Hydrodynamic Function of Cilia in Living Creatures

Transcription

1 Journal of JSEM, Vol.9, Special Issue (2009) Copyright C 2009 JSEM Hydrodynamic Function of Cilia in Living Creatures Seiichi SUDO 1, Nao MATSUI 1, Katsuya SEKINE 1, Mikiko SHIMIZU 1, Tetsuya YANO 1 and Shigenari SHIDA 2 1 Faculty of Systems Science and Technology, Akita Prefectural University, Yurihonjo , Japan 2 College of Science and Engineering, Iwaki Meisei University, Iwaki , Japan (Received 27January 2009; received in revised form 3 June 2009; accepted 4 July 2009) Abstract This paper describes the hydrodynamic function of minute hairs of living creatures. Many living creatures have minute hairs on their bodies. The swimming analysis of small aquatic creatures and the sinking analysis of dandelion seed were performed using a digital high speed video camera system. Microscopic observation of swimming legs of small aquatic creatures and pappus of dandelion seed was conducted using a scanning electron microscope. Flow visualization around a opossum shrimp was conducted by slow shutter photographic technique. The role of minute hairs for hydrodynamic drag generation was revealed through these analyses. Key words Hydrodynamics, Locomotive Organ, Drag Force, Swimming, Planktons, Dandelion Pappus 1. Introduction A wide variety of living creatures live on this planet. An astounding number of micro organisms, fungi, plants, and animals now live on the planet. Life appeared around 3.5 billion years ago. Throughout its history, Earth has undergone continuous change. On the other hand, mechanical engineering has been developing in combination with other fields. Especially, biotechnology and bioengineering have been developing by analyzing and utilizing a variety of functions of organism. Therefore, extensive investigations on the locomotion of a great many animals have been conducted [1-4], and extensive investigations on the mechanical designs and the structures of a great many plants have been conducted by a number of researchers [5-8]. In general, small aquatic creatures swim by using their swimming legs as underwater paddles to produce thrust. These swimming legs are modified to form a rowing apparatus by the addition of swimming hairs. In our previous paper, the swimming behavior of small shrimplike creature and small planktonic copepods was analyzed by a digital high speed video camera system [9]. The swimming characteristics of small aquatic creatures were revealed by the swimming analysis. During the power stroke, their legs beat and are fully extended, with the swimming hairs automatically spread and the flat surface turned perpendicular to the direction of movement. Swimming hairs play an important role to produce thrust. Jiang et al. studied theoretically the three-dimensional flow field around a free-swimming copepod in steady motion [10]. Their study was based on coupling the Navier-Stokes equations with the dynamic equations for an idealized body of a copepod. They performed three-dimensional, numerical simulations of the flow field around a freely swimming model-copepod using a finite-volume code [11]. They also calculated the deformation of the active space surrounding an alga entrained within the flow field around a freely swimming copepod [12]. Malkiel et al. tried to measure the three-dimensional trajectory of a free-swimming freshwater copepod and the instantaneous 3-D velocity field around this copepod using the digital in-line holography technique [13]. Roast et al. reported a sensitive laboratory technique, using an annular flume, to determine the effects of an organophosphate pesticide on the swimming behavior of Neomysis integer [14]. However, no study has been published on the details of real motions of swimming organ of small aquatic creatures. On the other hand, there are also much thin hairs in flower seeds. In dandelions, the flower head matures into a spherical clock containing many seeds. Each seed is attached to a pappus of fine hairs. Dandelion seeds are carried far and wide by the wind. This paper is concerned with the locomotive organ of small aquatic creatures and flower seeds with pappus. Opossum shrimps have 8 pairs of thoracic legs, most of which have natatory exopodites. Copepods have the swimming thoracic legs. Their swimming legs are clothed in minute hair [9]. The pappus of dandelion seed consists of many thin hairs. These hairs play an important role as the locomotive organ. This paper is the first step study for the purpose of clarifying the whole aspect of the role of biological cilia of these living creatures. The hydrodynamic functions of cilia in these living creatures are studied experimentally. The role of biological cilia of living creatures was revealed experimentally. It was found that minute hairs of living creatures were the advantageous organ for generation of hydrodynamic drag. 2. Experimental Apparatus and Procedures In this report, the experiments for swimming of small aquatic creatures and sinking of dandelion seeds were conducted. For the purpose of the investigation on the morphological structure of swimming legs of small aquatic creatures and the pappus of dandelion seed, microscopic observations were conducted with a scanning electron microscope (HITACHI S-800). 2.1 Experiment of sinking of dandelion seeds The experiment on sinking behavior of dandelion seeds was conducted by use of a high speed video camera system. A -145-

2 S. SUDO, N. MATSUI, K. SEKINE, M. SHIMIZU, T. YANO and S. SHIDA Fig. 1 Block diagram of experimental apparatus Fig. 2 Block diagram of experimental apparatus block diagram of the experimental apparatus is shown in Fig.1. The experimental system is composed of a high speed video camera, a control unit, a video cassette recorder, a video monitor, and a personal computer. A series of frames of free sinking behavior of the dandelion seed are analyzed by the personal computer. The test dandelion seeds were collected in the field at Yurihonjo in Japan. 2.2 Experiment of swimming of aquatic creatures A schematic diagram of the experimental apparatus to study swimming characteristics of small aquatic creatures is shown in Fig.2. The experimental apparatus consists of the water container system and the optical measurement system. Swimming behavior of two kinds of aquatic creatures was examined. Test aquatic creatures were opossum shrimps and planktonic copepods. The container was filled with sea water for opossum shrimp swimming, and with fresh water for copepod swimming. The small aquatic creatures were released in the water container. Free swimming behavior of the small aquatic creature was observed optically with the high speed video camera. A series of frames of free swimming behavior of small aquatic creatures were analyzed by the personal computer. In the experiment of tethered swimming analyses, a live small aquatic creature was pasted up on human hair with the adhesive. The motion of the swimming legs of small aquatic creatures was recorded by the high speed video camera. A series of frames of the leg motion during swimming behavior of aquatic creatures were analyzed by the personal computer. The experiments were performed under the condition of the room temperature in summer of 2007 (water temperature ). 3. Experimental Results and Discussion 3.1 Seed sinking of dandelion The sinking velocity of dandelion seed was measured with the high speed video camera system. The force of gravity acting on extremely small creature body does not prevent them from floating easily in turbulent air or water, using the drag force. In seed sinking experiment, the movie for analysis was chosen from many records, because the Fig. 3 Sinking behavior of dandelion seed measurement x-z plane and the optical focus had to be secured. Figure 3 shows sinking behavior of the dandelion seed. In this experiment, the seed was dropped in the side of pappus. The achene is rotating centering on the pappus in the beginning of descent. Then, the seed sifts to the stable sinking. Figure 4 shows the descent trajectory of the achene tip in the x-z plane. This trajectory curve shows attenuation vibration. Vibration is decreased in short time. Figure 5 shows the variation of the sinking rate in the z-axis. At first, the sinking rate U increases rapidly, and the sinking rate shows a peak near z = 0.03 m. After a peak period, it decreases rapidly to z = 0.05 m. The sinking rate is gradually stabilized in the range of z > 0.05 m. This stabilization is pappus effect. Figure 6 shows the photograph of the pappus of a dandelion seed. The pappus consists of many thin hairs

3 Journal of JSEM, Vol.9, Special Issue (2009) 0 Dandelion Taraxacum officinale Weber z [m] x [m] Fig. 4 Sinking trajectory of achene tip Fig. 6 Photograph of dandelion pappus 1.0 Dandelion Taraxacum officinale Weber 0.8 U [m/s] z [m] Fig. 5 Variation of the sinking rate of seed Fig. 7 Scanning electron micrograph of cross section of fine hair Rigid hairs spread out radially, and they are mm long. There are about 180 bristles. The seed-like fruits, with their attached bristles, are carried far and wide by the wind. The pappus of dandelion seed functions as a parachute and causes the relatively low falling velocity. In general, the drag coefficient of a circular cylinder in an uniform flow are given by Eq.(1) as a function of the Reynolds number [1]. C d 10.9 Re (0.87 log Re) (1) where Re is the Reynolds number based on the diameter of the cylinder. In dandelion pappus, the drag increases with the decrease of the Reynolds number. The drag increases with the total length of each hair. The seeds of dandelion can be suspended in the air by the larger drag. It is the reason that dandelion seeds have much fine hairs. Fig. 8 Scanning electron micrograph of tip of fine hair -147-

4 S. SUDO, N. MATSUI, K. SEKINE, M. SHIMIZU, T. YANO and S. SHIDA t=0.00 ms t=14.96 ms t=3.74 ms t=18.70 ms Fig. 10 Trajectories of each points of opossum shrimp body t=7.48 ms t=22.44 ms t=11.22 ms t=26.18 ms Fig. 9 Swimming behavior of an opossum shrimp Figure 7 shows scanning electron micrograph of cross section of fine hair in dandelion pappus. Each fine hair is composed of some finer tubes. The lighter structure of dandelion pappus results from these hollow tubes. The fine hair composed of many tubes brings higher strength in pappus structure of dandelion seeds. Figure 8 shows also scanning electron micrograph of the tip of the fine hair. The number of fine tubes is decreased in comparison with the root of fine hair. The diameter of one tube of fine hairs is about 6 m in Figure 8. The Reynolds number of the flow around the pappus tip in a sinking seed is described as follows; Ul Ul Re 0.12 (2) where is the density, is the dynamic viscosity, l is the characteristic length, and is the kinematic viscosity. This Reynolds number in sinking of dandelion seed leads to the larger drag coefficient C d 51 in Eq. (1). 3.2 Swimming of opossum shrimp Opossum shrimps are a group of the Mysidacea. The Mysidacea have a worldwide distribution, the majority of species inhabiting coastal and open sea water. Figure 9 shows a sequence of photographs showing the free swimming behavior of opossum shrimp. The process of leg movement for the opossum shrimp swimming is clear. The right- and left-legs beat almost synchronously. During the power stroke they are stretched and move. Figure 10 Fig. 11 Scanning electron micrograph of the swimming legs of the opossum shrimp shows the trajectories of some points (right- and left tips, head, and tail) of the opossum shrimp. The orbits at the tip of the leg draw the character e. The thrust-generating mechanism is related to the motion of the right- and leftlegs. Figure 11 shows the scanning electron micrograph of the rowing legs of opossum shrimp. It can be seen the detail of the rowing appendages, i.e. fine hairs. Figure 12 shows one scene of a high-speed movie during the leg rowing of the opossum shrimp. Many fine hairs on the swimming legs of opossum shrimp are opened during the power stroke. Swimming hairs are observed inside two circles in Fig. 12(a). Swimming hairs are opened right-angled to the movement direction of legs as shown in Fig. 12(b). These leg movements produce the water flow which goes back. Figure 13 shows the visualization photograph of flow around the tethered opossum shrimp. The exposure time of the photograph in Fig. 13 is 1/15 s. The swimming legs press backwards against the water, which pushes the -148-

5 Journal of JSEM, Vol.9, Special Issue (2009) v mm/s (a) high-speed photograph t ms Fig. 14 Velocity variation of a swimming leg of opossum shrimp (b) rough sketch of swimming legs Fig. 12 Swimming motion of legs t=0.00 ms t=6.66 ms t=2.22 ms t=8.88 ms Fig. 13 Flow visualization around the opossum shrimp opossum shrimp forwards. These fine hairs show a higher drag coefficient in the lower Reynolds number flow. Figure 14 shows the velocity variation of a swimming leg through the cruise swimming of the opossum shrimp. The opossum shrimp swims by rowing swimming legs which fringed with many fine hairs as shown in Figure 11. In general, thrust of an opossum shrimp arises from the drag which resists the motion of the swimming legs. The swimming legs of opossum shrimps oscillate. The thickness of thin hair is about 1.2 m, and the velocity at the leg tip is about 0.24 m/s in cruising swimming of the opossum shrimp. Therefore, the maximum Reynolds number of the flow around fine hairs is described as follows; vmaxl Re max 0.29 (3) where v max is the maximum velocity of leg oscillating motion. This value leads also the higher drag coefficient. The steady driving force T D generated by the fluid dynamic drag, which is proportional to the dynamic pressure of the relative speed v-v b, can be expressed in the formula [1]. T D t=4.44 ms t=11.10 ms Fig. 15 The frame sequence of the swimming motion for the copepod 1 ( v vb ) v vb SC (4) d 2 where v b is the opossum shrimp swimming velocity and S is the frontal area. 3.3 Swimming of planktonic copepod Planktonic copepods are small, transparent shrimp-like animals swimming in the water. Most fresh-water species live in shallow water, swimming from plant to plant

6 S. SUDO, N. MATSUI, K. SEKINE, M. SHIMIZU, T. YANO and S. SHIDA (1) The mean terminal sinking velocity of dandelion seeds is about 0.3 m/s. Many fine hairs of dandelion pappus function as a drag generator through sinking of seeds. (2) The right- and left-legs of an opossum shrimp beat almost synchronously during swimming motion. During the power stroke, they are stretched and move. The rowing legs have many hairs for increase of the drag force. (3) The swimming abdominal legs of copepods are formed as shallow caps to increase the hydrodynamic drag and inertial force during the power stroke. Ultra fine hairs are attached to the fine hairs on the swimming legs of copepods. (4) The Reynolds number of the flow around fine hairs of dandelion pappus, opossum shrimp swimming legs, and copepod swimming legs is distributed over the range of In this range of the Reynolds number, the drag coefficient of circular cylinder corresponds to C d Fig. 16 Scanning electron micrograph of the swimming legs of the copepod Copepods exhibit various swimming patterns ranging from continuous to intermittent locomotion. Figure 15 shows a sequence of photographs showing the free swimming behavior by the swimming legs. It can be seen from Fig. 15 that the swimming abdominal legs are formed as shallow caps to increase the hydrodynamic drag and inertial force during the power stroke. In the swimming legs of copepods, many fine hairs were observed in the same manner as opossum shrimp legs. Figure 16 shows scanning electron micrograph of swimming legs of the copepod. In Fig. 16, the thickness of fine hair of swimming legs is about 2.5 m. In this case, ultra fine hairs are attached to the fine hairs. Such morphology of swimming legs leads to the higher value of drag coefficient. Yen & Strickler [15] reported that the Reynolds number of the feeding current of copepods is less than 1. The Reynolds number of swimming by copepods is around The Reynolds number of escaping is around In our experiment as shown in Fig.15, the Reynolds number of the flow around fine hairs is Re The swimming leg structure constituted by fine hairs can produce the higher drag for thrust of copepods. Copepods have evolved to be just the right size ( mm long) and speed to utilize the physical structure of water at this interface for their advantage [15]. 4. Conclusions This paper is the first step study for the purpose of clarifying the whole aspect of the role of biological cilia of living creatures. For this purpose, the sinking of dandelion seed and the swimming of small aquatic creatures were observed by the high speed video camera. The results obtained are summarized as follows: Acknowledgements This work was financially supported in part by the Grant-in- Aid for Scientific Research (C) (No ) from the Ministry of Education, Science and Culture, Japan. References [1] Azuma, A.: The Biokinetics of Flying and Swimming, Springer-Verlag, Tokyo (1992), [2] Alexander, R.M.: The Quarterly Review of Biology, 58 (1983), [3] Ellington, C.P.: Amer. Zool., 24 (1984), [4] Maxworthy, T.: Ann. Rev. Fluid Mech., 13 (1987), [5] King, M.J. and Vincent, J.V.: Proc. R. Soc. Lond. B, 263 (1996), [6] Gibson, L.J., Ashby, M.F., and Easterling, K.E.: J. Mater. Sci., 23 (1998), [7] James, K.R., Haritos, N., and Ades, P.K.,: American J. Botany, 93 (2006), [8] Mix, M.C., Farber, P., and King, K.I.: Biology: The Network of Life, Harper Collins Publishers, New York (1992), [9] Sudo, S., Sekine, K., Shimizu, M., Shida, S., Yano, T., and Tanaka, Y.: J. Biomech. Sci. Eng., 4 (2009), [10] Jiang, H., Osborn, T.R., and Meneveau, C.: J. Plankton Res., 24 (2002), [11] Jiang, H., Meneveau, C., and Osborn, T.R.: J. Plankton Res., 24 (2002), [12] Jiang, H., Osborn, T.R., and Meneveau, C.: J. Plankton Res., 24 (2002), [13] Malkiel, E., Sheng, J., Katz, J., and Strickler, J.R.: J. Exp. Biol., 206 (2003), [14] Roast, S.D., Widdows, J., Jones, M.B.: Aquatic Toxicology, 47 (2000), [15] Yen, J. and Strickler, J.R.: Invertebrate Biology, 115 (1996),