# Latest papers in fluid mechanics

### Printing quality improvement for laser-induced forward transfer bioprinting: Numerical modeling and experimental validation

Laser-induced-forward-transfer (LIFT)-based laser assisted bioprinting (LAB) has great advantages over other three-dimensional (3D) bioprinting techniques, such as none-contact, free of clogging, high precision, and good compatibility. In a typical LIFT based LAB process, a jet flow transfers the bioink from the ribbon to the substrate due to bioink bubble generation and collapse, and the printing quality is highly dependent on the jet flow regime (stable or unstable), so it is a great challenge to understand the connection between the jet flow and the printing outcomes. To tackle this challenge, a novel computational-fluid-dynamics (CFD)-based model was developed in this study to accurately describe the jet flow regime and provide guidance for optimal printing process planning, and a great agreement with the difference of less than 14% can be achieved when the length of induced jet is compared with experiments. By adopting the printing parameters recommended by the CFD model, the printing quality was greatly improved by forming a stable jet regime and organized printing patterns on the substrate, and the size of printed droplet could also be accurately predicted using the CFD simulation results through a static equilibrium model. Then, a well-organized pattern with alphabets “UT-CUMT” according to the chosen printing parameters was successfully printed. The ultimate goal of this research is to develop a solid connection between mechanical engineering community and bioprinting community by utilizing the proposed CFD model to direct the LAB process and eventually improve the quality of bioprinting.

### Secondary lock-in of vortex-induced vibration and energy transfer characteristics of a vibrating cylinder subject to cross buoyancy

The hydrodynamic and thermal characteristics of a freely vibrating circular cylinder subject to cross buoyancy are numerically investigated at low Reynolds numbers. The structural responses and onset of vortex-induced vibration (VIV) are documented over a range of parameter space, [math] reduced velocity (Ur) [math] Prandtl number (Pr) [math] and [math] Richardson number (Ri) [math]. The fluid and structural coefficients are chosen as Reynolds number [math], mass ratio [math], and damping ratio [math]. A phenomenon of secondary VIV lock-in is found in the cases of Ri = 2.0 (the cross buoyancy effect becomes influential), [math] and [math]. An extended VIV lock-in region is formed over a wide range of reduced velocity values together with a tremendous kinetic energy transfer between fluid and structure. This finding is significant for the research of hydropower harvesting. On the other hand, the influence of structural dynamics on heat convection over the surface of a heated circular cylinder is recorded and discussed as well. The significance and mutual influence between Prandtl and Richardson numbers on hydrodynamics, structural dynamics, and heat convection are discussed in detail. The temperature contours are found concentrating around the cylinder's surface in the cases of high Prandtl numbers, which are also associated with higher mean Nusselt number ([math]) values. The influence on heat convection over a cylinder's surface is quantified via the computation of [math] and its fluctuation for different circumstances. The energy transfer coefficient is employed to quantify the kinetic energy transfer between the fluid and a heated structure in mixed convective flow. The phase angle difference between the transverse displacement and lift force is used to support the discussions of energy transfer in fluid.

### Shock wave structures in an isentropically unstable heat-releasing gas

In this work, we analytically and numerically investigate the types of stationary gasdynamic waves formed in a heat-releasing medium with isentropic (acoustic) instability. As the mathematical model, the system of one-dimensional gasdynamic equations is used, in which the heating and cooling processes are taken into account using the generalized heat-loss function. Our analysis reveals that the type of stationary structures depends on their velocity W and heating/cooling processes acting in the medium. In an isentropically unstable medium, it is shown that the type of structures depends on whether they propagate faster or slower than the critical velocity Wcr. If [math], a shock wave is formed, in which, after the shock-wave compression, the gas expands to a stationary value. The characteristic size of the expansion region depends on the characteristic heating time, which is determined by the specific type of the heat-loss function. If [math], the shock wave turns out to be unstable and decays into a sequence of autowave (self-sustaining) pulses. The amplitude and velocity ([math]) of the autowave pulse, found analytically in the article, are also determined by the type of the heat-loss function. The comparison of analytical predictions of the developed method with the results of nonlinear equation previously obtained using the perturbation theory, as well as with the numerical simulations, confirms the high accuracy of the method.

### Similarity solutions for strong shock waves in non-ideal magnetogasdynamics under the effect of monochromatic radiation

This manuscript aims to deal with the one-dimensional unsteady flow of non-ideal gas with monochromatic radiation under the influence of a magnetic field, where the invariance method of the Lie group of transformations is applied in a cylindrically symmetric motion. The density is assumed to be uniform in the undisturbed medium. The radiation flux is considered to move through the non-ideal gas. The self-similar solutions of the considered model are obtained for the power-law and the exponential-law shock paths. The effects of the adiabatic exponent, radiation parameter, ambient magnetic field, and the parameter of non-idealness on the flow variables are shown graphically. Numerical calculations are performed to obtain the self-similar solutions.

### Variational balance models for the three-dimensional Euler–Boussinesq equations with full Coriolis force

We derive a semi-geostrophic variational balance model for the three-dimensional Euler–Boussinesq equations on the nontraditional f-plane under the rigid lid approximation. The model is obtained by a small Rossby number expansion in the Hamilton principle, with no other approximations made. We allow for a fully non-hydrostatic flow and do not neglect the horizontal components of the Coriolis parameter; that is, we do not make the so-called “traditional approximation.” The resulting balance models have the same structure as the “L1 balance model” for the primitive equations: a kinematic balance relation, the prognostic equation for the three-dimensional tracer field, and an additional prognostic equation for a scalar field over the two-dimensional horizontal domain, which is linked to the undetermined constant of integration in the thermal wind relation. The balance relation is elliptic under the assumption of stable stratification and sufficiently small fluctuations in all prognostic fields.

### Hybrid lattice-Boltzmann finite-difference simulation of ternary fluids near immersed solid objects of general shapes

In this paper, a hybrid lattice-Boltzmann finite-difference method is developed for the simulation of ternary fluids near immersed solid objects of general shapes. The flow equations are solved by the lattice-Boltzmann method and the coupled Cahn–Hilliard equations for interface evolutions are solved by the finite-difference method. A special implementation of the wetting boundary condition on a surface of general shapes immersed inside the domain was extended for ternary fluids within the phase-field framework with no need to use complicated interpolations. Several two and three dimensional problems with three immiscible fluids were studied by using the proposed method and the results agree well with analytical predictions and/or previous numerical and experimental studies. In particular, the inclusion of properly chosen free energy to handle total spreading enabled us to numerically reproduce the encapsulation of a small droplet by another bigger one of different component on a round fiber. The proposed method is expected to be useful to investigate a variety of multiphase problems involving ternary fluids and surfaces with different configurations, including the challenging total spreading regime.

### Between droplets and fluid thread—the role of gravity in meso-scale flow

How gravity affects immiscible liquid co-flow is best illustrated through experiments in inclined conduits. In the macro-domain, gravity leads to flow stratification while in the microscale, the phase distribution is practically insensitive to conduit tilt. The influence of flow orientation in the intermediate scale conventionally known as meso-domain or milli-channel, although noted, has not been discussed earlier. In the present study, flow morphology is experimentally investigated during up, down, and horizontal co-flow of a biphasic liquid mixture in a glass conduit of diameter 2.38 mm. In all orientations, the dispersed phase flows either as droplets/plugs or as a continuous thread. Gravity modulates the process of thread pinch off and regulates the domain of thread/droplet flow. Apart from flow orientation, we also note entry arrangement to influence droplet detachment in horizontal conduit. The experimental observations are explained from a simplified analysis based on momentum and energy considerations; the defining parameters are fluid properties and flow rates, conduit dimension, and flow orientation. The proposed analysis, albeit the approximations, has successfully predicted thread pinch off for the present experiments. Pinch off from the thread tip is noted to be cyclic and comprises several steps, of which inception of necking to its completion is only a part.

### Linear stability of a thin fluid film interacting with its surrounding bulk fluid

Thin films can become unstable when attractive van der Waals forces overcome the stabilizing effects of surface tension and viscous forces. In many applications, the effect of the surrounding bulk fluid cannot be neglected when considering a thin film subject to perturbations. In this work, we examine the two limits of potential flow and Stokes flow in the surrounding bulks to derive dispersion relations in each limit. We show that the effect of the surrounding bulks cannot be ignored for many film–bulk fluid pairings and film thicknesses and present conditions for the validity of each regime. In particular, the potential-flow regime exists when van der Waals forces are sufficiently strong, while the Stokes-flow regime exists when the bulk dynamic viscosity is sufficiently large. Due to the nature of the dispersion relation in the Stokes-flow limit, several distinct scenarios are identified in the corresponding stability diagram, each involving the interplay of different forces. For example, a novel instability regime involving capillary–viscous interactions is identified for large film thicknesses. Finally, by enlisting multiple realistic fluid pairings and film thicknesses wherein such instabilities can occur, we demonstrate the practical relevance of our theoretical findings. This work enables the extension of thin film stability theory to the analysis of antibubbles, splashing molten metals and ionic liquids, Mesler entrainment of microbubbles in breaking waves, and emulsion stability.

### Droplet impact dynamics on an aluminum spinning disk

Droplet impact on a spinning surface has been observed in different industries and plays an important role in the performance of industrial systems. In the current study, the dynamics of water droplet impact on a hydrophilic spinning disk is investigated. An experimental setup is designed in a way that droplet diameter, impact velocity, disk rotational speed, and location of impact are precisely controlled. While the droplet diameter is fixed in the present study, other mentioned parameters are changed and their effects on the droplet behavior are discussed. High-speed imaging is used to record the droplet dynamics under various operating conditions. It is demonstrated that after impact, droplet spreads on the surface due to a high adhesion between water and the hydrophilic substrate. It is indicated that the wetted area is a function of time, impact velocity, disk rotational speed, and centrifugal acceleration. Furthermore, depending on the mentioned parameters, different phenomena such as rivulet formation, fingering, and detachment of secondary droplet(s) are observed. In the angular direction, in general, the wetted length increases as time passes. However, in the radial direction, the droplet first spreads on the surface and reaches a maximum value, and then recedes until a plateau is attained. At this instant, a bulk of liquid, which is called wave in this study, moves radially outward from the inner boundary of the droplet toward its outer boundary due to the effect of centrifugal force. Once the wave reaches the outer boundary, depending on its size and momentum, fingers or rivulets are formed, and small droplet(s) may detach. The process is analyzed comprehensively, and different empirical correlations for wetted lengths in radial and angular directions, secondary droplet formation, number of fingers, the onset of fingering, and wave velocity are developed.

### Influence of magnetic field in the control of Taylor column phenomenon in the translation of a sphere in a rotating fluid

A numerical investigation has been performed to capture how the magnetic field interferes with Taylor column—a spectacular phenomenon occurring as a result of the Coriolis effect. In this pursuit, at first, we have considered the incompressible flow past a translating sphere in a rotating viscous fluid. This setup allows us to capture the Taylor column in the upstream region at critical values of inverse Rossby number ([math]) along with the subsequent formation of a cyclonic vortex in the downstream region as [math] is increased. However, flow separation of any kind is considered to be an undesirable flow feature from industrial perspectives. We found that an application of magnetic field aligned with the motion of the sphere induces Lorentz force into the flow field that suppresses the Taylor column for lower values of [math], and, it dissolves the cyclonic vortex formed at higher values of [math]. The strength of the Coriolis and Lorentz forces, their mutual interaction, and the value of inverse Rossby number determines the growth and decay of the Taylor column and the cyclonic vortex, thereby, regulating the ultimate nature of the flow.

### Exact solution to the main turbulence problem for a compressible medium and the universal [math]8/3 law turbulence spectrum of breaking waves

An exact analytical solution to the one-dimensional compressible Euler equations in the form of a nonlinear simple wave is obtained. In contrast to the well-known Riemann solution, the resulting solution and the time of its collapse [math] have an explicit dependence on the initial conditions. For the non-zero dissipation the regularization of the solution over an unlimited time interval is justified. Based on this solution of the Euler equations, an exact explicit and closed description for any single- and multi-point characteristics of turbulence in a compressible medium are obtained, and Onsager's dissipative anomaly is considered. The exact turbulence energy universal spectrum [math], corresponding to the time [math] of the shock arising, is stated. That spectrum is more relevant to the strong acoustic turbulence than the well-known spectrum [math]. Installed, spectrum−8/3 is also matched with the observed compressible turbulence spectrum in the magnetosheath and solar wind. The turbulence energy dissipation rate fluctuations universal spectrum [math] is obtained and corresponds to the known observation data in the atmospheric surface layer.

### Path instability of a no-slip spheroidal bubble in isotropic turbulence

Author(s): Gihun Shim, Jongsu Kim, and Changhoon Lee

Path instability of a millimetric spheroidal bubble in isotropic turbulence is investigated by direct numerical simulation combined with an immersed boundary method. The zigzag frequency and the degree of obliquity of the bubble are enhanced with the strength of the background turbulence.

[Phys. Rev. Fluids 6, 073603] Published Tue Jul 13, 2021

### Lord Kelvin's isotropic helicoid

Author(s): Darci Collins, Rami J. Hamati, Fabien Candelier, Kristian Gustavsson, Bernhard Mehlig, and Greg A. Voth

Can a propeller be isotropic? Nearly 150 years ago, Lord Kelvin proposed the isotropic helicoid, but there are no published measurements on his particle. We 3D-printed his particle and unexpectedly found no measurable translation-rotation coupling. We explain these results by demonstrating theoretically and computationally that Kelvin’s proposed coupling exists, but it is small since it is only due to a weak breaking of a symmetry of non-interacting vanes in Stokes flow.

[Phys. Rev. Fluids 6, 074302] Published Tue Jul 13, 2021

### Fluid dynamics investigation of a large array

The influence of surrounding fluid on a large array of oscillators is important to study for applications in fields such as medicine, biology, and atomic force microscopy. In the present study, we investigate a large array of cantilever beams oscillating in an unbounded fluid to better understand the fluid dynamic behavior. The two-dimensional boundary integral method is applied to analyze a large array of cantilever oscillators using an analytical solution approach for the unsteady Stokes and continuity equations. We analyze array sizes from 5 to 50 beams by comparing hydrodynamic transverse force and velocity profiles for two different velocity configurations. Including the interactions of neighbor and non-neighbor members leads to distinct array effects. With an increase in the number of oscillators in an array, the array effect influences the overall dynamics. Furthermore, to justify the influence of an array effect, the hydrodynamic loading is compared to the same and varying array surface area of different array sizes. Our analysis and new findings strengthen our hypothesis that the predictions of existing knowledge obtained from small-size arrays and coupled oscillators cannot readily inform dynamic predictions of large-size arrays. The underlying reason being the additional array effect(s) which are not present in a small-size array. The novelty of this paper is the ability to model such large arrays and investigate the array effect in an unbounded fluid.

### A deterministic model for bubble propagation through simple and cascaded loops of microchannels in power-law fluids

This paper investigates the path selection of bubbles suspended in different power-law carrier liquids in microfluidic channel networks. A finite volume-based numerical method is used to analyze the two-dimensional incompressible fluid flow in microchannels, while the volume of fluid method is used to capture the gas–liquid interface. To instill the influences of shear thinning, Newtonian, and shear-thickening fluids, the range of power-law indices (n) is varied from 0.3 to 1.5. We have validated our numerical model with the available literature data in good agreement. We have investigated the nonlinearity in the hydrodynamic resistance which arises due to single-phase non-Newtonian fluid flow. The path selection of a bubble in power-law fluids is examined from the perspective of velocity distribution and bubble deformation. We have found that the bubble indeed goes to the channel with a higher flow rate for all power-law fluids, but interestingly it did not always take the shorter route channel at a junction for n = 0.3. Our results suggest that long channels need not be more resistant for every fluid and that the longest arm becomes the least resistant resulting in the bubble leading into the long arm at a junction for shear-thinning fluid. We have proposed a deterministic model that enables predicting the second bubble path in a single bubble system for any location of the first bubble. We believe that the present study results will help design future generation microfluidic systems for efficient drug delivery and biomedical and biochemical applications.

### A direct relaxation process for particle methods in gas-kinetic theory

The multi-scale flow mechanism is crucial for the force and heat loaded on near-space vehicles, the control of spacecraft, and the propelling and cooling of microelectromechanical systems. Since the continuum and rarefied flows often coexist, the prediction of multi-scale flow is complicated. One efficient way is constructing numerical methods by adopting the multi-scale temporal integral solutions (or characteristic line solutions) for model equations in the gas-kinetic theory. The model equations can be classified into the Fokker–Planck type and Bhatnagar–Gross–Krook type (BGK-type). Since these numerical methods are strictly based on model equations, they are also restricted by the model equations. The difficulty in constructing a model equation that has complete asymptotic preserving property for gas mixture with non-equilibrium internal energy will prevent the further extension of these methods. Therefore, this paper addresses the question whether a multi-scale numerical method can be established by directly adopting the relaxation rates of macroscopic variables, such as stress and heat flux, because these relaxation rates are the aggregate effect of particle collisions and are the essential constrains when constructing model equations. Since the particle-BGK method is concise, its collision term is replaced by the direct relaxation process, where the macroscopic variables first evolve according to their relaxation rates, and then, the after-collision molecules get their velocities from the after-evolution macroscopic variables. Therefore, the modified particle-BGK method does not depend on model equations. Finally, the validity and accuracy of the present method are examined with homogenous relaxation case, shock tube, shock structure, cavity flow, and hypersonic cylinder flow in transitional regime.

### Analytical and experimental modeling of the hydrocarbon slick form and its spreading on the water surface

This paper is devoted to the effect of different physical and chemical properties of contacting media on the hydrocarbon spreading process on the water surface as well as the comparison of analytically acquired expressions for the form of the hydrocarbon slick observed in experiments. The equations that define the quasi-stationary form of the hydrocarbon slick are presented and numerically solved. Experiments on the compact oil slick field growth under different physical conditions are made. It is shown that the growth of the oil spill slick area with time is greater on fresh water than on saline and also depends on the oil volume and its properties. The dependency of spreading area size on the salinity of water is also revealed.

### On the theory of Biot-patchy-squirt mechanism for wave propagation in partially saturated double-porosity medium

Reservoir rocks have a coherent heterogeneous porous matrix saturated by multiple fluids. At long wavelength limit, the composite material of solid skeleton is usually regarded as homogeneous media. However, at grain scale or high loading rate, non-uniform fluid flow plays an essential role in wave dispersion and attenuation. Formulating wave propagation in partially saturated and fractured rocks is challenging and is of great interest in geoscience. Recent studies have shown that the mechanisms of wave attenuation caused by viscous dissipation, patchy-saturation, and squirt flow are different. However, the relationship among these mechanisms and the combined effect on wave attenuation are not clear. Here, a Biot-patchy-squirt (BIPS) model is proposed to characterize wave dispersion/attenuation in fractured poroelastic media saturated by immiscible fluids. BIPS model incorporates local fluid-interface flow (LFIF) and squirt flow into global fluid flow simultaneously. Theoretical analysis shows that BIPS is consistent with the Biot theory, squirt flow, and LFIF models, and is reduced to these models under extreme conditions. More interestingly, numerical simulations reveal that the existence of squirt flow partially counterbalances the dissipative effect of LFIF at the patch interface. The attenuation-frequency relationship observed in experiments capturing evidence of squirt flow and patchy-saturation interface flow is reproduced by using the BIPS model. The results show that BIPS model is computationally reliable and is in reasonably good agreement with laboratory data. The findings advance understanding of the physics of wave propagation in natural reservoir rocks and push forward the potential applications of the triple dispersion/attenuation mechanism to wave velocity prediction.

### Turbulence of melt-blowing airflow field: Comparison of a convergent jet and a typical free jet

The turbulent characteristics of the melt-blowing convergent jet and a typical free jet are compared based on the data obtained from hot-wire measurements. For the first time, the effects of the impingement, which is created by the two jet branches issuing from a convergent jet nozzle, on the turbulence intensity, Reynolds shear stress, and power spectral density of turbulent velocities, are investigated. The results show that the impingement leads to greater and faster spread of the additional turbulent shear stress and a larger portion of higher frequency components. The characteristics of the dual-impinging jets under the slot-die nozzle provide the possibility of controlling the melt-blowing airflow field.

### Drag reduction of a D-shaped bluff-body using linear parameter varying control

In this work, we report on a closed-loop flow control strategy that consistently reduces the drag of a D-shaped bluff body under variable freestream velocity conditions. The control strategy is guided by open-loop tests with pulsed Coanda blowing at two freestream velocities that yield optimal frequencies (Strouhal number of 0.33 and 1.3), which reduce the drag by up to 40%. The strong correlation between drag coefficient (Cd) and the wake fluctuations is exploited for the feedback signal, where a microphone signal is used to measure the pressure fluctuations at the model base. The results demonstrate the ability to perform accurate and robust [math]-based control for drag reduction using solely the wake pressure fluctuations at the model base as feedback signal. The robust control strategy at constant freestream velocity is shown to improve output stability and enhance performance in terms of settling time, even when employing simple models of the flow response with large uncertainty. Building on that success, an [math]-based linear parameter varying controller is designed and implemented to reduce drag under free stream variations and/or fluctuations. Similarly, the results demonstrate improved robustness and performance enhancements.