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1. Laboratory study of bed shear stress in gradually varied flow over a sudden change in bed roughness

   https://doi.org/10.1007/s10652-025-10024-6  

   Jamil, Muhammad Farrukh; Ting, Francis_C K; Kafle, Monika (April 2025, Environmental Fluid Mechanics)

   Abstract The evolution of bed shear stress in open-channel flow due to a sudden change in bed roughness was investigated experimentally for rough-to-smooth (RTS) and smooth-to-rough (STR) transitions. The velocity field was measured in the longitudinal-vertical plane from upstream to downstream using a Particle Image Velocimetry system. The bed shear stress was determined from the measured velocity profile and water depth using various methods. It was found that the variation of bed shear stress in gradually varied flow through a roughness transition was influenced by both flow depth and bottom roughness. In both RTS and STR transitions, the bed shear stress adjusted to the new bed condition almost immediately even though the velocity profile away from the bed was still evolving, but unlike external and close-conduit flows the bed shear stress in open-channel flows continued to evolve until the flow depth was uniform. It is shown that the evolution of bed shear stress in a STR transition is dependent on the choice of the displacement height on the rough bed, which affects the mixing length used to derive the logarithmic velocity profile and equivalent roughness. Bed shear stress variation consistent with published data was obtained when the$${k}_{s}/{d}_{90}$$ $k_s/d_{90}$ratio was determined as a function of the$$h/{d}_{90}$$ $h/d_{90}$ratio, where$${k}_{s}$$ $k_s$is the equivalent roughness height,$$h$$ $h$is the flow depth, and$${d}_{90}$$ $d_{90}$is the grain diameter with 90% of finer particles. 

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2. Comparison between shadow imaging and in-line holography for measuring droplet size distributions

   https://doi.org/10.1007/s00348-023-03633-8  

   Erinin, Martin A; Néel, Baptiste; Mazzatenta, Megan T; Duncan, James H; Deike, Luc (May 2023, Experiments in Fluids)

   Kähler, C; Longmire, E; Westerweel, J (Ed.)

   Abstract A direct comparison of the droplet size and number measurements using in-line holography and shadow imaging is presented in three dynamically evolving laboratory scale experiments. The two experimental techniques and image processing algorithms used to measure droplet number and radii are described in detail. Droplet radii as low as$$r = 14$$ $r=14$ µm are measured using in-line holography and$$r = 50$$ $r=50$ µm using shadow imaging. The droplet radius measurement error is estimated using a calibration target (reticle) and it was found that the holographic technique is able to measure droplet radii more accurately than shadow imaging for droplets with$$r \le 625$$ $r\le 625$ µm. Using the measurements of droplet number and size we quantitatively cross-validate and assess the accuracy of the two measurement techniques. The droplet size distributions,N(r), are measured in all three experiments and are found to agree well between the two measurement techniques. In one of the laboratory experiments, simultaneous measurements of droplets ($$r \ge 14$$ $r\ge 14$ µm, using holography) and dry aerosols ($$0.07 \lessapprox r \lessapprox 2$$ $0.07⪅r⪅2$ µm, using an scanning mobility particle sizer and$$0.15 \lessapprox r \lessapprox 5$$ $0.15⪅r⪅5$ µm using an optical particle sizer) are reported, one of the first such comparison to the best of our knowledge. The total number and volume of droplets is found to agree well between both techniques in the three experiments. We demonstrate that a relatively simple shadow imaging technique can be just as reliable when compared to a more sophisticated holographic measurement technique over their common droplet radius measurement range. The agreement in results is shown to be valid over a large range of droplet concentrations, which include experiments with relatively sparse droplet concentrations as low as 0.02 droplets per image. Advantages and disadvantages for the two techniques are discussed in the context of our results. The main advantages to in-line holography are the greater accuracy in droplet radius measurement, greater spatial resolution, larger depth of field, and the high repetition rate and short pulse duration of the laser light source. In comparison, the main advantages to shadow imaging are the simpler experimental setup, image processing algorithm, and fewer computer resources necessary for image processing. Droplet statistics like number and size are found to be very reliable between the two methods for large range of droplet densities,$${\mathcal {P}}_{r>50}$$ $P_{r>50}$, ranging from$$10^{-4} \le {\mathcal {P}}_{r>50} \le 10^{-1}$$ ${10}^{-4}\le P_{r>50}\le {10}^{-1}$cm$$^{-3}$$ ${}^{-3}$, when the two techniques are implemented as shown in this paper. 

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3. A multiple-timing analysis of temporal ratcheting

   https://doi.org/10.1140/epje/s10189-024-00421-y  

   Hashemi, Aref; Gilman, Edward T.; Khair, Aditya S. (April 2024, The European Physical Journal E)

   AbstractWe develop a two-timing perturbation analysis to provide quantitative insights on the existence of temporal ratchets in an exemplary system of a particle moving in a tank of fluid in response to an external vibration of the tank. We consider two-mode vibrations with angular frequencies$$\omega $$ $\omega$and$$\alpha \omega $$ $\alpha \omega$, where$$\alpha $$ $\alpha$is a rational number. If$$\alpha $$ $\alpha$is a ratio of odd and even integers (e.g.,$$\tfrac{2}{1},\,\tfrac{3}{2},\,\tfrac{4}{3}$$ $\frac{2}{1},\frac{3}{2},\frac{4}{3}$), the system yields a net response: here, a nonzero time-average particle velocity. Our first-order perturbation solution predicts the existence of temporal ratchets for$$\alpha =2$$ $\alpha =2$. Furthermore, we demonstrate, for a reduced model, that the temporal ratcheting effect for$$\alpha =\tfrac{3}{2}$$ $\alpha =\frac{3}{2}$and$$\tfrac{4}{3}$$ $\frac{4}{3}$appears at the third-order perturbation solution. More importantly, we find closed-form formulas for the magnitude and direction of the induced net velocities for these$$\alpha $$ $\alpha$values. On a broader scale, our methodology offers a new mathematical approach to study the complicated nature of temporal ratchets in physical systems. Graphic abstract 

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4. The Transition from Darcy to Nonlinear Flow in Heterogeneous Porous Media: I—Single-Phase Flow

   https://doi.org/10.1007/s11242-024-02070-3  

   Arbabi, Sepehr; Sahimi, Muhammad (March 2024, Transport in Porous Media)

   Abstract Using extensive numerical simulation of the Navier–Stokes equations, we study the transition from the Darcy’s law for slow flow of fluids through a disordered porous medium to the nonlinear flow regime in which the effect of inertia cannot be neglected. The porous medium is represented by two-dimensional slices of a three-dimensional image of a sandstone. We study the problem over wide ranges of porosity and the Reynolds number, as well as two types of boundary conditions, and compute essential features of fluid flow, namely, the strength of the vorticity, the effective permeability of the pore space, the frictional drag, and the relationship between the macroscopic pressure gradient$${\varvec{\nabla }}P$$ $\nabla P$and the fluid velocityv. The results indicate that when the Reynolds number Re is low enough that the Darcy’s law holds, the magnitude$$\omega _z$$ ${\omega }_z$of the vorticity is nearly zero. As Re increases, however, so also does$$\omega _z$$ ${\omega }_z$, and its rise from nearly zero begins at the same Re at which the Darcy’s law breaks down. We also show that a nonlinear relation between the macroscopic pressure gradient and the fluid velocityv, given by,$$-{\varvec{\nabla }}P=(\mu /K_e)\textbf{v}+\beta _n\rho |\textbf{v}|^2\textbf{v}$$ $-\nabla P=(\mu /K_e)v+{\beta }_n\rho {\left|v\right|}^{2}v$, provides accurate representation of the numerical data, where$$\mu$$ $\mu$and$$\rho$$ $\rho$are the fluid’s viscosity and density,$$K_e$$ $K_e$is the effective Darcy permeability in the linear regime, and$$\beta _n$$ ${\beta }_n$is a generalized nonlinear resistance. Theoretical justification for the relation is presented, and its predictions are also compared with those of the Forchheimer’s equation. 

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5. Wave optics of imaging with contact ball lenses

   https://doi.org/10.1038/s41598-023-32826-8  

   Maslov, A V; Jin, B; Astratov, V N (December 2023, Scientific Reports)

   Abstract Recent progress in microspherical superlens nanoscopy raises a fundamental question about the transition from super-resolution properties of mesoscale microspheres, which can provide a subwavelength resolution$$\sim \lambda /7$$ $\sim \lambda /7$, to macroscale ball lenses, for which the imaging quality degrades because of aberrations. To address this question, this work develops a theory describing the imaging by contact ball lenses with diameters$$30 $30<D/\lambda <4000$covering this transition range and for a broad range of refractive indices$$1.3<2.1$$ $1.3<n<2.1$. Starting from geometrical optics we subsequently proceed to an exact numerical solution of the Maxwell equations explaining virtual and real image formation as well as magnificationMand resolution near the critical index$$n\approx 2$$ $n\approx 2$which is of interest for applications demanding the highestMsuch as cellphone microscopy. The wave effects manifest themselves in a strong dependence of the image plane position and magnification on$$D/\lambda $$ $D/\lambda$, for which a simple analytical formula is derived. It is demonstrated that a subwavelength resolution is achievable at$$D/\lambda \lesssim 1400$$ $D/\lambda \lesssim 1400$. The theory explains the results of experimental contact-ball imaging. The understanding of the physical mechanisms of image formation revealed in this study creates a basis for developing applications of contact ball lenses in cellphone-based microscopy. 

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