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Solute transport and mixing in heterogeneous porous media are important to many processes of practical applications. Most of the previous studies focused on solute transport in flow of Newtonian fluids, whereas there are many processes in which the phenomenon takes place in flow of a non-Newtonian fluid. In this paper, we develop a computational approach to evaluate and upscale dispersion of a solute in flow of a shear-thinning (ST) fluid in a heterogeneous porous medium. Our results indicate that the dispersivity is a non-monotonic function of the Péclet number and the shear rate, and this behavior is accentuated by the heterogeneity of the pore space and spatial correlations between the local permeabilities. As a result, solute transport in ST fluids deviates significantly from the same phenomenon in Newtonian fluids. Moreover, the shear-dependence of the dispersivity strongly influences the fate of solute transport in porous media at large length scales, including larger effluent concentration at the breakthrough point, which also occurs much faster than Newtonian fluids. To provide further evidence for the numerical findings, we compare dispersion in flow of a power-law fluid in a single tube with the same in a bundle of such tubes. Our results emphasize the shortcomings of the current theories of dispersion to account for the role of fluid rheology in solute mixing and spreading. [ABSTRACT FROM AUTHOR]

Theoretical models for the frequency response of a cantilever beam immersed in a viscous fluid commonly assume that the fluid is unbounded. Experimental measurements show, however, that proximity to a surface can significantly affect the frequency response of a cantilever beam. In this article, we rigorously calculate the effect of a nearby surface on the frequency response of a cantilever beam immersed in a viscous fluid, and present a general theoretical model. Due to its practical relevance to applications of the atomic force microscope and microelectromechanical systems, detailed results are presented for cantilever beams with rectangular geometries executing flexural and torsional oscillations. It is found that dissipative loading in the fluid is primarily responsible for the observed variation in the frequency response, whereas inertial loading exerts a relatively weak influence. [ABSTRACT FROM AUTHOR]

A general scaling law connecting the stiffness and dissipative properties of a linear mechanical oscillator immersed in a viscous fluid is derived. This enables the noninvasive experimental determination of the stiffness of small elastic bodies of arbitrary shape by measuring their resonant frequency and quality factor in fluid (typically air). In so doing, we elucidate the physical basis of the method of Sader et al. [Rev. Sci. Instrum. 70, 3967 (1999)] for determining the stiffness of rectangular atomic force microscope cantilevers, and discuss its applicability. The validity of the derived general technique is demonstrated by calibrating atomic force microscope cantilevers with complex geometries, and its implications to small bodies in general are discussed. [ABSTRACT FROM AUTHOR]

A two-dimensional lattice-Boltzmann model (LBM) with fluid-fluid interactions was used to simulate first-order phase separation in a thin fluid film. The intermediate asymptotic time dependence of the mean island size, island number concentration, and polydispersity were determined and compared with the predictions of the distribution-kinetics model. The comparison revealed that the combined effects of growth, coalescence, and Ostwald ripening control the phase transition process in the LBM simulations. However, the overall process is dominated by coalescence, which is independent of island mass. As the phase transition advances, the mean island size increases, the number of islands decrease, and the polydispersity approaches unity, which conforms to the predictions of the distribution-kinetics model. The effects of the domain size on the intermediate asymptotic island size distribution, scaling form of the island size distribution, and the crossover to the long-term asymptotic behavior were elucidated. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The frequency response of a cantilever beam is strongly dependent on the fluid in which it is immersed. In a companion study, Sader [J. Appl. Phys. 84, 64, (1998)] presented a theoretical model for the flexural vibrational response of a cantilever beam, that is immersed in a viscous fluid, and excited by an arbitrary driving force. Due to its relevance to applications of the atomic force microscope (AFM), we extend the analysis of Sader to the related problem of torsional vibrations, and also consider the special case where the cantilever is excited by a thermal driving force. Since longitudinal deformations of AFM cantilevers are not measured normally, combination of the present theoretical model and that ofthe companion study enables the complete vibrational response of an AFM cantilever beam, that is immersed in a viscous fluid, to be calculated. [ABSTRACT FROM AUTHOR]

New analytical solutions are presented for steadily translating von Kármán vortex streets made up of two infinite rows of hollow vortices. First, the solution for a single row of hollow vortices due to Baker et al. ["Structure of a linear array of hollow vortices of finite cross-section," J. Fluid Mech. 74, 469 (1976)] is rederived, in a modified form, and using a new mathematical approach. This approach is then generalized to find relative equilibria for both unstaggered and staggered double hollow vortex streets. The method employs a combination of free streamline theory and conformal mapping ideas. The staggered hollow vortex streets are compared with analogous numerical solutions for double streets of vortex patches due to Saffman and Schatzman ['Properties of a vortex street of finite vortices,' SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. 2, 285 (1981)] and several common features are found. In particular, within the two different inviscid vortex models, the same street aspect ratio of approximately 0.34-0.36 is found to have special significance for the equilibria. [ABSTRACT FROM AUTHOR]

The hydrodynamic loading on a solid body moving in a viscous fluid can be strongly affected by its proximity to a surface. In this article, we calculate the hydrodynamic load on an infinitely long rigid beam of zero thickness that is undergoing small amplitude oscillations. The presence of a solid surface an arbitrary distance from the beam is rigorously accounted for using a boundary integral formulation. [ABSTRACT FROM AUTHOR]

Two methods commonly used to measure the normal spring constants of atomic force microscope cantilevers are the added mass method of Cleveland et al. [J. P. Cleveland et al., Rev. Sci. Instrum. 64, 403 (1993)], and the unloaded resonance technique of Sader et al. [J. E. Sader, J. W. M. Chon, and P. Mulvaney, Rev. Sci. Instrum. 70, 3967 (1999)]. The added mass method involves measuring the change in resonant frequency of the fundamental mode of vibration upon the addition of known masses to the free end of the cantilever. In contrast, the unloaded resonance technique requires measurement of the unloaded resonant frequency and quality factor of the fundamental mode of vibration, as well as knowledge of the plan view dimensions of the cantilever and properties of the fluid. In many applications, such as frictional force microscopy, the torsional spring constant is often required. Consequently, in this article, we extend both of these techniques to allow simultaneous calibration of both the normal and torsional spring constants. We also investigate the validity and applicability of the unloaded resonance method when a mass is attached to the free end of the cantilever due to its importance in practice. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The in-plane deformation of atomic force microscope (AFM) cantilevers under lateral loading is commonly assumed to have negligible effect in comparison to other deformation modes and ignored. In this article, we present a theoretical study of the behavior of cantilevers under lateral loading, and in so doing establish that in-plane deformation can strongly contribute to the total deformation, particularly for rectangular cantilevers of high aspect ratio (length/width). This has direct implications to lateral force microscopy, where the neglect of in-plane deformation can contribute to significant quantitative errors in force measurements and affect the interpretation of measurements. Consequently, criteria and approaches for minimizing the effects of in-plane deformation are presented, which will be of value to users and designers of AFM cantilevers. Accurate analytical formulas for the in-plane spring constants of both rectangular and V-shaped cantilevers are also presented. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A correction to the article "Frequency response of cantilever beams immersed in viscous fluids near a solid surface with applications to the atomic force microscope," that was published in the previous issue is presented.

A two-dimensional lattice-Boltzmann model (LBM) with fluid-fluid interactions was used to simulate first-order phase separation in a thin fluid film. The intermediate asymptotic time dependence of the mean island size, island number concentration, and polydispersity were determined and compared with the predictions of the distribution-kinetics model. The comparison revealed that the combined effects of growth, coalescence, and Ostwald ripening control the phase transition process in the LBM simulations. However, the overall process is dominated by coalescence, which is independent of island mass. As the phase transition advances, the mean island size increases, the number of islands decrease, and the polydispersity approaches unity, which conforms to the predictions of the distribution-kinetics model. The effects of the domain size on the intermediate asymptotic island size distribution, scaling form of the island size distribution, and the crossover to the long-term asymptotic behavior were elucidated.