Measurements of two- and three-dimensional waves in a channel,including the vicinity of cut-off frequencies

Measurements of water wave profiles were performed in a rectangular flume equipped with a modular wavemaker. This particular wavemaker could generate both two- and three-dimensional waves. A method is proposed to evaluate quantitatively the deviations of a spacial flow field from the two-dimensional one. Plane propagating waves, as well as pure sloshing waves with their crests parallel to the walls, were generated in the flume. In all cases the measured amplitudes were compared against linear theory predictions.     

Soft Neutral Elastic Inhomogeneities with Membrane-type Interface Conditions

A foreign body, called an “inhomogeneity,” when introduced in a host solid disturbs the stress field which is present in it. One can explore the possibility of modifying the contact mechanism between the inhomogeneity and the host body so as to leave the stress field in the host solid undisturbed. If such a procedure succeeds, then the inhomogeneity is called “neutral.” Modification of the contact mechanism between the inhomogeneity and the host solid can be achieved, for example, by a suitably designed thick or thin interphase between them. When the interphase is thin, it can be represented by an “imperfect interface” model. In the present study we consider “soft” inhomogeneities which are more compliant than the host body. A “membrane-type interface” which models a thin and stiff interphase is used in rendering such inhomogeneities neutral. Illustrative examples are constructed for cylindrical neutral inhomogeneities of elliptical cross section under a triaxial loading, and for spheroidal inhomogeneities subjected to an axisymmetric loading.      

Parametric study of ship maneuverability in laterally restricted waters: Stochastic control approach

A stochastic control approach is used in a parametric study of ship maneuverability in a restricted channel of prescribed geometry. A realistic method, based on some empirical data, is used for the mathematical modelling of the ship motion in deep water.The authors are grateful to Mr. Lodewyk Wessels, Department of Electrical and Electronic Engineering, University of Pretoria, for generating the plots in this article.     

Electrorotation of leaky-dielectric and conducting microspheres in asymmetric electrolytes and angular velocity reversal

We consider the central problem of polarizable and leaky-dielectric uncharged spherical particle freely suspended in an unbounded nonsymmetric binary electrolyte, which is forced by an ambient time-harmonic uniform electric field. Under the assumption of a “weak field,” we employ the linearized standard electrokinetic model of binary electrolytes to account for such anion/cation asymmetry. A simplified generalized asymmetric dipole-term approximation, valid for a dielectric/conducting microsphere, is analytically derived for an arbitrary Debye scale and for any mismatch between ion diffusivities and valances. A two-peak unified dispersion spectrum covering all range of practical frequencies (KHz to MHz), is found for the case of a rotating electric field (ROT). The angular velocity of a free polarized particle is composed of dielectrophoretic contribution, resulting from the electrical torque (dipole term) as well as from the induced electroosmotic (ICEO) flow field. The two effects usually act in opposite directions. Under ROT excitation, we obtain a cofield rotation at high frequencies (MHz) and a counter-field behavior at low frequencies (KHz). The low-frequency dispersion is generally governed by electric double-layer charging and the high frequency by a Maxwell–Wagner relaxation process. ICEO generally dominates the low-frequency cofield response; however, it can be shown that depending on the electrolyte asymmetry, yet another dielectrophoretic related switching (reversal) point might exist. Furthermore, for large frequencies and depending on the complex permittivity ratio between the particle and electrolyte, we find a second switching point. Explicit expressions for the above two frequency reversal values are obtained in terms of the problem physical parameters and are compared against experimental results. Finally, we provide an analytical solution for the ROT ICEO velocity field of a microsphere as a function of electrolyte asymmetry and Debye length and compare it with numerical simulations.     

Induced-charge electrophoresis of uncharged dielectric spherical Janus particles

We derive the equations governing the dipolophoretic motion of an electrically inhomogeneous Janus particle composed of two hemispheres with differing permittivities. The general formulation is valid for any electric forcing, including alternating current (AC) and makes no assumptions regarding the size of the electric double layer (EDL). The solution is thus valid even for nanoparticles where the particle radius can be of the same order as the EDL thickness. Semi-analytic and numerical solutions for the linear phoretic velocity and angular rotation of a single Janus particle suspended in an infinite medium are given in the limit of uniform direct current (DC) electric forcing. It is determined that particle mobility is a function of the permittivity in each hemisphere and the contrast between them as well as the EDL length. For a particle in which both hemispheres are characterized by a finite permittivity, we discover that maximum mobility and rotation is not obtained in the Helmholtz-Smoluchowski thin EDL limit but is rather a function of the permittivity and EDL properties.     

On the control and guidance of the motion of an immersed body: Some problems in stochastic control

In this work, the following problem is considered. A rigid body is moving immersed in a fluid of infinite depth. Its goal is to hit another body which floats on the surface of the fluid. Using stochastic control methods, a sequence of subproblems concerning the guidance and control of the immersed rigid body are dealt with.     

Theoretical analysis of heat and mass transfer through eccentric spherical fluid shells at large peclet number

A mathematical analysis of the transport of heat or mass through eccentric spherical closed fluid shells at large Peclet numbers is presented. The bispherical coordinates system is utilized to solve the flow of heat or mass between the two spherical boundaries. The analysis also includes an approximate solution for the motion, if exists, of the inner sphere within the external one. These solutions are then employed in analysing the problem of the evaporation of three-phase liquid drop. The general analysis presented here might prove useful also in the general case of soap bubble (as in foam) or in liquid-liquid systems.Nomenclature a constant - A constant (=a/R ₀) - C _D drag coefficient - g gravitational acceleration - G density ratio (= ₁/ _v) - h , h , h linearizing factors of bispherical coordinates - k thermal conductivity of fluid enclosed between the shells - unit vector in the direction of gravitational acceleration - K drag constant (=16.0 to 24.0) - l distance between the image doublet and outer sphere center - L _r longtitudal reference scale (=R ₀) - P* pressure of the system - q heat flux through the sphere area - q _av average rate of heat absorption in the case of concentric spheres (=q _c/t _c) - q _n heat flux per unit area of a sphere - Q dimensionless heat flux (=q/q _c) - r _i radius of interior sphere - r ₀ radius of exterior sphere - Re, c characteristic Reynolds number (= 2R ₀(R ₀/t _c)/) - R ₁ radius of liquid mother drop - R ₀ initial value of R ₁ - R _v radius of inner vapour bubble - s distance between centers of spheres - S dimensionless distance between centers of spheres (=s/R ₀) - t time - t _c time required for complete evaporation in the case of concentric system - t _r reference scale for time (=t _c) - T temperature - T _i temperature of inner spherical surface - T ₀ temperature of outer spherical surface - T* saturation temperature corresponding to P* - T temperature of undisturbed field - T temperature driving force (T–T*) - u _c translatory velocity of inner bubble (u _c=u _c ) - V volume of inner bubble - x cartesian coordinate - y cartesian coordinate - z cartesian coordinate - dimensionless radius (=r/R ₀ or R/R ₀) - point doublet strength - ₁ first image of - ₁ density of fluid enclosed between the shells (liquid) - _v density of fluid enclosed in the inner sphere (vapour) - ₁ kinematic viscosity of fluid enclosed between the shells (liquid) - heat of evaporation - bispherical coordinate, liquid viscosity in eq. (25) - bispherical coordinate - bispherical coordinate - dimensionless time (=t/t _c)     

Collision Avoidance by a Ship with a Moving Obstacle: Computation of Feasible Command Strategies

A ship moving from a point A to a point B detects a moving small obstacle at close range. Hence, the ship has to perform a maneuver to avoid collision with the moving obstacle. Using a realistic model of a tanker ship, a method is proposed for computing feasible rudder command strategies for performing the collision-avoidance maneuver.     

Dipolophoresis of Janus nanoparticles in a microchannel

A nonlinear dipolophoretic analysis is applied to analytically explain the counterintuitive experimental results of Gangwal et al. [16, 17] that an uncharged micro/nanosize dielectric Janus particle is attracted to the wall of a microchannel when exposed to an AC‐uniform electric field in the direction parallel to the no‐slip boundaries. We employ the so‐called “weak” field assumption and consider a metallodielectric Janus colloid comprising two semispheres of distinct dielectric properties subject to an oscillating‐uniform electric field with moderate frequency (below the Maxwell–Wagner limit). The Debye scale (ratio of electric double layer thickness to particle size) is considered unrestricted. Under the low Reynolds number hypothesis, Faxén's theorem and the Green's function (Stokeslet) method of singularities, including appropriate images with respect to the no‐slip boundary, are applied under the remote‐field approximation to determine the dynamics and trajectory of a small colloid moving near a wall. When assuming maximum dielectric contrasts between hemispheres and relatively low Debye scale (compared to particle radius), a rather simple relation for the equilibrium position of the colloid (i.e. tilt angle and distance from the wall) is obtained and found to be in qualitative good agreement with the experimental observations of Gangwal et al. [16, 17] and the predictions of Kilic and Bazant [12].