Mathematical study of a single leukocyte in microchannel flow

The recruitment of leukocytes and subsequent rolling, activation, adhesion and transmigration are essential stages of an inflammatory response. Chronic inflammation may entail atherosclerosis, one of the most devastating cardiovascular diseases. Understanding this mechanism is of crucial importance in immunology and in the development of anti-inflammatory drugs. Micropipette aspiration experiments show that leukocytes behave as viscoelastic drops during suction. The flow of non-Newtonian viscoelastic fluids can be described by differential, integral and rate-type constitutive equations. In this study, the rate-type Oldroyd-B model is used to capture the viscoelasticity of the leukocyte which is considered as a drop. Our main goal is to analyze a mathematical model describing the deformation and flow of an individual leukocyte in a microchannel flow. In this model we consider a coupled problem between a simplified Oldroyd-B system and a transport equation which describes the density considered as non constant in the Navier–Stokes equations. First we present the mathematical model and we prove the existence of solution, then we describe its numerical approximation using the level set method. Through the numerical simulations we analyze the hemodynamic effects of three inlet velocity values. We note that the hydrodynamic forces pushing the cell become higher with increasing inlet velocities.

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Study of Maneuverability of Container Ship With Nonlinear and Roll-Coupled Effects by Numerical Simulations Using RANSE-Based Solver

Journal of Offshore Mechanics and Arctic Engineering ◽

10.1115/1.4032895 ◽

2016 ◽

Vol 138 (4) ◽

Cited By ~ 1

Author(s):

R. Rajita Shenoi ◽

P. Krishnankutty ◽

R. Panneer Selvam

Keyword(s):

Mathematical Model ◽

High Speed ◽

Stokes Equations ◽

Navier Stokes ◽

Container Ship ◽

Navier Stokes Equations ◽

Hydrodynamic Derivatives ◽

Computational Fluid Dynamics Cfd ◽

Experimental Values ◽

The Mathematical Model

The examination of maneuvering qualities of a ship is necessary to ensure its navigational safety and prediction of trajectory. The study of maneuverability of a ship is a three-step process, which involves selection of a suitable mathematical model, estimation of the hydrodynamic derivatives occurring in the equation of motion, and simulation of the standard maneuvering tests to determine its maneuvering qualities. This paper reports the maneuvering studies made on a container ship model (S175). The mathematical model proposed by Son and Nomoto (1981, “On Coupled Motion of Steering and Rolling of a High Speed Container Ship,” J. Soc. Nav. Arch. Jpn., 150, pp. 73–83) suitable for the nonlinear roll-coupled steering model for high-speed container ships is considered here. The hydrodynamic derivatives are determined by numerically simulating the planar motion mechanism (PMM) tests in pure yaw and combined sway–yaw mode using an Reynolds-Averaged Navier–Stokes Equations (RANSE)-based computational fluid dynamics (CFD) solver. The tests are repeated with the model inclined at different heel angles to obtain the roll-coupled derivatives. Standard definitive maneuvers like turning tests at rudder angle, 35 deg and 20 deg/20 deg zig-zag maneuvers are simulated using the numerically obtained derivatives and are compared with those obtained using experimental values.

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Mathematical Model of Spool Valve with Rectangular Grooves

Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University ◽

10.1051/jnwpu/20183630516 ◽

2018 ◽

Vol 36 (3) ◽

pp. 516-521

Author(s):

Jia Chen ◽

Zhaohui Yuan ◽

Qiang Guo

Keyword(s):

Numerical Simulation ◽

Mathematical Model ◽

Coordinate System ◽

Stokes Equations ◽

Lateral Force ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Cylindrical Coordinate ◽

Spool Valve ◽

The Mathematical Model

A spool valve of aerospace hydraulic breaks down because of uneven pressure distribution between sleeve and spool, which is called as hydraulic lock. The rectangular grooves on the spool surface can effectively weaken the lateral force, thereby preventing the hydraulic lock. So the mathematical model of spool valve with rectangular grooves is established according to the Navier-Stokes equations based on the cylindrical coordinate system. To verify the effectivity of the mathematical model, the numerical simulation is compared and used to modified the mathematical model.

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Water wave overwash of a step

Journal of Fluid Mechanics ◽

10.1017/jfm.2017.857 ◽

2018 ◽

Vol 839 ◽

pp. 293-312 ◽

Cited By ~ 10

Author(s):

D. M. Skene ◽

L. G. Bennetts ◽

M. Wright ◽

M. H. Meylan ◽

K. J. Maki

Keyword(s):

Mathematical Model ◽

Water Wave ◽

Stokes Equations ◽

Navier Stokes ◽

Cfd Model ◽

Two Phase ◽

Navier Stokes Equations ◽

Spatial Dimensions ◽

Incident Waves ◽

The Mathematical Model

Water wave overwash of a step by small steepness, regular incident waves is analysed using a computational fluid dynamics (CFD) model and a mathematical model, in two spatial dimensions. The CFD model is based on the two-phase, incompressible Navier–Stokes equations, and the mathematical model is based on the coupled potential-flow and nonlinear shallow-water theories. The CFD model is shown to predict vortices, breaking and overturning in the region where overwash is generated, and that the overwash develops into fast-travelling bores. The mathematical model is shown to predict bore heights and velocities that agree with the CFD model, despite neglecting the complicated dynamics where the overwash is generated. Evidence is provided to explain the agreement in terms of the underlying agreement of mass and energy fluxes.

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Numerical approximation of incompressible Navier-Stokes equations based on an auxiliary energy variable

Journal of Computational Physics ◽

10.1016/j.jcp.2019.03.012 ◽

2019 ◽

Vol 388 ◽

pp. 1-22 ◽

Cited By ~ 11

Author(s):

Lianlei Lin ◽

Zhiguo Yang ◽

Suchuan Dong

Keyword(s):

Numerical Approximation ◽

Stokes Equations ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Energy Variable

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Mathematical and Physical Modeling of Three-Phase Gas-Stirred Ladles

MRS Proceedings ◽

10.1557/opl.2016.14 ◽

2016 ◽

Vol 1812 ◽

pp. 29-34

Author(s):

Juan A. López ◽

Marco A. Ramírez-Argáez ◽

Adrián M. Amaro-Villeda ◽

Carlos González

Keyword(s):

Mathematical Model ◽

Physical Model ◽

Stokes Equations ◽

Steel Slag ◽

Flow Patterns ◽

Navier Stokes ◽

Steel Ladle ◽

Phase System ◽

Navier Stokes Equations ◽

Three Phase

ABSTRACTA very realistic 1:17 scale physical model of a 140-ton gas-stirred industrial steel ladle was used to evaluate flow patterns measured by Particle Image Velocimetry (PIV), considering a three-phase system (air-water-oil) to simulate the argon-steel-slag system and to quantify the effect of the slag layer on the flow patterns. The flow patterns were evaluated for a single injector located at the center of the ladle bottom with a gas flow rate of 2.85 l/min, with the presence of a slag phase with a thickness of 0.0066 m. The experimental results obtained in this work are in excellent agreement with the trends reported in the literature for these gas-stirred ladles. Additionally, a mathematical model was developed in a 2D gas-stirred ladle considering the three-phase system built in the physical model. The model was based on the Eulerian approach in which the continuity and the Navier Stokes equations are solved for each phase. Therefore, there were three continuity and six Navier-Stokes equations in the system. Additionally, turbulence in the ladle was computed by using the standard k-epsilon turbulent model. The agreement between numerical simulations and experiments was excellent with respect to velocity fields and turbulent structure, which sets the basis for future works on process analysis with the developed mathematical model, since there are only a few three-phase models reported so far in the literature to predict fluid dynamics in gas-stirred steel ladles.

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Approximation of attractors for nongradient systems

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210500030328 ◽

1995 ◽

Vol 125 (4) ◽

pp. 739-758

Author(s):

I. N. Kostin

Keyword(s):

Large Class ◽

Metric Space ◽

Numerical Approximation ◽

Stokes Equations ◽

Hausdorff Metric ◽

Navier Stokes ◽

Lorenz Equations ◽

Navier Stokes Equations ◽

Suggested Procedure ◽

Nongradient Systems

The problem of approximation of attractors for semidynamical systems (SDSs) in a metric space is studied. Let some (exact) SDS possessing an attractor M be inaccurately defined, i.e. let another (approximate) SDS, which is close in some sense to the exact one, be given. The problem is to construct a set , which is close to M in the Hausdorff metric.The suggested procedure for constructing is finite, which makes it possible to use it in computations. The results obtained are suitable for numerical approximation of attractors for a rather large class of semidynamical systems, including ones generated by the Lorenz equations and the Navier–Stokes equations.

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Dynamic Response of Base-Isolated Concrete Rectangular Liquid-Storage Structure Under Large Amplitude Sloshing

Archives of Civil Engineering ◽

10.1515/ace-2017-0003 ◽

2017 ◽

Vol 63 (1) ◽

pp. 33-45 ◽

Cited By ~ 1

Author(s):

Xuansheng Cheng ◽

De Li ◽

Peijiang Li ◽

Xiaoyan Zhang ◽

Guoliang Li

Keyword(s):

Wave Height ◽

Large Amplitude ◽

Stokes Equations ◽

Seismic Intensity ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Storage Structure ◽

Liquid Storage ◽

Rectangular Liquid Storage Structure ◽

The Mathematical Model

AbstractConsidering concrete nonlinearity, the wave height limit between small and large amplitude sloshing is defined based on the Bernoulli equation. Based on Navier-Stokes equations, the mathematical model of large amplitude sloshing is established for a Concrete Rectangle Liquid-Storage Structure (CRLSS). The results show that the seismic response of a CRLSS increases with the increase of seismic intensity. Under different seismic fortification intensities, the change in trend of wave height, wallboard displacement, and stress are the same, but the amplitudes arc not. The areas of stress concentration appear mainly at the connections between the wallboards, and the connections between the wallboard and the bottom.

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Combined Natural Convection and Volumetric Radiation in a Horizontal Annulus: Spectral and Finite Volume Predictions

Journal of Heat Transfer ◽

10.1115/1.2826023 ◽

1999 ◽

Vol 121 (3) ◽

pp. 610-615 ◽

Cited By ~ 25

Author(s):

D.-C. Kuo ◽

J. C. Morales ◽

K. S. Ball

Keyword(s):

Heat Transfer ◽

Natural Convection ◽

Stokes Equations ◽

Control Volume ◽

Navier Stokes ◽

Differential Approximation ◽

Navier Stokes Equations ◽

Influence Matrix ◽

Potential Benefits ◽

The Mathematical Model

Combined natural convection and radiation in a two-dimensional horizontal annulus filled with a radiatively participating gray medium is studied numerically by using a control-volume-based finite difference method and a spectral collocation method coupled with an influence matrix technique. The mathematical model includes the continuity equation, the incompressible Navier-Stokes equations, the energy equation, and the radiative transfer equation (RTE), which is modeled using the P1 differential approximation. Computed results for two Rayleigh numbers, Ra = 104 and Ra = 105, for several combinations of the radiation-conduction parameter, NR, and the optical thickness, τ, are presented. The differences observed in the predicted flow structures and heat transfer characteristics are described. Furthermore, an unusual flow structure is studied in detail, and multiple solutions are found. Finally, the potential benefits of applying spectral methods to problems involving radiative heat transfer are demonstrated.

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Mathematical and Experimental Investigation of Liquid-Gas Interfaces in Porous Wicks

Heat Transfer, Volume 5 ◽

10.1115/imece2002-39180 ◽

2002 ◽

Author(s):

Yuelei Yang ◽

Frank M. Gerner ◽

H. Thurman Henderson

Keyword(s):

Mathematical Model ◽

Experimental Investigation ◽

Stokes Equations ◽

Small Diameter ◽

Flow In Porous Media ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Vapor Interface ◽

Porous Plastic ◽

Capillary Pore

This paper focuses on the investigation of the liquid-gas (or vapor) interface, which occurs in very small diameter pores. A mathematical model is built to formulate the movements of a liquid column trapped in a capillary pore. The Navier-Stokes equations are applied to the liquid side with assumed no-slip conditions, while the Young-Laplace equation is used to formulate the shape of the interface. This theoretical model calculates both velocity profiles in the liquid side and transient profiles of the interface itself; and of particular interest, it predicts the pressure difference, oscillation frequency and amplitude required to burst this interface. These predicted parameters are examined by the experiments with both oscillating Coherent Porous Silicon (CPS) wicks and porous plastic wicks. This research helps better understanding the phenomena such as multiphase flow in porous media or de-watering process that happens in vibro-separators.

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