The biomimetic flow at different scales has been discussed at length. The need of looking into the biological surfaces and morphologies and both geometrical and physical similarities to imitate the technological products and processes has been emphasized. The complex fluid flow and heat transfer problems, the fluid-interface and the physics involved at multiscale and macro-, meso-, micro- and nano-scales have been discussed. The flow and heat transfer simulation is done by various CFD solvers including Navier-Stokes and energy equations, lattice Boltzmann method and molecular dynamics method. Combined continuum-molecular dynamics method is also reviewed.

Introduction

Human knowledge is getting enriched from the four billion years' worth of R & D in the natural world of plants and animals and other lower level living creatures and microorganisms, which have evolved through the ages to nicely adapt to the environment. Man has now drawn his attention to soil creatures like earthworms, dung beetle, sea animals like shark and plants and trees like lotus leaf and pastes like termites. In the nature, we see examples of effortless and efficient non-sticking movement in mud or moist soil, high-speed swimming aided by built-in drag-reduction mechanism, water repellant contaminant-free surface cleaning mechanism and natural ventilation and air conditioning, [1–8]. By nature, feather of the penguin shows staying warm naturally, Figure 1 [4]. The leaf of the lotus is hydrophobic to the extent that water running across the surface of the leaf retains particles of dirt caused by a thick layer of wax on the surface and the sculpture of that surface, Figure 2 [9–11]. This forces the droplets of water to remain more or less spherical when in contact with the leaf, and reduces the tendency of other contaminants to stick to the leaf. It has been proved that water repellency causes an almost complete surface purification (self-cleaning effect): contaminating particles are picked up by water droplets or they adhere to the surface of the droplets and are then removed with the droplets as they roll off the leaves. This characteristic has been utilized in exterior-quality paint, 'Lotusan', which makes surfaces self-cleaning. Hooks occur in nature as a vast array of designs and in a diversity of animals and plants. The commercial application of this technology of 'Nature' can be found in Velcro [5] having the cheapest and most reliable bur hook-substrate combination. There are now thousands of patents quoting Velcro. This is how the subject of biomimetics has developed. Biomimetics is the application and abstraction of biological methods, systems and good designs found in nature to the study and design of efficient and sustainable engineering systems and modern technology. The transfer of technology between lifeforms and manufactures is desirable because evolutionary pressure typically forces living organisms, including fauna and flora, to become highly optimized and efficient. Generally there are three areas in biology after which technological solutions can be modelled.

Replicating natural manufacturing methods as in the production of chemical compounds by plants and animals.

Mimicking mechanisms found in nature such as Velcro and Gecko tape.

Imitating organizational principles from social behaviour of organisms like ants, bees and microorganisms.

Russia has developed a systematic means for integrating the natural knowledge into humankind's technology using 'Teoriya Resheniya Izobretatelskikh Zadatch (TRIZ)', i.e. the theory of inventive problem solving, which provides an objective framework based on functionality for accessing solutions from other technologies and sciences. TRIZ also prevents waste of time trying to find a solution where none exists. The four main tools of TRIZ are a knowledge database arranged by function, analysis of the technical barriers to progress (contradictions), the way technology develops (ideality) and the maximization of resource usage. The biology-based technology 'Biomimetics' suggests new approaches resulting in patents and some into production:

Extrusion technology based on the spinneret of the spider [3],

Self-cleaning surfaces based on the surface of the lotus leaf [17].

The importance of Biomimetics will increase as the incidence of genetic manipulation increases and the genetic manufacturing is developed. In the result, the area between living and non-living materials, where biology interacts with engineering, e.g. bioengineering and biomechatronics, is benefited.

There are innumerable examples of interactions with the environment and balanced and efficient heat, mass, momentum and species transfer through the microstructures in the fluid flow in the manifested living world of plants, animals and other living creatures. Biomimetics involve mimicking these interactions across the functional surfaces with the surrounding environments in the technological design. The physical nature is numerically modelled and simulated using computational fluid dynamics (CFD).

Geometrical analogy as well as physical similarity is to be studied to design technological functional surfaces imitating microstructural and biological functional surface morphologies. CFD at micro- or meso-scales and other numerical methodologies are necessary for this [18–24].

The meso- and micro-scale methods are also being developed in parallel with the continuum theory-based conventional CFD techniques-using finite volume method (FVM) and finite element method (FEM). In the mesoscopic lattice Boltzmann method (LBM), fluid flow is simulated by tracking the development of distribution functions of assemblies of molecules. It is difficult to capture the interfacial dynamics, which is essential for multiphase flow, at the macroscopic level. LBM captures the interaction of fluid particles and is, therefore, helpful for multiphase flow with phase segregation and surface tension. Also, the LBM is computationally more efficient than molecular dynamics (MD) method since it does not track individual molecules; the solution algorithm is explicit, easy to implement and parallel computation can be done. Micro/nano-scale simulations in micro/nano-scale geometries and micro time scales are done in MD method and direct simulation of Monte Carlo (DSMD) method. Coupled macro-scale simulation is being done using high performance computer (HPC). This article makes a review of the advances in multiscale biomimetic fluid flow modelling and simulation of difficult physics problems with complex biological interfaces.

Macroscopic biomimetic flow modelling

The locomotion, power and manoeuvring of aquatic animals like swimming fish having superior and efficient utilization of propulsion through a rhythmic unsteady motion of the body and fin resulting in unsteady flow control has been engineered for the transportation in the underwater vehicles. The fish senses and manipulates large-scale vortices and repositions the vortices through tail motion. The timing of formation and shedding of vortices are important. CFD application by mimicking the swimming of fish and underwater dolphin kicking has been utilized to understand active drag and propulsive net thrust and this has resulted in better sailing performance, Olympic ski jumping, Formula 1 racing, Speedo's new Fastskin FSII swimsuit and an optimal kick profile in swim starts and turns. The undulatory propulsion in aquatic vertebrates is achieved by sending alternating waves down the body towards the tip of the tail and causing sinusoidal oscillation of the body, a jet in the wake and a forward thrust. Two modes of propulsive technique utilized by fish are anguilliform and carangiform, Figure 3 [25]. The carangiform mode is also termed as 'lunate-tail swimming propulsion'.

The unsteady incompressible Navier-Stokes equations of turbulent flow are solved in the simulation by applying the Reynolds-averaged Navier-Stokes (RANS) equations with usual boundary conditions to obtain the fluctuating velocity fields. The equations in Cartesian tensor form are:

(1)

(2)

(3)

(4)

(5)

(6)

(7)

where x and u are Cartesian coordinates and velocities, respectively, and t is time. Velocity u, density ρ, viscosity μ and other solution variables represent ensemble-averaged (or time-averaged) values. Reynolds stress, is modelled and related to the mean velocity gradients by Boussinesq hypothesis. k is the turbulence kinetic energy, ε the kinetic energy dissipation rate and μ_{t} the turbulent viscosity. C is constant, σ the Prandtl number. G_{k} represents the generation of turbulence kinetic energy due to the mean velocity gradients. μ_{t} is the turbulent viscosity.

The turbulent flow induced by the fish-tail oscillation is characterized by fluctuating velocity fields. The instantaneous governing equations are time averaged to reduce the computational time and complexity which is done in the form of turbulence models like the semi-empirical k-ε work-horse turbulence model for practical engineering flow calculations.

To calculate the flow field using the dynamic mesh, the integral form of the conservation equation for a general scalar φ on an arbitrary control volume V with moving boundary is employed:

(8)

where is the flow velocity vector, is the grid velocity of the moving mesh, Γ is the diffusion coefficient, S_{φ} is the source term of φ and ∂V is the boundary of the control volume V.

The flow is characterized by spatially travelling waves of body bound vorticity. The mix between longitudinal and transverse flow features varies with the phase of oscillation and the unsteady velocity field varies throughout an oscillation cycle. The dynamic pressure distribution contour and the effect of the tail movement on the unsteady flow field of the fish-like body will show that there are high pressure zones at the rear of the body indicating strong vortex and turbulence. The kinematic parameters like Strouhal number, wavelength and oscillating frequency are based on the forward locomotion in a straight line with constant speed in the cruising direction. Figure 4 shows the computational geometric forms of (a) the Robo Tuna, (b) tuna with dorsal/ventral finlets and (c) giant danio [26]. Fish swimming kinematic data shows that the non-dimensional frequencies are close to the value predicted by the instability analysis. Figure 5, from Rohr et al. [27], shows Strouhal number as a function of the Reynolds number for numerous observations of trained dolphins with good agreement between theory and experiment.

Other example of using CFD to study biomimetic fluid flow problems include simulation of air flow around flapping insect wings, numerical simulation of electro-osmotic flow near earthworm surface and simulation of explosive discharge of the bombardier beetle.

Kroger [28] made a CFD simulation study of air flow around flapping insect wings. The interest in the flapping-wing technique [29, 30] is growing recently due to the fact, that the developments in micro-technology permit people to think about building very small and highly manoeuvrable micro-aircraft that could be used for search and rescue missions or to detect harmful substances or pollutants in areas that are not accessible by or too dangerous for humans. There are three basic principles that contribute to unsteady flapping-wing aerodynamics: delayed stall, rotational circulation and wake capture. However, the exact interactions between them are still subject to ongoing research by CFD simulation. Figure 6 shows surface mesh on fly body.

The dynamic mesh CFD model is used to examine critical flight simulations of normal aircraft, like the undercarriage lowering at low air speed, or the movement of sweep wings of fighter jets at high air speed. Next to flight applications, the dynamic mesh model can also simulate moving heart valves in the biomedical area, or small flapping membrane valves in micro-fluidics or the flow around any arbitrary moving part in other industry or sports applications.

The electro-osmotic flow controlled by the Navier-Stokes equations near an earthworm surface has been simulated by Zu and Yan [31] numerically to understand the anti soil adhesion mechanism of earthworm. A lattice Poisson method (LPM), which is a derived form of LBM, has been employed to solve externally applied electric potential φ and charge distributions in the electric double layer along the earthworm surface. The external electric field is obtained by solving a Laplace equation. The simulation [32–35] showed that moving vortices, contributing to the anti soil adhesion, are formed near earthworm body surface by the non-uniform and variational electric force acting as lubricant. Figure 7 shows the electro-osmotic flow field between the surfaces of soil and earthworm.

A biomimetic CFD study [36–39] of the bombardier beetle's explosive discharge apparatus and unique natural 'combustion' technique in its jet-based defence mechanism helps designing a short mass ejection system and a long range of spray ejection pertinent to reigniting a gas turbine aircraft engine which has cut out, when the cold outside air temperature is extremely low. The beetle can eject a hot discharge to around 200 to 300 times the length of its combustor. Figure 8 shows a bombardier beetle (brachina) ejecting its water-steam jet at 100°C forward from the tip of its abdomen (from left to right).

Nanoscale systems such as GaAsMESFETs and SiMOSFETs semiconductor devices, ultra-fast (picoseconds or femtoseconds) pulsed lasers do not conform to the classical Fourier heat diffusion theory in which the mean free path of the energy carriers becomes comparable to or larger than the characteristic length scale of the particle device/system or the time scale of the processes becomes comparable to or smaller than the relaxation time of the energy carriers. Although numerical techniques like Boltzmann transport equation (BTE) or atomic-level simulation (MD) and Monte Carlo simulation (MCS) can capture the physics in this regime, they require large computational resources. The C-V hyperbolic equation, which is not subject to the Fourier law assumption of infinite thermal propagation speed, is also not free from anomalies.

Limitations of continuum description of a system

Finite difference and finite element methods serve well for continuum description of a system governed by a set of differential equations and boundary conditions. However, the problem arises when the system has atomic fabric of matter such as in the case of friction problems and phase-change problems of fluid freezing into a solid or dynamic transition such as intermittent stick-slip motion [40].

The molecular dynamics (MD) method

When a system is modelled on the atomic level such as in case of MD, the motion of individual atoms or molecules is approximated. The particle motion is controlled by interaction potentials and equations of motion. MD is used for systems on the nanometre scale.

Coupling MD-continuum

Coupling two very different descriptions of fluids at MD-continuum interface is a serious issue. The overlapping region of two descriptions must be coupled over space as well as time giving consistent physical quantities like density, momentum and energy and their fluxes must be continuous. Quantities of particles may be averaged locally and temporally to obtain boundary conditions of continuum equations. Getting microscopic quantities from macroscopic non-unique ensembles is, however, difficult.

Coupling schemes

Several coupling schemes [40–44] have been developed and the two solutions relax in a finite overlap region before they are coupled. Equations of motion are the language of particles and these are coupled with the continuum language, i.e. the differential equations. The coupling mechanism transmits mass flux, momentum flux and energy flux across the domain boundary. If the remaining boundaries are sealed, i.e. the simulated system is closed; the coupling ensures conservation of mass, momentum and energy.

The two domains are coupled to each other by ensuring that the flux components normal to the domain boundary match. If particles flow towards the boundary, a corresponding amount of mass, momentum and energy must be fed into the continuum. Conversely, any transport in the vicinity of the boundary on the part of the continuum must provide a boundary condition for transport on the part of the particles.

Figure 9 shows the velocity and temperature profiles observed in a simulation using Lennard-Jones particles and a Navier-Stokes continuum.

Smoothed particle hydrodynamics

Sousa [45] presented a scientific smoothed particle hydrodynamic (SPH) multiphysics simulation tool applicable from macro to nanoscale heat transfer. SPH [45] is a meshless particle based Lagrangian fluid dynamic simulation technique; the fluid flow is represented by a collection of discrete elements or pseudo particles. These particles are initially distributed with a specified density distribution and evolve in time according to the fluid heat, mass, species and momentum conservation equations. Flow properties are determined by an interpolation or smoothing of the nearby particle distribution with the help of a weighting function called the smoothing kernel. SPH is advantageous in (1) tracking problems dealing with multiphysics, (2) handling complex free surface and material interface, (3) parallel computing with relatively simple computer codes, (4) dealing with transient fluid and heat transport.

Following the original approach of Olfe [46] and Modest [47] in case of radiative heat transfer, Sousa [45] made the SPH numerical modelling for the ballistic-diffusive heat conduction equation. In this method, the heat carriers inside the medium are split into two components: ballistic and diffusive. The ballistic component is determined from the prescribed boundary condition and/or nanoscale heat sources and it experiences only outscattering; the transport of the scattered and excited heat carriers inside the medium is treated as diffusive component.

Intrinsic complex issues in hybrid method

The development and optimization of the performance of micro and nano fluidic devices requires numerical modelling of fluid flow inside micro and nanochannels. The nature of the phenomena involved in these devices invariably and predominantly has the interfacial interactions because of high surface-to-volume ratio and is characterized by an inherent multiscale nature [48–62]. The traditional continuum models do not capture the flow physics inside the micro and nano scale systems because they neglect the microscopic mechanisms at these scales. The MD is a microscopic model and this can be used where macroscopic constitutive equations and boundary conditions are inadequate. Figure 10 [48] shows the schematic representation of a molecular region in a hybrid simulation. The MD are well suited for the study of slip generation in the solid-fluid interface and other surface properties like nanoroughness and wettability and the boundary conditions. However, high computational cost restricts the molecular simulations to their applications to nanoscale systems and time scales below microseconds. This disparity of spatial and temporal scales is overcome in the hybrid atomistic-continuum multiscale frameworks where the molecular description models only a small part of the computational domain, since the physics of this part of the system cannot be represented by the continuum model. The boundary condition is transferred accurately and efficiently between the atomistic and continuum description in the hybrid methods. Since the microscopic description requires more degrees of freedom than the macroscopic one, the transfer of macroscopic information on a molecular simulation becomes all the more a challenging task.

MD model and the Maxwell-Boltzmann velocity distribution

The MD atomistic model in the micro-scale framework is a deterministic method. In this model, the evolution of the molecular system is obtained by computing the trajectories of the particles based on the classical molecular model. The continuum conditions can be applied to molecular domain either by the method based on continuous rescaling of atomic velocities or by the periodic resampling method of atomistic velocities that employs velocity distribution functions such as Maxwell-Boltzmann or Chapman-Enskog distribution for non-equilibrium situations of hybrid simulations in dilute gases employing geometrical decomposition and state coupling. The Maxwell-Boltzmann velocity distribution is the natural velocity distribution of an atomic or molecular system in an equilibrium state defining the probability of one-dimensional velocity components of an atom assuming a specific value based on temperature and the atomic mass. The reflective plane placed at the upper boundary of the boundary condition transfer region maintains every particle inside the molecular domain. This scheme is simpler than the velocity reversing scheme, but this can be applied only to incompressible flows because the normal pressure is a result of the reflected atoms.

Rescaling techniques

In the rescaling techniques, in addition to the velocity restrictions, the continuum pressure applies to the atomistic region. The normal pressure is applied through external forces generating a potential energy field. Energy is decreased because of the reduction of potential energy of the atoms moving towards the continuum boundary. The resulting energy oscillations in the molecular system are reduced by velocity reversing of the outermost atoms. This scheme is simple and robust because of uncontrolled transfer of energy. The continuum temperature to the molecular system is accomplished by an energy transfer scheme. The energy is added or removed from the microscopic system to parallel the macroscopic temperature without modifying the mean velocity of the particles. The energy transfer takes place independent of each dimension and is accomplished by the velocity vectors of the atoms [42, 61–68].

Issues related to boundary conditions in hybrid multiscaling modelling

Drikakis and Asproulis [69] applied macroscopic boundary conditions in hybrid multiscale modelling. MD microscopic simulation was employed. They employed the methods for various liquid and gas flows with heat transfer and identified specific parameters for accuracy and efficiency. Their work has shown that knowledge about boundary conditions development and application is needed in multiscale computational frameworks. Continuum temperature and velocity as well as macroscopic pressure constrain molecular domain. Inconsistent pressure can shrink the simulation domain and the particles may drift away generating errors and instabilities in the hybrid procedure. Also, the size of the regions for the application of velocity constrains is important to avoid unrealistic heat transfer across the computational domain and inconsistencies between the molecular and continuum state. Resampling frequency and the termination of the atomistic region have significant impact in the resampling techniques and these can influence trapping of particles in the constrained region and may cause deviations between the macroscopic and microscopic velocities. The domain termination needs correct continuum pressure application.

Challenge in biomimetic flow simulation

The task of imitating biological functional surfaces with variety of complex three-dimensional micro- and nano-structures is very challenging in biomimetic flow simulation. The transfer of biological morphologies of plants and animals by imitating both geometrical and physical similarity to technological applications is to be identified [70–127]. Studies on micro surface structures of different species are to be made by scanning electron microscope (SEM) and atomic force microscope (AFM) to imitate engineering functional surfaces. The mesoscopic LBM has been applied in studying electro-osmotic driving flow within the micro thin liquid layer near an earthworm body surface [128]. The moving vortices give the effect of anti soil adhesion. Few multiphase LBM models are the pseudo-potential model, the free energy model and the index-function model [129–132]. In LBM, effective interaction potential describes the fluid-fluid interaction. Interface is introduced by modelling the Boltzmann collision operator imposing phase separation. Also, the fluid-fluid interactions are represented by a body force term in Boltzmann equation. In this case, second-order terms in the pressure tensor are removed and more realistic interfacial interactions are produced.

Hard spheres fluids, square well fluids and Lennard-Jones fluids are model fluids in MD. The fluid flow and heat transfer in micro-scale and nano-scale systems get microscopic and nanoscopic insight from MD [133].

Conclusions

A comprehensive and state-of-the-art review of CFD techniques for numerical modelling of some biomimetic flows at different scales has been done. Fluid-fluid interfaces contacting with functional solid surfaces have been discussed. The multiphysics modelling at different scales by Navier-Stokes and energy equations, mesoscopic LBM, MD method and combined continuum-MD method with appropriate coupling schemes have been dealt with in detail.

Abbreviations

AFM:

atomic force microscope

BTE:

Boltzmann transport equation

CFD:

computational fluid dynamics

DSMD:

direct simulation of Monte Carlo

FEM:

finite element method

FVM:

finite volume method

HPC:

high performance computer

LBM:

lattice Boltzmann method

LPM:

lattice Poisson method

MCS:

Monte Carlo simulation

MD:

molecular dynamics

RANS:

Reynolds-averaged Navier-Stokes

SEM:

scanning electron microscope

SPH:

smoothed particle hydrodynamic

TRIZ:

Teoriya Resheniya Izobretatelskikh Zadatch.

Declarations

Authors’ Affiliations

(1)

Mechanical Engineering Department, Bengal Engineering and Science University

(2)

ENEA Casaccia Research Centre, Institute of Thermal Fluid Dynamics

Ellington CP: The novel aerodynamics of insect flight: applications to micro-air vehicles. J Exp Biol 1999, 202: 3439–3448.

Knight DP, Vollrath F: Liquid crystals and flow elongation in a spider's silk production line. Proc R Soc Lond B 1999, 266: 519–523. 10.1098/rspb.1999.0667

Dawson C, Vincent JFV, Jeronimidis G, Rice G, Forshaw P: Heat transfer through penguin feathers. J Theoret Biol 1999, 199: 291–295. 10.1006/jtbi.1999.0959

Velcro SA: Improvements in or relating to a method and a device for producing a velvet type fabric. Swiss patent no. 721338 1955.

Vincent JFV, Mann DL: Systematic technology transfer from biology to engineering. Philos Trans R Soc Lond A 2002, 360: 159–173. 10.1098/rsta.2001.0923

Skordos A, Chan PH, Vincent JFV, Jeronimidis G: A novel strain sensor based on the campaniform sensillum of insects. Philos Trans R Soc Lond A 2002, 360: 239–253. 10.1098/rsta.2001.0929

Vincent JFV, King MJ: The mechanism of drilling by wood wasp ovipositors. Biomimetics 1996, 3: 187–201.

Barthlott W, Neinhuis C: The Lotus-effect: non-adhesive biological and biomimetic technical surfaces. In Proceedings of 1st International Industrial Conference BIONIK. Hannover, Germany; 2004:211–214.

Barthlott W, Neinhuis C: The lotus-effect: Nature's model for self-cleaning surfaces. Int Text Bull 2001, 8: 10–12.

Barthlott W, Neinhuis C: Purity of the sacred lotus, or escape from contamination in biological surfaces. Planta 1997, 202: 1–8. 10.1007/s004250050096

Guest SD, Pellegrino S: Inextensional wrapping of flat membranes. In Proceedings of International Seminar Structure Morphology. LMGC Universite Montpellier II, Montpellier; 1992:203–215.

Jackson AP, Vincent JFV, Turner RM: A physical model of nacre. Compos Sci Technol 1989, 36: 255–266. 10.1016/0266-3538(89)90024-9

Bechert DW, Bruse M, Hage W, Meyer R: Biological surfaces and their technological application--laboratory and flight experiments on drag reduction and separation control. In Proceedings of 28th AIAA Fluid Dynamics Conference. Snowmass Village, CO, USA; 1997.

Chaplin RC, Gordon JE, Jeronimidis G: Development of a novel fibrous composite material. US patent no. 4409274 1983.

Holl SM, Hansen D, Waite JH, Schaefer J: Solid-state NMR analysis of cross-linking in a mussel protein glue. Arch Biochem Biophys 1993, 302: 255–258. 10.1006/abbi.1993.1207

Barthlott W, Neinhuis C: Lotusblumen und Autolacke: Ulstrastruktur, Pflanzucher, Grenzflachen und biomimetische unverschmutzbare Werkstoffe. In BIONA Report 12. Edited by: Nachtigall W, Wisser A. Gesellschaft fur Technische Biologie und Bionik, Universitat des Saarlandes; 1999:281–293.

McIntosh A, Forman M: The efficiency of the explosive discharge of the bombardier beetle with possible biomimetic application. In Design and Nature II--Comparing Design in Nature with Science and Engineering. Edited by: Collins MW, Brebbia CA. Southampton & Boston: WIT Press; 2004:227–236.

Amon CH: Advances in computational modeling of nano-scale heat transfer. In Proceedings of 12th International Heat Transfer Conference. Grenoble, France; 2002:41–53.

Chen S, Doolen GD: Lattice Boltzmann method for fluid flows. Annu Rev Fluid Mech 1998, 30: 329–364. 10.1146/annurev.fluid.30.1.329

Maruyama S: Molecular dynamics methods in microscale heat transfer. In Heat Transfer and Fluid Flow in Microchannels. Edited by: Celata GP. New York: Begell House Inc; 2002.

Bird GA: Molecular gas Dynamics and Direct Simulation of Gas Flows. New York: Oxford Univ. Press; 1994.

Prizjev NV, Darhuber AA, Troian SM: Slip behavior in liquid films on surfaces of patterned wettability: Comparison between continuum and molecular dynamics simulations. Phys Rev E 2005, 71: 041608. 10.1103/PhysRevE.71.041608

Adkins D, Yan YY: CFD simulation of fish-like body moving in viscous liquid. J Bionic Eng 2006, 3: 147–153. 10.1016/S1672-6529(06)60018-8

Zhu Q, Wolfgang MJ, Yue DKP, Triantafyllou MS: Three-dimensional flow structures and vorticity control in fish-like swimming. J Fluid Mech 2002, 468: l-28. 10.1017/S002211200200143X

Rohr JJ, Hendricks EW, Quigley L, Fish FE, Gilpatrick JW, Scardina-Ludwig J: Observations of dolphin swimming speed and Strouhal number. In Space and Naval Warfare Systems Center Technical Report 1769. San Diego; 1998.

Kroger R: Simulation of airflow around flapping insect wings. In Proceedings of 1st International Industrial Conference BIONIK. Hannover, Germany; 2004:185–190.

Nachtigall W: Biona-Report 11, Biology and Related Natural Sciences. Stuttgart: Fischer Verlag; 1997:115–156.

Zu YQ, Yan YY: Numerical simulation of electroosmotic flow near earthworm surface. J Bionic Eng 2006, 3: 179–186. 10.1016/S1672-6529(07)60001-8

Ren L, Tong J, Li J, Cheng B: Soil adhesion and biomimetics of soil-engaging components: a review. J Agricult Eng 2001, 79: 239–263. 10.1006/jaer.2001.0722

Ma J: Creatures and Bionics. Tianjin: Tianjin Science and Technology Press; 1984.

Yan YY, Hull JB: The concept of electroosmotically driven flow and its application to biomimetics. J Bionic Eng 2004, 1: 46–52.

Yan YY, Ren L, Li J: The electroosmotic driven flow near an earthworm surface and the inspired bionic design in engineering. Int J Des Nat 2007, 1: 135–145. 10.2495/D&N-V1-N2-135-145

Beheshti N, Mcintosh AC: A biomimetic study of the explosive discharge of the bombardier beetle. Int J Des Nat 2007, 1: 61–69. 10.2495/D&N-V1-N1-61-69

Aneshansley DJ, Eisner T: Spray aiming in the bombardier beetle: photographic evidence. Proc Natl Acad Sci USA 1999, 96: 9705–9709. 10.1073/pnas.96.17.9705

Aneshansley DJ, Eisner T, Widom M, Widom B: Biochemistry at 100°C: explosive secretory discharge of bombardier beetles (brachinus). Science 1969, 165: 61–63. 10.1126/science.165.3888.61

Dean J, Aneshansley DJ, Edgerton H, Eisner T: Defensive spray of the bombardier beetle: a biological pulse jet. Science 1990, 248: 1219–1221. 10.1126/science.2349480

O'Connell ST, Thompson PA: Molecular dynamics-continuum hybrid computations: a tool for studying complex fluid flows. Phys Rev E 1995, 52: 792–795.

Priezjev NV, Darhuber AA, Troian SM: Slip behavior in liquid films on surfaces of patterned wettability: comparison between continuum and molecular dynamics simulations. Phys Rev E 2005, 71: 041608/1–041608/11. 10.1103/PhysRevE.71.041608

Qian T, Wang X: Hydrodynamic slip boundary condition at chemically patterned surfaces: a continuum deduction from molecular dynamics. Phys Rev E 2005, 72: 022501. 10.1103/PhysRevE.72.022501

Hadjiconstantinou NG: Combining atomistic and continuum simulations of contact-line motion. Phys Rev E 1999, 59: 2475. 10.1103/PhysRevE.59.2475

Sousa ACM: Multiphysics modeling with SPH: from macro to nanoscale heat transfer. Proceedings of IHTC-13, KN 29, Sydney, Australia 2006.

Olfe DB: A modification of the differential approximation for radiative transfer. AIAA J 1967, 5: 638–643. 10.2514/3.4041

Modest MF: The modified differential approximation for radiative transfer in general three-dimensional media. J Thermophys Heat Transf 1989, 3: 283–288. 10.2514/3.28773

Asproulis N, Drikakis D: Nanoscale materials modelling using neural networks. J Comput Theoret Nanosci 2009, 6: 514–518. 10.1166/jctn.2009.1062

Wijesinghe HS, Hadjiconstantinou NG: A hybrid atomistic-continuum formulation for unsteady, viscous, incompressible flows. CMES 2004, 5: 515–526.

Wijesinghe HS, Hornung RD, Garcia AL, Hadjiconstantinou NG: Three dimensional hybrid continuum-atomistic simulations for multiscale hydrodynamics. J Fluids Eng 2004, 126: 768–777. 10.1115/1.1792275

Nie XB, Robbins MO, Chen SY: Resolving singular forces in cavity flow: multiscale modeling from atomic to millimeter scales. Phys Rev Lett 2006, 96: 1–4.

De Fabritiis G, Delgado-Buscalioni R, Coveney PV: Modeling the mesoscale with molecular specificity. Phys Rev Lett 2006, 97: 134501. 10.1103/PhysRevLett.97.134501

Schwartzentruber TE, Scalabrin LC, Boyd ID: A modular particle-continuum numerical method for hypersonic non-equilibrium gas flows. J Comput Phys 2007, 225: 1159–1174. 10.1016/j.jcp.2007.01.022

Bhattacharya DK, Lie GC: Nonequilibrium gas flow in the transition regime: a molecular-dynamics study. Phys Rev 1991, 43: 761–767. 10.1103/PhysRevA.43.761

Delgado-Buscalioni R, Coveney P: Hybrid molecular-continuum fluid dynamics. Philos Trans R Soc Lond A 2004, 362: 1639–1654. 10.1098/rsta.2004.1401

Hadjiconstantinou NG: Discussion of recent developments in hybrid atomistic continuum methods for multiscale hydrodynamics. Bull Pol Acad Sci Tech Sci 2005, 53: 335–342.

Kalweit M, Drikakis D: Coupling strategies for hybrid molecular continuum simulation methods. Proc Inst Mech Eng C J Mech Eng Sci 2008, 222: 797–806. 10.1243/09544062JMES716

Hadjiconstantinou NG, Patera AT: Heterogeneous atomistic-continuum representations for dense fluid systems. Int J Mod Phys 1997, 8: 967–976. 10.1142/S0129183197000837

Cao BY: Non-maxwell slippage induced by surface roughness for microscale gas flow: a molecular dynamics simulation. Mol Phys 2007, 105: 1403–1410. 10.1080/00268970701361322

Delgado-Buscalioni R, Coveney PV: Continuum-particle hybrid coupling for mass, momentum and energy transfers. Phys Rev E 2003, 67: 046704. 10.1103/PhysRevE.67.046704

Liu J, Chen SV, Nie XB, Robbins MO: A continuum-atomistic simulation of heat transfer in micro- and nano-flows. J Comput Phys 2007, 227: 279–291. 10.1016/j.jcp.2007.07.014

Nie XB, Chen SY, Robbins MO: A continuum and molecular dynamics hybrid method for micro- and nano-fluid flow. J Fluid Mech 2004, 500: 55–64. 10.1017/S0022112003007225

Kalweit M, Drikakis D: Multiscale methods for micro/nano flows and materials. J Comput Theoret Nano Sci 2008, 5: 1923–1938. 10.1166/jctn.2008.906

Ren W, Weinan E: Heterogeneous multiscale method for the modeling of complex fluids and micro-fluidics. J Comput Phys 2005, 204: 1–26. 10.1016/j.jcp.2004.10.001

Schwartzentruber TE, Scalabrin LC, Boyd ID: Hybrid particle-continuum simulations of hypersonic flow over a hollow-cylinder-flare geometry. AIAA J 2008, 46: 2086–2095. 10.2514/1.36681

Werder T, Walther JH, Koumoutsakos P: Hybrid atomistic-continuum method for the simulation of dense fluid flows. J Comput Phys 2005, 205: 373–390. 10.1016/j.jcp.2004.11.019

Yan YY, Lai H, Gentle CR, Smith JM: Numerical analysis of fluid flow inside and around a liquid drop using an incorporation of multi-block iteration and moving mesh. Trans IChE Chem Eng Res Des 2002, 80: 325–331. 10.1205/026387602753582132

Drikakis D, Asproulis N: Multi-scale computational modeling of flow and heat transfer. Int J Num Methods Heat Fluid Flow 2010, 20: 517–528. 10.1108/09615531011048222

Ahlborn B, Chapman S, Stafford R, Blake RW, Harper D: Experimental simulation of the thrust phases of fast-start swimming of fish. J Theor Biol 1997, 200: 2301–2312.

Drucker EG, Lauder GV: Locomotor forces on a swimming fish: three-dimensional vortex wake dynamics quantified using digital particle image velocimetry. J Exp Biol 1999, 202: 2393–2412.

Ahlborn B, Harper D, Blake R, Ahlborn D, Cam M: Fish without footprints. J Theor Biol 1991, 148: 521–533. 10.1016/S0022-5193(05)80234-6

Bandyopadhyay P, Castano J, Rice J, Philips R, Nedderman W, Macy W: Low speed maneuvering hydrodynamics of fish and small underwater vehicles. J Fluids Eng 1997, 119: 136–144. 10.1115/1.2819099

Cheng HK, Murillo LE: Lunate-tail swimming propulsion as a problem of curved lifting line in unsteady flow. Part 1. Asymptotic theory. J Fluid Mech 1984, 143: 327–350. 10.1017/S0022112084001373

Ellington CP: The aerodynamics of hovering insect flight. V. A vortex theory. Philos Trans R Soc Lond B 1984, 305: 115–144. 10.1098/rstb.1984.0053

Dewar H, Graham J: Studies of tropical tuna swimming performance in a large water tunnel--I, energetics. J Exp Biol 1994, 192: 13–31.

Dewar H, Graham J: Studies of tropical tuna swimming performance in a large water tunnel--III, kinematics. J Exp Biol 1994, 192: 45–59.

Domenici P, Blake RW: The kinematics and performance of fish fast-start swimming. J Exp Biol 1997, 200: 1165–1178.

Ellington CP, van den Berg C, Thomas A: Leading edge vortices in insect flight. Nature 1996, 384: 6–26. 10.1038/384626a0

Lighthill MJ: A quatic animal propulsion of high hydromechanical efficiency. J Fluid Mech 1970, 44: 265–301. 10.1017/S0022112070001830

Lighthill MJ: Large-amplitude elongated-body theory of fish locomotion. Proc R Soc Lond B 1971, 179: 125–138. 10.1098/rspb.1971.0085

Fish F: Power output and propulsive efficiency of swimming bottlenose dolphins. J Exp Biol 1993, 185: 179–193.

Gray J: The locomotion of nematodes. J Exp Biol 1964, 13: 135–154.

Kayan YP, Pyatetskiy VY: Kinematics of bottlenose dolphins swimming as related to acceleration mode. Bionika 1977, 11: 36–41.

Kato N: Locomotion by mechanical pectoral fins. J Mar Sci Technol 1998, 3: 113–121. 10.1007/BF02492918

Gray J: Studies in animal locomotion. VI. The propulsive powers of the dolphin. J Exp Biol 1936, 13: 192–199.

Lighthill MJ: Note on the swimming of slender fish. J Fluid Mech 1960, 9: 305–317. 10.1017/S0022112060001110

Lighthill MJ: Hydromechanics of aquatic animal propulsion. Annu Rev Fluid Mech 1969, 1: 413–445. 10.1146/annurev.fl.01.010169.002213

Liu H, Ellington CP, Kawachi K, van den Berg C, Wilmlmott AP: A computational fluid dynamic study of hawkmoth hovering. J Exp Biol 1998, 201: 461–477.

Liu H, Wassenberg R, Kawachi K: The three-dimensional hydrodynamics of tadpole swimming. J Exp Biol 1997, 200: 2807–2819.

Maxworthy T: Experiments on theWeis-Fogh mechanism of lift generation by insects in hovering flight. Part I. Dynamics of the fling. J Fluid Mech 1979, 93: 47–63. 10.1017/S0022112079001774

Muller U, van den Heuvel B, Stamhuis E, Videler J: Fish foot prints: morphology and energetics of the wake behind a continuously swimming mullet ( Chelon labrosus risso).J Exp Biol 1997, 200: 2893–2896.

Weihs D: The mechanism of rapid starting of slender fish. Biorheology 1973, 10: 343–350.

Wolfgang M, Anderson JM, Grosenbaugh MA, Yue DKP, Triantafyllou MS: Near body flow dynamics in swimming fish. J Exp Biol 1999, 202: 23032327.

Newman JN, Wu T: A generalized slender-body theory for fish-like forms. J Fluid Mech 1973, 57: 673–693. 10.1017/S0022112073001953

Wu T: Hydromechanics of swimming fishes and cetaceans. Adv Appl Math 1971, 11: 1–63.

Rome L, Swank D, Corda D: How fish power swimming. Science 1993, 261: 340–343. 10.1126/science.8332898

Triantafyllou GS, Triantafyllou MS, Grosenbaugh MA: Optimal thrust development in oscillating foils with application to fish propulsion. J Fluids Struct 1993, 7: 205–224. 10.1006/jfls.1993.1012

Triantafyllou MS, Triantafyllou GS: An efficient swimming machine. Sci Am 1995, 272: 64–70. 10.1038/scientificamerican0395-64

Weihs D: A hydrodynamical analysis of fish turning maneuvers. Proc R Soc Lond Ser B 1972, 182: 59–72. 10.1098/rspb.1972.0066

Triantafyllou MS, Barrett DS, Yue DKP, Anderson JM, Grosenbaugh MA: A new paradigm of propulsion and maneuvering for marine vehicles. Trans Soc Naval Architects Mar Eng 1996, 104: 81–100.

Fierstine H, Walters V: Studies in locomotion and anatomy of scombroid fishes. Mem Soc South Calif Acad Sci 1968, 6: 1–31.

Videler JJ, Muller UK, Stamhuis EJ: Aquatic vertebrate locomotion: wakes from body waves. J Exp Biol 1999, 202: 3423–3430.

Kagemoto H, Wolfgang M, Yue D, Triantafyllou M: Force and power estimation in fish-like locomotion using a vortex-lattice method. Trans ASME J Fluids Eng 2000, 122: 239–253. 10.1115/1.483251

Newman J: The force on a slender fish-like body. J Fluid Mech 1973, 58: 689–702. 10.1017/S0022112073002429

Lan C: The unsteady quasi-vortex-lattice method with applications to animal propulsion. J Fluid Mech 1979, 93: 747–765. 10.1017/S0022112079002019

Triantafyllou MS, Barrett DS, Yue DKP, Anderson JM, Grosenbaugh MA, Streitlien K, Triantafyllou GS: A new paradigm of propulsion and maneuvering for marine vehicles. Trans Soc Naval Architect Mar Eng 1996, 104: 81–100.

Pedley TJ, Hill SJ: Large-amplitude undulatory fish swimming: fluid mechanics coupled to internal mechanics. J Expl Biol 1999, 202: 3431–3438.

Triantafyllou G, Triantafyllou M, Yue DKP: Hydrodynamics of fish swimming. Annu Rev Fluid Mech 2000, 32: 33–53. 10.1146/annurev.fluid.32.1.33

Liu H, Wassersug RJ, Kawachi KA: Computational fluid dynamic study of tadpole swimming. J Exp Biol 1996, 199: 1245–1260.

Anon: Biomimetics: Strategies for Product Design Inspired by Nature. Bristol: Department of Trade and Industry; 2007.

Barthelat F, Tang H, Zavattieri PD, Li CM, Espinosa HD: On the mechanics of mother-of-pearl: a key feature in the material hierarchical structure. J Mech Phys Solids 2007, 55: 306–337. 10.1016/j.jmps.2006.07.007

Bhushan B, Jung YC: Wetting, adhesion and friction of superhydrophobic and hydrophilic leaves and fabricated micro/nanopatterned surfaces. J Phys Condens Matter 2008, 20: 225010. 10.1088/0953-8984/20/22/225010

Bhushan B, Sayer RA: Surface characterization and friction of a bio-inspired reversible adhesive tape. Microsyst Technol 2007, 13: 71–78. 10.1007/s00542-006-0256-2

Elbaum R, Gorb S, Fratzl P: Structures in cell wall that enable hygroscopic movement of wheat awns. J Struct Biol 2008, 164: 101–107. 10.1016/j.jsb.2008.06.008

Gorb S, Varenberg M, Peressadko A, Tuma J: Biomimetic mushroom-shaped fibrillar adhesive microstructure. J R Soc Interface 2007, 4: 271–275. 10.1098/rsif.2006.0164

Goswami L, Dunlop JWC, Jungniki K, Eder M, Gierlinger N, Coutand C, Jeronimidis G, Fratzl P, Burgert I: Stress generation in the tension wood of poplar is based on the lateral swelling power of the G-layer. Plant J 2008, 56: 531–538. 10.1111/j.1365-313X.2008.03617.x

Koch K, Bhushan B, Barthlott W: Multifunctional surface structures of plants: an inspiration for biomimetics. Prog Mater Sci 2009, 54: 137–178. 10.1016/j.pmatsci.2008.07.003

Luz GM, Mano JF: Biomimetic design of materials and biomaterials inspired by the structure of nacre. Philos Trans R Soc A 2009, 367: 1587–1605. 10.1098/rsta.2009.0007

Reed EJ, Klumb L, Koobatian M, Viney C: Biomimicry as a route to new materials: what kinds of lessons are useful? Philos Trans R Soc A 2009, 367: 1571–1585. 10.1098/rsta.2009.0010

Stegmaier T, Linke M, Planck H: Bionics in textiles: flexible and translucent thermal insulations for solar thermal applications. Philos Trans R Soc A 2009., 367: 10.1098/rsta.2009.0019

van der Zwaag S, van Dijk N, Jonkers H, Mookhoek S, Sloof W: Self healing behaviour in man-made engineering materials: bio-inspired but tasking into account their intrinsic character. Philos Trans R Soc A 2009., 367: 10.1098/rsta.2009.0020

Youngblood JP, Sottos NR: Bioinspired materials for self-cleaning and self-healing. MRS Bull 2008, 33: 732–738. 10.1557/mrs2008.158

Yan YY: Recent advances in computational simulation of macro-, meso-, and micro-scale biomimetics related fluid flow problems. J Bionic Eng 2007, 4: 97–107. 10.1016/S1672-6529(07)60021-3

Shan X, Chen H: Lattice Boltzmann model for simulating flows with multiple phases and components. Phys Rev E 1993, 47: 1815–1819. 10.1103/PhysRevE.47.1815

Shan X, Chen H: Simulation of non-ideal gases and liquid-gas phase transitions by a lattice Boltzmann equation. Phys Rev E 1994, 49: 2941–2948. 10.1103/PhysRevE.49.2941

Swift MR, Osborn WR, Yeomans JM: Lattice Boltzmann simulation of non-ideal fluids. Phys Rev Lett 1995, 75: 830–833. 10.1103/PhysRevLett.75.830

He XY, Chen SY, Zhang RY: A lattice Boltzmann scheme for incompressible multiphase flow and its application in simulation of Rayleigh-Taylor instability. J Comput Phys 1999, 152: 642–663. 10.1006/jcph.1999.6257

Ji CY, Yan YY: A molecular dynamics simulation of liquid-vapor-vapor-solid system near triple-phase contact line of flow boiling in a microchannel. Appl Therm Eng 2008, 28: 195–202. 10.1016/j.applthermaleng.2007.03.029

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