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arXiv2018

Hydrodynamic Impedance Correction for Reduced-Order Modeling and Real-Time Control of Spermatozoa-Like Soft Micro-Robots for Medicine

Hydrodynamic interactions play a key role in the swimming behavior and power consumption of bio-inspired and bio-mimetic micro-swimmers, Cybernetic or artificial alike. As micro-robotic devices, bio-inspired micro-swimmers require fast and reliable numerical models for robust control in order to carry out demanding therapeutic tasks as envisaged for more than sixty years. The fastest known numerical model, the resistive force theory (RFT), incorporates local viscous force coefficients with the local velocity of slender bodies in order to find the resisting hydrodynamic forces, however, omitting the induced far field altogether. In this scheme, the forces are calculated for a pure fluid resistance, however, at the expense of time-dependent hydrodynamic interaction effects. As a result, the power requirement cannot be predicted accurately although the supply of necessary power is one of the biggest obstacles impeding the micro-robotic efforts. In this study, an analysis strategy is proposed to improve the RFT-based analysis, particularly for spermatozoa and spermatozoa-inspired micro-swimmers with elastic slender tails, in order to present a practical solution to the problem. The required analytical correction and the necessary correction coefficients are based on hydrodynamic impedance analysis via intensive computational fluid dynamics (CFD) models, i.e., the time-dependent solution of 3-dimensional Navier-Stokes equations incorporated with deforming mesh and subject to conservation of mass. The CFD-based model results are then used to extract the correction coefficients with the help of a cost function written based on the hydrodynamic power required to sustain the continuous swimming of selected shape and design. The performance of the corrections embedded in the RFT model is finally validated against the CFD model by means of hydrodynamic power comparisons.

physics.flu-dyn↗

arXiv2019

CFD simulation of the wind field over a terrain with sand fences: Critical spacing for the protected soil area

Sand fences are often erected to reduce wind speed, prevent aeolian soil erosion, and induce sand deposition and dune formation in areas affected by sand encroachment and desertification. However, the search for the most efficient array of fences by means of field experiments alone poses a challenging task given that field experiments are affected by weather conditions. Here we apply Computational Fluid Dynamic simulations to investigate the three-dimensional structure of the turbulent wind field over an array of fences of different sizes, porosity and spacing. Our goal is to perform a quantitative analysis of this structure in the absence of saltation or suspension transport, as first step toward the development of a continuum simulation of the aeolian soil in presence of the fences. We find that the area of soil protected against direct aerodynamic entrainment has two regimes, depending on the spacing $L_x$ between the fences. When $L_x$ is smaller than a critical value $L_{xc}$, the wake zones associated with each fence are inter-connected (regime A), while these wake zones appear separated from each other (regime B) when $L_x$ exceeds this critical value of spacing. The system undergoes a second order phase transition at $L_x = L_{xc}$, with the cross-wind width of the protected zone scaling with $\left[{1-{L}_x}/{L}_{xc}\right]^β$ in regime A, with $β\approx 0.32$. Our findings have implication for a better understanding of aeolian transport in the presence of sand fences, as well as to develop optimization strategies for measures to protect soils from wind erosion.

physics.flu-dyn↗

arXiv2018

Effect of layout on asymptotic boundary layer regime in deep wind farms

The power output of wind farms depends strongly on spatial turbine arrangement, and the resulting turbulent interactions with the atmospheric boundary layer. The main goal of this work is to study the effect of turbine layout on the power output for large wind farms approaching a fully-developed regime. For this purpose we employ an experimental setup of a scaled wind farm with one-hundred porous disk models, of which sixty are instrumented with strain gages. Our experiments cover a parametric space of fifty-six different layouts for which the turbine-area-density is constant, focusing on different turbine arrangements including non-uniform spacings. The strain-gage measurements are used to deduce surrogate power and unsteady loading on turbines for each layout. Our results indicate that the power asymptote at the end of the wind farm depends on the layout in different ways. Firstly, for layouts with a relatively uniform spacing we find that the power asymptote in the fully developed regime reaches approximately the same value, similarly to the prediction of available analytical models. Secondly, we show that the power asymptote in the fully-developed regime can be lowered by inefficient turbine placement, for instance when a large number of the turbines are located in the near wake of upstream turbines. Thirdly, our experiments indicate that an uneven spacing between turbines can improve the overall power output for both the developing and fully-developed part of large wind farms. Specifically, we find a higher power asymptote for a turbine layout with a significant streamwise uneven spacing (i.e. a large streamwise spacing between pairs of closely spaced rows that are slightly staggered). Our results thereby indicate that such a layout may promote beneficial flow interactions in the fully-developed regime for conditions with a strongly prevailing wind direction.

physics.flu-dyn↗

arXiv2018

On the optimal focusing of solitons and breathers in long wave models

Conditions of optimal (synchronized) collisions of any number of solitons and breathers are studied within the framework of the Gardner equation with positive cubic nonlinearity, which in the limits of small and large amplitudes tends to other long-wave models, the classic and the modified Korteweg -- de Vries equations. The local solution for an isolated soliton or breather within the Gardner equation is obtained. The wave amplitude in the focal point is calculated exactly. It exhibits a linear superposition of partial amplitudes of the solitons and breathers. The crucial role of the choice of proper soliton polarities and breather phases on the cumulative wave amplitude in the focal point is demonstrated. Solitons are most synchronized when they have alternating polarities. The straightforward link to the problem of synchronization of envelope solitons and breathers in the focusing nonlinear Schrödinger equation is discussed (then breathers correspond to envelope solitons propagating above a condensate).

nlin.PS↗

arXiv2018

Microscopic theory of capillary pressure hysteresis based on pore-space accessivity and radius-resolved saturation

Continuum models of porous media use macroscopic parameters and state variables to capture essential features of pore-scale physics. We propose a macroscopic property "accessivity" ($α$) to characterize the network connectivity of different sized pores in a porous medium, and macroscopic state descriptors "radius-resolved saturations" ($ψ_w(F),ψ_n(F)$) to characterize the distribution of fluid phases within. Small accessivity ($α\to0$) implies serial connections between different sized pores, while large accessivity ($α\to1$) corresponds to more parallel arrangements, as the classical capillary bundle model implicitly assumes. Based on these concepts, we develop a statistical theory for quasistatic immiscible drainage-imbibition in arbitrary cycles, and arrive at simple algebraic formulae for updating $ψ_n(F)$ that naturally capture capillary pressure hysteresis, with $α$ controlling the amount of hysteresis. These concepts may be used to interpret hysteretic data, upscale pore-scale observations, and formulate new constitutive laws by providing a simple conceptual framework for quantifying connectivity effects, and may have broader utility in continuum modeling of transport, reactions, and phase transformations in porous media.

cond-mat.soft↗

arXiv2018

A Universal Fractional Model of Wall-Turbulence

Modeling of wall-bounded turbulent flows is still an open problem in classical physics, with only modest progress made in the last few decades beyond the so-called `log law', which describes only the intermediate region in wall-bounded turbulence, i.e., $30-50 y^+ \text{ to } 0.1-0.2 R^+$ (in wall units) in a pipe of radius $R$. Here we propose a fundamentally new approach based on fractional calculus to model the {\em entire} mean velocity profile from the wall to the centerline of the pipe. Specifically, we represent the Reynolds stresses with a non-local fractional derivative of {\em variable order} that decays with the distance from the wall. Surprisingly, we find that this variable fractional order has a universal form for all Reynolds numbers and for three different flow types, i.e., channel flow, Couette flow, and pipe flow. We first use existing data bases from direct numerical simulations (DNS) to learn the variable fractional order function, and subsequently we test it against other DNS data and experimental measurements, including the Princeton superpipe experiments. Taken together, our findings reveal the continuous and decaying change of rate of turbulent diffusion from the wall as well as the strong non-locality of turbulent interactions that intensify away from the wall.

physics.flu-dyn↗

arXiv2020

Computational study of geometric effects of bottom wall microgrooves on cell docking inside microfluidic devices

Single cell and regularly cells docking inside the microstructure of microfluidic systems are advantageous in different analyses of single cells exposed to equal drug concentration and mechanical stimulus. In this study, we investigated bottom wall microgrooves with semicircular and rectangular geometries with different sizes which are suitable for single cell docking along the length of the microgroove in x direction and numerous cells docking regularly in one line inside the microgroove in a 3D microchannel. We used computational fluid dynamics to analyze the fluid recirculation area inside different microgrooves. The height of recirculation area in the bottom of microgroove can affect the cell attachment, and also materials delivery to attached cells, so the height of recirculation area has to be optimum amount. In addition, we analyzed the fluid drag force on cell movement toward the microgroove. This parameter was proportional to the fluid velocities in x and y directions changing in different microgrooves geometries. In different microgrooves geometries the fluid velocity in y direction does not change. If the fluid velocity in x direction decreases inside the microgroove, the cell movement time inside the microgroove will increase, and also the drag force in y direction can push the cells toward the bottom due to the lower drag force in x direction. The percentages of negative shear stress and average shear stress on the adhered cell surface were also calculated. The lower average shear stress, and negative shear stress around 50% on the cell surface are against cell detachment from the substrate. The results indicated that at the constant fluid inlet velocity and microchannel height, microgroove geometry and ratio of cell size to the microgroove size play pivotal roles in the cell initial adhesion to the substrate as well as the cell detachment.

physics.bio-ph↗

arXiv2018

Deep Reinforcement Learning achieves flow control of the 2D Karman Vortex Street

The Karman Vortex Street has been investigated for over a century and offers a reference case for investigation of flow stability and control of high dimensionality, non-linear systems. Active flow control, while of considerable interest from a theoretical point of view and for industrial applications, has remained inaccessible due to the difficulty in finding successful control strategies. Here we show that Deep Reinforcement Learning can achieve a stable active control of the Karman vortex street behind a two-dimensional cylinder. Our results show that Deep Reinforcement Learning can be used to design active flow controls and is a promising tool to study high dimensionality, non-linear, time dependent dynamic systems present in a wide range of scientific problems.

physics.flu-dyn↗

arXiv2019

Hydrodynamic interactions in polar liquid crystals on evolving surfaces

We consider the derivation and numerical solution of the flow of passive and active polar liquid crystals, whose molecular orientation is subjected to a tangential anchoring on an evolving curved surface. The underlying passive model is a simplified surface Ericksen-Leslie model, which is derived as a thin-film limit of the corresponding three-dimensional equations with appropriate boundary conditions. A finite element discretization is considered and the effect of hydrodynamics on the interplay of topology, geometric properties and defect dynamics is studied for this model on various stationary and evolving surfaces. Additionally, we consider an active model. We propose a surface formulation for an active polar viscous gel and exemplarily demonstrate the effect of the underlying curvature on the location of topological defects on a torus.

physics.comp-ph↗

arXiv2018

An axis symmetric 2D description of the process of the growth of a single crystal Si tube growth from the melt by pulling down method. Part1

This paper is the first part of an axis symmetric description of a single crystal tube growth process by micro-pulling-down method.the description concerns the following aspects:the free surfaces equations and the pressure difference across the free surfaces (section 2) , limits of the pressure differences across the free surfaces (section 3) ;static stability of the capillary free surfaces (section 4). In section 5 the above aspects are numerically investigated in case of a silicon tube growth.This investigation can be helpful in the better understanding the growth process and in the automation of manufacturing.In section 6 some general conclusion are given.Section 7 is an annex which contains the proof of the general statements formulated in sections 3 and 4.

physics.app-ph↗

arXiv2018

Opto Propeller Effect on Chiral Micro-Rotors

Manipulating mega biomolecules and micro-devices with light is highly appealing. Opto driving torque can propel micro-rotors to translational motion in viscous liquid, and then separate microsystems according to their handedness. We study the torque of dielectric loss generated by circular polarized lasers. The unwanted axial force which causes the handedness independent translational motion is cancelled by the counter propagating reflection beams. The propelling efficiency and the friction torque of water are obtained by solving the Navier-Stokes equation. In the interesting range of parameters, the numerical friction torque is found to be linear in the angular velocity with a slope depending on the radius or rotor as $r^3$. The time-dependent distribution of angular velocity is obtained as a solution of the Fokker-Planck equation, with which the thermal fluctuation is accounted. The results shed light on the micro-torque measurement and suggest a controllable micro-carrier.

physics.flu-dyn↗

arXiv2019

A comparative study on instability of steady flows in helical pipes

A computational study of three-dimensional instability of steady flows in a helical pipe of arbitrary curvature and torsion is carried out for the first time. The problem is formulated in Germano coordinates in two equivalent but different forms of the momentum equation, so that results obtained using both formulations cross verify each other. An additional formulation in the cylindrical coordinates is applied for a limiting case of the toroidal pipe. The calculations are performed by the finite volume and finite difference methods. Grid independence of the results is established for both steady flows, the eigenvalues associated with the linear stability problem, and the critical parameters. The calculated steady flows agree well with experimental measurements and previous numerical results. The computed critical Reynolds numbers corresponding to the onset of oscillatory instability agree well with the most recent experimental results, but disagree with the earlier ones. Novel results related to the parametric stability study are reported.

physics.flu-dyn↗

arXiv2020

Hierarchies of new invariants and conserved integrals in inviscid fluid flow

A vector calculus approach for the determination of advected invariants is presented for inviscid fluid flow. This approach describes invariants by means of Lie dragging of scalars, vectors, and skew-tensors with respect to the fluid velocity, which has the physical meaning of characterizing tensorial quantities that are frozen into the flow. Several new main results are obtained. First, simple algebraic and differential operators that can be applied recursively to derive a complete set of invariants starting from the basic known local and nonlocal invariants are constructed. Second, these operators are used to derive infinite hierarchies of local and nonlocal invariants for both adiabatic fluids and isentropic fluids that are either incompressible, or compressible with barotropic and non-barotropic equations of state. Each hierarchy is complete in the sense that no further invariants can be generated from the basic local and nonlocal invariants. All of the resulting new invariants are related to Ertel's invariant, the Ertel-Rossby invariant, and Hollmann's invariant. In particular, for incompressible fluid flow in which the density is non-constant across different fluid streamlines, a new variant of Ertel's invariant and several new variants of Hollmann's invariant are derived, where the entropy gradient is replaced by the density gradient. Third, the physical meaning of these new invariants and the resulting conserved integrals are discussed, and their relationship to conserved helicities and cross-helicities is described.

physics.flu-dyn↗

arXiv2018

Turbulence modulation in channel flow of finite-size spheroidal particles

We study the effect of particle shape on the turbulence in suspensions of spheroidal particles at volume fraction $ϕ= 10\%$ and show how the near-wall particle dynamics deeply changes with the particle aspect ratio and how this affects the global suspension behavior. The turbulence reduces with the aspect ratio of oblate particles, leading to drag reduction with respect to the single phase flow for particles with aspect ratio $\mathcal{AR}\leq1/3$, when the significant reduction in Reynolds shear stress is more than the compensation by the additional stresses, induced by the solid phase. Oblate particles are found to avoid the region close to the wall, travelling parallel to it with small angular velocities, while preferentially sampling high-speed fluid in the wall region. Prolate particles, also tend to orient parallel to the wall and avoid its vicinity. Their reluctancy to rotate around spanwise axis reduce the wall-normal velocity fluctuation of the flow and therefore the turbulence Reynolds stress similar to oblates; however, they undergo rotations in wall-parallel planes which increases the additional solid stresses due to their relatively larger angular velocities compared to the oblates. These larger additional stresses compensates for the reduction in turbulence activity and leads to a wall-drag similar to that of single-phase flows. Spheres on the other hand, form a layer close to the wall with large angular velocities in spanwise direction, which increases the turbulence activity in addition to exerting the largest solid stresses on the suspension, in comparison to the other studied shapes. Spherical particles therefore increase the wall-drag with respect to the single-phase flow.

physics.flu-dyn↗

arXiv2018

Exponential Scaling in Early-stage Agglomeration of Adhesive Particles in Turbulence

We carry out direct numerical simulation together with an adhesive discrete element method calculation (DNS-DEM) to investigate agglomeration of particles in homogeneous isotropic turbulence (HIT). We report an exponential-form scaling for the size distribution of early-stage agglomerates, which is valid across a wide range of particle inertia and inter-particle adhesion values. Such scaling allows one to quantify the state of agglomeration using a single scale parameter. An agglomeration kernel is then constructed containing the information of agglomerate structures and the sticking probability. An explicit relationship between the sticking probability and microscale particle properties is also proposed based on the scaling analysis of the equation for head-on collisions. Our results extend Smoluchowski's theory to the condition of non-coalescing solid adhesive particles and can reproduce DNS-DEM results with a simple one-dimensional simulation.

physics.flu-dyn↗

arXiv2018

Confinement effects on gravity-capillary wave turbulence

The statistical properties of a large number of weakly nonlinear waves can be described in the framework of the Weak Turbulence Theory. The theory is based on the hypothesis of an asymptotically large system. In experiments, the systems have a finite size and the predictions of the theory may not apply because of the presence of discrete modes rather than a continuum of free waves. Our study focusses on the case of waves at the surface of water at scales close to the gravity-capillarity crossover (of order 1~cm). Wave turbulence has peculiar properties in this regime because 1D resonant interactions can occur as shown by Aubourg \& Mordant. Here we investigate the influence of the confinement on the properties of wave turbulence by reducing gradually the size of our wave tank along one of its axis, the size in the other direction being unchanged. We use space-time resolved profilometry to reconstruct the deformed surface of water. We observe an original regime of coexistence of weak wave turbulence along the length of the vessel and discrete turbulence in the confined direction.

physics.flu-dyn↗

arXiv2018

Dynamics and wetting behavior of soft particles at a fluid-fluid interface

We investigate the conformation, position, and dynamics of core-shell nanoparticles (CSNPs) composed of a silica core encapsulated in a cross-linked poly-N-isopropylacrylamide shell at a water-oil interface for a systematic range of core sizes and shell thicknesses. We first present a free-energy model that we use to predict the CSNP wetting behavior at the interface as a function of its geometrical and compositional properties in the bulk phases, which gives good agreement with our experimental data. Remarkably, upon knowledge of the polymer shell deformability, the equilibrium particle position relative to the interface plane, an often elusive experimental quantity, can be extracted by measuring its radial dimensions after adsorption. For all the systems studied here, the interfacial dimensions are always larger than in bulk and the particle core resides in a configuration wherein it just touches the interface or is fully immersed in water. Moreover, the stretched shell induces a larger viscous drag at the interface, which appears to depend solely on the interfacial dimensions, irrespective of the portion of the CSNP surface exposed to the two fluids. Our findings indicate that tailoring the architecture of CSNPs can be used to control their properties at the interface, as of interest for applications including emulsion stabilization and nanopatterning.

cond-mat.soft↗

arXiv2018

The influence of velocity field on simple chemical reactions in viscous flow

The nonlinear dynamics of viscous, flow in a compressible spatially homogeneous fluid with chemical reactions are studied. Time-dependent but exact solution of the Piseuille type is obtained. Proceeding from this solution, the influence of a viscosity effect and a chemical reaction on the characteristics of nonequilibrium temporal states of the system is considered. Special attention is drawn to the effect of density collapses on the development of chemical reactions.

physics.flu-dyn↗