real value. Using a corrected, lower speed in determining flow rates for these barnacles would lower the volume flow rate values. This would then yield constancy in the ordinates of Fig. 13 to demonstrate that smaller mass barnacles have relatively larger cirral net areas to maintain flow rates per barnacle size approximately equal to those of larger barnacles. In B. nubilus net area increases slightly to a maximum as mainstream speed increases, and then area decreases noticeably. This decrease may result as the barnacle tries to take advantage of the faster current, an obvious aid for suspension feeders, while minimizing drag as much as possible. Since drag increases rapidly with mainstream speed (drag is proportional to the square of speed), retraction of the cirral net to decrease area, and thus drag, almost seems a necessity. The mechanism by which barnacles decrease cirral area appears to be retraction of the cirri, rather than decrease of ramal spacing. Changing ramal spacing has no substantial effect on drag because the intrinsic shape of the net does not change much. When ramal spacing changes, setae overlap still remains and the cirral net retains its same overall concave, arched structure. Moreover, greater decreases in height than width of the net at higher speeds indicate height is the area component more responsible for the area change. The barnacle probably withdraws the cirri vertically, and any change in ramal spacing is merely a physical requirement to bring the cirri through the operculum. The barnacles examined here do not, as previously reported (Crisp and Southward, 1961) put their net edge on to the flow to dodge drag. Not once did I observe a barnacle put its net edge on to the flow, although I used mainstream speeds up to 100 cm/s. While putting edge on to flow minimizes Fisher drag, such an action makes no sense metabolically or mechanically. A barnacle with edge on flow cannot sieve water well because the interception area of the net, relative to the current, is near zero. Facing the direction of maximal drag permits maximal water flow across the sieve and thus maximal feeding. Moreover, as Wainwright and Dillon (1969) explain, an orientation parallel to the current is less stable than normal to current, on the basis of torques. Small deviations from an orientation normal to the current produce only small twisting movements, whereas small deviations from the parallel orientation cause much greater twisting movements. CONCLUSION 1. Smaller mass barnacles have cirral nets with greater area relative to their body mass. Smaller barnacles have disproportionately larger cirral nets to permit flow rates, relative to barnacle size, comparable to those of larger barnacles. 3. Barnacles minimize drag of the extended cirral net in increasing current speeds primarily through vertically withdrawing their cirri. Barnacles do not turn their net edge on to the flow to dodge drag, Fisher ACKNOWLEDGEMENT I would like to thank my advisor Mark Denny for his continual help, patience, support, and encouragement throughout my project. Thanks also go to Charles Baxter, William Gilly, Freya Sommer, and everyone else at Hopkins Marine Station during spring 1984. They made my work a pleasure. 12 Fisher LITERATURE CITED Anderson, D. T. 1978. Cirral activity and feeding in the coral-inhabiting barnacle Boscia anglicum. J. Mar. Biol. Assn. U.K. 58:607-26. Anderson, D. T. 1980. Cirral activity and feeding in the verrucomorph barnacles Verruca recta and V. stroemia (0. F. Muller) (Cirripedia). J. Mar. Biol. Assn. U.K. 60:349-66. Barnes, H., and M. Barnes. 1959. Studies on the metabolism of cirripedes, The relation between body weight, oxygen uptake, and species habitat. Veröff. Inst. Meeresforsch Bremerhaven 6:515-23. Barnes, H., and E. S. Reese. 1959. Feeding in the pedunculate cirripede Pollicipes polymerus J. B. Sowerby. Proc. Zool. Soc. London 132:569-85. Crisp, D. J., and A. J. Southward. 1961. Different types of cirral activity of barnacles. Philos. Trans. Roy. Soc. London, Ser. B 243:271-308. Darwin, C. 1854. A Monograph on the Sub-class Cirripedia: Balanidae, Verrucidae, etc. London: Ray Society. Johnson, L. 1982. Hydrodynamic constraints on barnacle feeding. Unpublished ms., University of Washington. Southward, A. J. 1955a. On the behaviour of barnacles. I. The relation of cirral and other activities to temperature. J. Mar. Biol. Assn. U.K. 34:403-22. Southward, A. J. 1955b. On the behaviour of barnacles. II. The influence of habitat and tide-level on cirral activity. J. Mar. Biol. Assn. U.K. 34:423-33. Southward, A. J., and D. J. Crisp. 1965. Activity rhythms of barnacles in relation to respiration and feeding. J. Mar. Biol. Assn. U.K. 45: 161-85. Stone, R. L., and H. S. Barnes. 1973. The general biology of Verruca stroemia (0. F. Muller). I. Geographical and regional distribution; cirral activity and feeding. J. Exp. Mar. Biol. Ecol. 12:167-85. Vogel, s. 1981. Life in Moving Fluids: The Physical Biology of Flow. Boston: Willard Grant Press. Vogel, S., and M. LaBarbera. 1978. Simple flow tanks for research and teaching. Bioscience 28:638-43. Wainwright, S. A., and J. R. Dillon. 1969. On the orientation of sea fans (genus Gorgonia). Biol. Bull. 136:130-9. 13 Fisher TABLE 1. Drag in relation to ramal spacing (with model). Ramal spacing, relative to Drag, N net height 0.05 0.029 0.10 0.028 0.15 0.032 0.20 0.032 1Mainstream speed = 17.3 cm/s. Fisher APPENDIX Balanomorph anatomy C13 C4 C2 Ci5 ooooc (ra Th 6 —G CL Em RS Diagram of a large balanomorph (based on Balanus hameri) to show arrange¬ ments of parts and spaces inside the shell. (Approx. x2.) A, section of shell in carino-rostral plane, with depressor muscles and branchia of one side removed to display prosoma and thorax. The distal segments of the large cirri (4 to 6) are not drawn. B, horizontal section across line B to B; C, section across line C to c. Ad, adductor muscle; Ci I to 6, individual cirri; Em, mass of developing eggs or larvae; G, branchiae; LS, lateral scutal depressor muscle; P. prosoma; KS, rostral scutal depressor muscle; Th, thorax; TD, tergal depressor muscle (from Crisp and Southward, 1961). Fisher FIGURE LEGENDS Figure 1 A small flow tank designed to rest on a laboratory bench. A mid-longitudinal section is shown. The trough, about 250 cm¬ in cross-sectional area, is of quarter-inch plexiglass, and the return circuit of polyvinyl chloride pipe. Two arrays of drinking straws, fixed with silicon sealant in removable plastic frames, serve as upstream collimators. The entire assembly is supported by the two wooden beams shown under the trough. Arrows give the direction of flow. c, collimator; d, drain; f, fairing plate; p, propellor; r, return circuit; s, screen; t, trough. Figure 2 Diagram of the model cirral net. The cirri and rami are made from flexible pipe cleaners, to allow rearrangement of configu¬ ration, and the setae are made from narrow gauge wire. Cirral diameter at the net base is twice ramal diameter. Ramal setae lengths run from 2.5x to lx ramal diameter. Typical net dimensions are 7 cmx 11 cm. The model is attached to a plexi¬ glass plate, dimensions 7.05 cmx 5.35 cmx 0.30 cm, which mounts on the drag transducer. Figure 3 Drag transducer. The model attaches upside-down on the dowel, A. A force on the cirral net stretches the spring-like mechanism, B. Movement of 6 then withdraws the core of a linearly variable differential transformer, C, to register a voltage change. This change is linearly proportional (correlation coefficient for line - 1.00) to change in force, and thus can be easily converted to drag. Figure 4 Area of the cirral net per barnacle body mass as a function of body mass in Tetraclita rubescens, Balanus glandula, and Balanus nubilus. Figure 5 Relative area of the cirral net in the test barnacle B. nubilus as a function of mainstream speed. Relative area of 1.00 corresponds to 231.9 mm2. All standarderrors for relative area are less than 0.034. Figure 6 Relative maximal width and height in the test barnacle B. nubilus. Relative width of 1.00 corresponds to 23.6 mm, and relative height of 1.00 corresponds to 17.2 mm. All standard errors for relative length are less than 0.027. Figure 7 Drag as a function of mainstream speed for the model. Points fit the function D = 1.26 u2:33, where D is drag and U is speed, in standard units. For (log U, log D), correlation coefficient - 0.96. Flags denote standard errors. Figure 8 Drag coefficient as a function of Reynolds number for the model. Fisher Drag as a function of orientation relative to flow for the Figure 9 model. 0° is when the cirral net is normal to flow, and 90° is when the net edge is on to the flow. Mainstream speed - 54.2 cm/s. Flags denote standard errors. Figure 10 Relative volume flow rate in B. nubilus as a function of mainstream speed. Figure 11 A theoretical calculation of relative volume flow rate per cirral net area as a function of barnacle mass. Figure 12 Relative volume flow rate per barnacle mass as a function of barnacle mass. Ordinate values are the product of ordinates in Figs. 4 and 11. 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