Effect Of Solid Boundaries Research Articles

Bioinspired reorientation strategies for application in micro/nanorobotic control

Engineers have recently been inspired by swimming methodologies of microorganisms in creating micro-/nanorobots for biomedical applications. Future medicine may be revolutionized by the application of these small machines in diagnosing, monitoring, and treating diseases. Studies over the past decade have often concentrated on propulsion generation. However, there are many other challenges to address before the practical use of robots at the micro-/nanoscale. The control and reorientation ability of such robots remain as some of these challenges. This paper reviews the strategies of swimming microorganisms for reorientation, including tumbling, reverse and flick, direction control of helical-path swimmers, by speed modulation, using complex flagella, and the help of mastigonemes. Then, inspired by direction change in microorganisms, methods for orientation control for microrobots and possible directions for future studies are discussed. Further, the effects of solid boundaries on the swimming trajectories of microorganisms and microrobots are examined. In addition to propulsion systems for artificial microswimmers, swimming microorganisms are promising sources of control methodologies at the micro-/nanoscale.

Thermal Counterflow in a Periodic Channel with Solid Boundaries

We perform numerical simulations of finite temperature quantum turbulence produced through thermal counterflow in superfluid $^4$He, using the vortex filament model. We investigate the effects of solid boundaries along one of the Cartesian directions, assuming a laminar normal fluid with a Poiseuille velocity profile, whilst varying the temperature and the normal fluid velocity. We analyze the distribution of the quantized vortices, reconnection rates and quantized-vorticity production as a function of the wall-normal direction. We find that the quantized vortex lines tend to concentrate close to the solid boundaries with their position depending only on temperature and not on the counterflow velocity. We offer an explanation of this phenomenon by considering the balance of two competing effects, namely the rate of turbulent diffusion of an isotropic tangle near the boundaries and the rate of quantized-vorticity production at the centre. Moreover, this yields the observed scaling of the position of the peak vortex line density with the mutual friction parameter. Finally we provide evidence that upon the transition from laminar to turbulent normal fluid flow, there is a dramatic increase in the homogeneity of the tangle, which could be used as an indirect measure of the transition to turbulence in the normal fluid component for experiments.

Effect of solid boundaries on swimming dynamics of microorganisms in a viscoelastic fluid.

We numerically study the effect of solid boundaries on the swimming behavior of a motile microorganism in viscoelastic media. Understanding the swimmer-wall hydrodynamic interactions is crucial to elucidate the adhesion of bacterial cells to nearby substrates which is precursor to the formation of the microbial biofilms. The microorganism is simulated using a squirmer model that captures the major swimming mechanisms of potential, extensile, and contractile types of swimmers, while neglecting the biological complexities. A Giesekus constitutive equation is utilized to describe both viscoelasticity and shear-thinning behavior of the background fluid. We found that the viscoelasticity strongly affects the near-wall motion of a squirmer by generating an opposing polymeric torque which impedes the rotation of the swimmer away from the wall. In particular, the time a neutral squirmer spends at the close proximity of the wall is shown to increase with polymer relaxation time and reaches a maximum at Weissenberg number of unity. The shear-thinning effect is found to weaken the solvent stress and therefore, increases the swimmer-wall contact time. For a puller swimmer, the polymer stretching mainly occurs around its lateral sides, leading to reduced elastic resistance against its locomotion. The neutral and puller swimmers eventually escape the wall attraction effect due to a releasing force generated by the Newtonian viscous stress. In contrast, the pusher is found to be perpetually trapped near the wall as a result of the formation of a highly stretched region behind its body. It is shown that the shear-thinning property of the fluid weakens the wall-trapping effect for the pusher squirmer.

Free surface and solid boundary effects on the free vibration of cantilevered composite plates

This paper investigates the effects of surrounding boundaries on the free vibration response of fully and partially submerged cantilevered composite plates and how these effects change due to material anisotropy. The results show that added mass significantly reduces the natural frequencies of cantilevered marine structures as a function of relative submergence depth, more so for composite plates than for steel plates because of the much lower ratio of effective structural mass to hydrodynamic added mass. Added mass effects are most dramatic for partially submerged plates as the plates move from being above to completely beneath the free surface. Free surface effects are shown to become negligible for a fully submerged plate parallel to the free surface when the depth of submergence exceeds 50% of the plate length. Solid boundaries are found to have limited effects for fully-submerged plates near a wall, where maximum decreases in resonance frequencies due to increases in added mass are only a few percent.

Analysis of forced convection heat transfer from a circular cylinder embedded in a porous medium

Time-dependent forced convection heat transfer from a single circular cylinder embedded in a horizontal packed bed of spherical particles under local thermal non-equilibrium condition is investigated numerically using the spectral-element method. The non-Darcian effects, i.e. inclusion of the effect of solid boundaries and inertia forces, and the effect of thermal dispersion, are taken into account. The influences of the presence of the porous material and its thermal properties: solid-to-fluid thermal conductivity ratio k r ∈ [ 0.01 , 1000 ] and Biot number B i ∈ [ 0.01 , 100 ] , on the rates of heat transfer and the hydrodynamic and thermal responses, are examined for the Reynolds number range R e D ∈ [ 1 , 250 ] . These effects are quantified. Perhaps not surprisingly, the results show that the presence of the porous particles suppresses significantly the wakes behind the cylinder and enhances considerably the heat transfer. A comparison that is made between the one- and two-equation energy model predictions shows that the former model predicts a continuous increase in Nu f against k r ; however, the trend of Nu f with k r , for k r > 10, is governed entirely by Bi when the latter model is used. Also, the increase in Bi decreases Nu f and increases Nu s , and high values of k r or Bi lead to establishing a thermal equilibrium status in the porous bed.

Verification of filtered two‐fluid models for gas‐particle flows in risers

AbstractThe effect of solid boundaries on the closure relationships for filtered two‐fluid models for riser flows was probed by filtering the results obtained through highly resolved kinetic theory‐based two‐fluid model simulations. The closures for the filtered drag coefficient and particle phase stress depended not only on particle volume fraction and the filter length but also on the distance from the wall. The wall corrections to the filtered closures are nearly independent of the filter length and particle volume fraction. Simulations of filtered model equations yielded grid length independent solutions when the grid length is ∼half the filter length or smaller. Coarse statistical results obtained by solving the filtered models with different filter lengths were the same and corresponded to those from highly resolved simulations of the kinetic theory model, which was used to construct the filtered models, thus verifying the fidelity of the filtered modeling approach. © 2010 American Institute of Chemical Engineers AIChE J, 2011

The decay of magnetohydrodynamic turbulence in a confined domain

The effect of nonperiodic boundary conditions on decaying two-dimensional magnetohydrodynamic turbulence is investigated. A circular domain with no-slip boundary conditions for the velocity is considered and where the normal component of the magnetic field vanishes at the wall. Different flow regimes are obtained by starting from random initial velocity and magnetic fields with varying integral quantities. These regimes, equivalent to the ones observed by Ting, Matthaeus, and Montgomery [Phys. Fluids 29, 3261 (1986)] in periodic domains, are found to subsist in confined domains. The effect of solid boundaries on the energy decay and alignment properties is examined. The final states are characterized by functional relationships between velocity and magnetic field.

The effects of solid boundaries on confined two-dimensional turbulence

This paper addresses the effects of solid boundaries on the evolution of two-dimensional turbulence in a finite square domain, for the cases of both decaying and continuously forced flow. Laboratory experiments and numerical flow simulations have revealed the crucial role of the solid no-slip walls as sources of vorticity filaments, which may significantly affect the flow evolution in the interior. In addition, the walls generally provide normal and tangential stresses that may exert a net torque on the fluid, which can change the total angular momentum of the contained fluid. For the case of decaying turbulence this is observed in so-called ‘spontaneous spin-up’, i.e. a significant increase of the total angular momentum, corresponding to a large domain-filling circulation cell in the organized ‘final’ state. For the case of moderate forcing this phenomenon may still be observed, although the filamentary vortex structures advected away from the walls may cause erosion and possibly a total destruction of the central cell. This disordered stage – characterized by a significantly decreased total angular momentum – is usually followed by a re-organization into a large circulation cell (in either the same or opposite direction) with an increased total angular momentum. The scaling behaviour of vorticity structure functions and the probability distribution function of vorticity increments have been investigated for forced turbulence and indicate a strong anisotropy of the turbulent flow in the range of Reynolds numbers considered.

The effect of solid boundaries on pore shrinkage in Stokes flow

Motivated by the viscous sintering of amorphous materials in the presence of a distribution of rigid platelet inclusions added to increase the strength of the final sintered medium, a simple model for the shrinkage of compressible pores close to a wall in Stokes flow is proposed. The model assumes that the pore remains elliptical/ellipsoidal in shape at all times. The model is expected to be valid provided the pore is not too far from spherical and not too close to the wall. It relies on a separation of the flow into ‘inner' and ‘outer' problems. The inner problem is to assume that the ellipsoid evolves in a linear ambient flow given by the first two terms in a local expansion of an outer flow produced by the image singularity distribution of a point-sink near a planar no-slip boundary. The focus of the present paper is to test the viability of the model in the planar case. Using a spectral method based on analytic functions and conformal mappings, the results of a full numerical simulation are compared with the predictions of the planar model. The effects of the proximity of the pore to the wall, the anisotropy in the pore shape and its relative orientation to the wall are all examined. It is observed that, as they shrink, pores drift towards the wall becoming elongated in the direction perpendicular to the wall.

The Asymmetric Collapse of Bubbles in Compressible Liquid**The project supported by National Natural Science Foundation of China (10247008), Natural Science Foundation of Gansu Province (YS021-A22-018), the Scientific Research Foundation (SRF) for the Returned Overseas Chinese Scholars (ROCF), State Education Ministry (SEM), and the Natural Science Foundation of Northwest Normal University (NWNU-KJCXGC-215)

The analytical solution of a bubble collapse close to a solid boundary in a compressible water is investigated by means of a perturbation method to first order in the bubble wall Mach number. It is shown, in this paper, that it is the Rayleigh–Plesset equation for incompressible liquid to zero order solution or similar to the Gilmore equation for compressible water to first order solution when the effect of solid boundary is negligibly small enough, i.e., sufficiently far away from the bubble center.

Momentum boundary layer and its influence on the convective heat transfer in porous media

Convective heat transfer in a channel filled with a porous medium has been analyzed in this paper. The flow field is analyzed considering both the inertia and solid boundary effects and the thickness of the momentum boundary layer is found as a function of the Darcy and the Reynolds number. The two-equation model is applied for the heat transfer analysis and theoretical solutions are obtained for both fluid and solid phase temperature fields. The Nusselt number is obtained in terms of the relevant physical parameters, such as the Biot number for the internal heat exchange, the ratio of effective conductivities between the fluid and solid phases, and the thickness of the momentum boundary layer. The results indicate that the influence of the velocity profile is characterized within two regimes according to the two parameters, the Biot number and the conductivity ratio between the phases. The decrease in the heat transfer due to the momentum boundary layer is 15% at most within a practical range of the pertinent parameters.

A hierarchical model for surface effects on chain conformation and rheology of polymer solutions. I. General formulation

The flow behavior of polymer solutions near a solid surface (either neutral or adsorbing) is modeled through a new, hierarchical (macroscopic and microscopic) approach which enables the thermodynamically consistent extension of equilibrium (static) considerations to nonequilibrium (flow) conditions. The approach involves two steps: First, the set of primary, independent, variables defining the state of the system at the macroscopic level is chosen, and a complete set of transport and constitutive equations is constructed for them through a two fluid, Hamiltonian model. In the present work, the macroscopic variables include the polymer chain concentration, the macroscopic fluid velocity, and the conformation tensor (defined as the tensor of the second moment of the chain end-to-end vector). The governing equations involve the (extended) free energy or Hamiltonian of the system, H, and are valid both in the bulk of the fluid and in the interfacial region. Thus, to solve them one needs to specify H. This is done in a second step, by invoking a microscopic model, which consistently takes into account the simultaneous effect on chain conformations of both the solid boundary and the imposed flow field. Solid boundary effects are taken into account in the solution of a diffusion equation for the chain propagator G(r,n;r0) which represents the weighted probability that an n-segment long chain which starts at r0 will end at position r. Flow field effects are taken into account through the definition of a generalized propagator G′(r,n;r0,α), which further depends on the apparent strain tensor α, representing chain deformation effects due to flow. The present part of the paper describes the general formulation of the approach and its relevance with previous works. Results from applying the methodology to the case of a polymer solution flowing past a purely repulsive surface (a wall) are presented in the second part of this work.

Thermal enhancement in laminar channel flow with a porous block

A study of a porous block mounted on a heated wall in a laminar flow channel to enhance convection heat transfer rate was investigated numerically. A numerical method of SIMPLEC is adopted to solve governing equations, as for the energy equation, one-equation thermal model with Van Driest's wall function is considered. The parameters that include porosity ε, particle diameter D p, Reynolds number Re, and blocked ratio HP are studied, and for simulating more realistically, the porosity is taken into consideration as variable. All the non-Darcian effects including the channeling effects, solid boundary effects, and inertial effects are also considered. The effects of the above parameters on the thermal performance of the heated wall are examined in detail. The results indicate that for HP = 0.5 case the thermal performances are enhanced by using a porous block with higher porosity and particle diameter. However, the results are the opposite for HP = 1.0.

Convection Heat Transfer of Horizontal-Spherical Particle Layer Heated From Below and Cooled From Above.

Heat transfer and pressure drop measurements were performed in a forced convection of air flow through a rectangular duct packed with spherical particles, which had upper cooled and lower heated surfaces. Four kinds of particles with different diameters and thermal conductivities were used as the packing materials. The effects of solid boundaries on fluid motion and heat transfer were discussed. The heat transfer rate from the surfaces was promoted by a thermal dispersion effect caused by a fluid mixing motion. However, it was decreased in the vicinity of the near-wall region due to low effective thermal conductivity and weak fluid mixing motion. It was clarified that the ratio of the thermal boundary layer thickness developed from the heat transfer surfacec to the size of the near-wall region was important in order to reduce the heat transfer data. Nondimensional heat transfer correlation equations were derived, using parameters expressing the average characteristics of the porous bed packed with spherical particles.

Wave plan computation method in study of the Calvi Bay erosion in Corsica, France

AbstractA study of linear monochromatic wave propagation is presented, based on a theory of potentials. The usual Berkhoff equation has been extended by the addition of partially pervious solid boundary effects and the bed friction.The problem has been solved by a hybrid finite element method including the effect of singular local elements such as the end of breakwaters or wharfs. This numerical method confirms the interest in quadratic Lagrangian finite elements.The comparisons with analytical solutions and existing numerical results show the validity of the method. Some original examples also prove the good performance of the proposed computation method.As an example, the study of the erosion of the beach of Calvi Bay in Corsica, France is presented. The phenomenon had started already in 1960, but the problem began to be very severe four years ago, after the implementation of a new harbour in 1982 and buildings, hotels, restaurants, and a main sewer on the beach. To consider the impact of these constructions and other factors like waves, currents and geomorphological aspects, the studies were divided into four parts: sedimentological, currents, wave propagation and geomorphological.This paper will describe the results of a complete two years study on the site, from February 1986 to December 1987.Findings show that the erosion process is due to the rise of the relative sea level with, as a catalyst, tourist behaviour and the implementation of the new constructions.

Jet type model for the three‐dimensional thermal plume in a crosscurrent and under wind

A dynamic three‐dimensional model for predicting water temperatures in a thermal plume has been formulated and tested. The plume that results from the discharge of heated water is described in terms of a buoyant, turbulent half jet. The effects of a crosscurrent and wind can be accommodated by the model. Mixing by turbulence, lateral spread due to buoyancy, heat transfer at the water surface, and deflection of the main trajectory under wind shear stress in a current are accounted for. Although it was necessary to make several broad assumptions, e.g., that all cross‐sectional temperature distributions are similar and that there is no distortion of the cross section by wind, the results show the overall behavior of the plume reasonably well. The model does not account for the effects of solid boundaries; its main features are its simplicity and comprehensiveness, its combination of the several processes having a major effect on plume behavior, and its ability to include possible future experimental or theoretical results without major changes in the program.

Effect of Solid Boundaries on Aerodynamic Sound

The theory of aerodynamic sound from turbulence near solid boundaries is re-examined. For nearly incompressible flows, it is shown that the surface integrals, believed to be the source of relatively strong surface sound, may, in fact, merely give the reflecting and diffracting effect of the surface on volume-generated sound. The apparently much larger acoustic effect of hydrodynamic pressure variations may be largely spurious. These characteristics are shown to follow from the use of a simple identity involving the incompressible pressure, which is defined. The present form of the result of this work gives Ribner's source term (known to be equivalent to Lighthill's) for the volume sound. Thus, the total amount of radiated sound can be estimated in the usual way to be proportional to Mach number to the eighth power. There is the usual complication caused by the dependence of the relative turbulence intensity on Mach number. In many boundary-layer applications, the effect of the surface is merely to multiply the intensity of such sound by four. Of course it is true that small objects placed in a uniform flow can generate relatively large velocity fluctuations and cause relatively large amounts of sound to be radiated by the volume sources. It also seems likely that volume sources near small objects will radiate a dipole pattern, though with a Mach number dependence the same as that of volume sources. This is in agreement with experimental observations. [Work was partly done at the Lockheed Palo Alto Research Laboratories; it has been partially supported by ONR].