Two-phase Fluid Model Research Articles

Magnetic targeting in the impermeable microvessel with two-phase fluid model—Non-Newtonian characteristics of blood

The present investigation deals with finding the trajectories of the drug dosed magnetic carrier particle in a microvessel with two-phase fluid model which is subjected to the external magnetic field. The radius of the microvessel is divided into the endothelial glycocalyx layer in which the blood is assumed to obey Newtonian character and a core and plug regions where the blood obeys the non-Newtonian Herschel–Bulkley character which is suitable for the microvessel of radius 50 μm. The carrier particles, bound with nanoparticles and drug molecules are injected into the vascular system upstream from malignant tissue, and captured at the tumor site using a local applied magnetic field. The applied magnetic field is produced by a cylindrical magnet positioned outside the body and near the tumor position. The expressions for the fluidic force for the carrier particle traversing in the two-phase fluid in the microvessel and the magnetic force due to the external magnetic field are obtained. Several factors that influence the magnetic targeting of the carrier particles in the microvasculature, such as the size of the carrier particle, the volume fraction of embedded magnetic nanoparticles, and the distance of separation of the magnet from the axis of the microvessel are considered in the present problem. An algorithm is given to solve the system of coupled equations for trajectories of the carrier particle in the invasive case. The trajectories of the carrier particle are found for both invasive and noninvasive targeting systems. A comparison is made between the trajectories in these cases. Also, the present results are compared with the data available for the impermeable microvessel with single-phase fluid flow. Also, a prediction of the capture of therapeutic magnetic nanoparticle in the impermeable microvasculature is made for different radii, distances and volume fractions in both the invasive and noninvasive cases.

Numerical simulation by computational fluid dynamics and experimental study on stirred bioreactor with punched impeller

Instantaneous flow field and temperature field of the two-phase fluid are measured by particle image velocimetry(PIV)and steady state method during the state of onflow.A turbulent two-phase fluid model of stirred bioreactor with punched impeller is established by the computational fluid dynamics(CFD),using a rotating coordinate system and sliding mesh to describe the relative motion between impeller and baffles.The simulation and experiment results of flow and temperature field prove their warps are less than 10% and the mathematic model can well simulate the fields, which will also provide the study on optimized-design and scale-up of bioreactors with reference value.

Microscopic Theory for the Quantum to Classical Crossover in Chaotic Transport

We present a semiclassical theory for the scattering matrix S of a chaotic ballistic cavity at finite Ehrenfest time. Using a phase-space representation coupled with a multibounce expansion, we show how the Liouville conservation of phase-space volume decomposes S as S=S(cl) plus sign in circle S(qm). The short-time, classical contribution S(cl) generates deterministic transmission eigenvalues T=0 or 1, while quantum ergodicity is recovered within the subspace corresponding to the long-time, stochastic contribution S(qm). This provides a microscopic foundation for the two-phase fluid model, in which the cavity acts like a classical and a quantum cavity in parallel, and explains recent numerical data showing the breakdown of universality in quantum chaotic transport in the deep semiclassical limit. We show that the Fano factor of the shot-noise power vanishes in this limit, while weak localization remains universal.

Breakdown of universality in quantum chaotic transport: the two-phase dynamical fluid model.

We investigate the transport properties of open quantum chaotic systems in the semiclassical limit. We show how the transmission spectrum, the conductance fluctuations, and their correlations are influenced by the underlying chaotic classical dynamics, and result from the separation of the quantum phase space into a stochastic and a deterministic phase. Consequently, sample-to-sample conductance fluctuations lose their universality, while the persistence of a finite stochastic phase protects the universality of conductance fluctuations under variation of a quantum parameter.

Experimental tests of two‐phase fluid model of drying consolidation

AbstractDrying of aggregated slurries proceeds through a stage of consolidation prior to bed desaturation. During this period, volume fraction profiles develop within the bed. The magnitude of volume fraction variation is controlled by the rate of mass transfer and the strength of the bed. A two‐phase fluid model for stress balances in conjunction with the compressive yield stress constitutive equation is explored to describe the temporal evolution of bed volume fraction profiles. For this purpose, the compressive rheology of the saturated bed is characterized through independent experiments that fix all adjustable parameters. Excellent agreement is found between model predictions and experimental results.

Consolidation of concentrated suspensions - shear and irreversible floc structure rearrangement

A mathematical model for a consolidation process of a highly concentrated, flocculated suspension is developed. The suspension is treated as a mixture of a fluid and solid particles by an Eulerian two-phase fluid model. We characterize the suspension by constitutive relations correlating the stresses, interaction forces, and inter-particle forces to concentration and velocity gradients. Irreversibility of the permeability and yield stress is modeled by a memory function. A simulation program using finite difference methods in time and space is applied to a two dimensional test case. Numerical experiments are carried out on consolidation under shear and gravity in a 2D box with moving bottom.

Simulations Of Turbulent, Cavitating Flows In AnInjector Slot/orifice

A recently developed two-phase homogeneous fluid model employing the k - W turbulence treatment was used to simulate the turbulent cavitating flow in an injector slot/orifice. The homogeneous model treats the twophase mixture as a single continuum by allowing the pseudo-density to vary between that of gas and liquid extremes. Grid refinement and the effect of inflow turbulence length scale on the flow downstream studies were performed. Computational results were obtained for both two-dimensional slots and circular orifices and compare well with experimental measurements of cavitation length and discharge coefficient. The turbulent code was also utilized to analyze the internal turbulent flow field in a nozzle slot for both cavitating conditions and non-cavitating conditions.

Magnetic fluid model for two-phase pulsatile flow of blood

A two-phase magnetic fluid model for pulsatile flow of blood has been investigated by using realistic input data (pressure gradient). Closed form analytic solutions have been obtained. It is observed that the existing analysis could be improved by including driving force profiles (this could help in detecting the numerical, algebraic or formulation error to some extent) and two types of velocity profiles. Further, a new nondimensional numberSN is introduced which can be used to control the flow and its behavior. It is possible to make the flow stable or unstable with a proper choice ofSN. This could be exploited for many interesting applications, e.g. in bloodless surgery, in designing magnetic band aids for first aid box (for snake bites and to stop the blood loss from injuries in accidents and wars).

Explosive dispersal of solid particles

Abstract. The rapid dispersal of inert solid particles due to the detonation of a heterogeneous explosive, consisting of a packed bed of steel beads saturated with a liquid explosive, has been investigated experimentally and numerically. Detonation of the spherical charge generates a blast wave followed by a complex supersonic gas-solid flow in which, in some cases, the beads catch up to and penetrate the leading shock front. The interplay between the particle dynamics and the blast wave propagation was investigated experimentally as a function of the particle size (100–925 $\mu$ m) and charge diameter (8.9–21.2 cm) with flash X-ray radiography and blast wave instrumentation. The flow topology during the dispersal process ranges from a dense granular flow to a dilute gas-solid flow. Difficulties in the modeling of the high-speed gas-solid flow are discussed, and a heuristic model for the equation of state for the solid flow is developed. This model is incorporated into the Eulerian two-phase fluid model of Baer and Nunziato (1986) and simulations are carried out. The results of this investigation indicate that the crossing of the particles through the shock front strongly depends on the charge geometry, the charge size and the material density of the particles. Moreover, there exists a particle size limit below which the particles cannot penetrate the shock for the range of charge sizes considered. Above this limit, the distance required for the particles to overtake the shock is not very sensitive to the particle size but remains sensitive to the particle material density. Overall, excellent agreement was observed between the experimental and computational results.

Numerical 2D models of consolidation of dense flocculated suspensions

A mathematical 2D model for a consolidation process of a highly concentrated, flocculated suspension is developed. The suspension is treated as a mixture of a fluid and solid particles by an Eulerian two-phase fluid model. The suspension is characterized by constitutive relations correlating the stresses, interaction forces, and inter-particle forces to concentration and velocity gradients. This results in three empirical material functions: a permeability, a non-Newtonian viscosity and a non-reversible particle interaction pressure. Parameters in the models are fitted to experimental data. A simulation program using finite difference methods both in time and space is applied to one and two dimensional test cases. The effect of different viscosity models as well as the effect of shear on consolidation rate is studied. The results show that a shear thinning viscosity model yields a higher consolidation rate compared to a model that only depends on the volume fraction. It is also concluded that the size of the viscosity influences the time scale of the process and that the expected effect of shear on the process is not weil reproduced with any of the models.

Consolidation of concentrated suspensions – numerical simulations using a two-phase fluid model

We investigate numerically a mathematical model of a consolidation process of a dense, flocculated suspension. The suspension is treated as a two-constituent mixture of a fluid and solid particles by an Eulerian two-phase fluid model. We characterize the suspension by constitutive relations concerning the stresses, interaction forces and inter-particle forces. A numerical solver for a two dimensional test case is developed using finite difference methods both in time and space. In the numerical experiments, the suspension is confined to a closed box and consolidates due to a constant gravity field directed toward the bottom. To study the effect of shear, 2D simulations are performed where the bottom wall of the box is moving with a constant speed.

Cytoplasm dynamics and cell motion: two-phase flow models

The motion of amoeboid cells is characterized by cytoplasmic streaming and by membrane protrusions and retractions which occur even in the absence of interactions with a substratum. Cell translocation requires, in addition, a transmission mechanism wherein the power produced by the cytoplasmic engine is applied to the substratum in a highly controlled fashion through specific adhesion proteins. Here we present a simple mechano-chemical model that tries to capture the physical essence of these complex biomolecular processes. Our model is based on the continuum equations for a viscous and reactive two-phase fluid model with moving boundaries, and on force balance equations that average the stochastic interactions between actin polymers and membrane proteins. In this paper we present a new derivation and analysis of these equations based on minimization of a power functional. This derivation also leads to a clear formulation and classification of the kinds of boundary conditions that should be specified at free surfaces and at the sites of interaction of the cell and the substratum. Numerical simulations of a one-dimensional lamella reveal that even this extremely simplified model is capable of producing several typical features of cell motility. These include periodic `ruffle' formation, protrusion–retraction cycles, centripetal flow and cell-substratum traction forces.

A Theory for a Vibrating Circular Rod Damping in a Two-Phase Bubbly Fluid : Bubbly Fluid Configuration

This paper deals with a theoretical analysis of damping ratio for a vibrating circular rod in a two-phase air-water bubbly fluid, showing a good agreement between both theoretical and experimental results. The two-phase fluid model presented here assumes the liquid-phase medium be incompressible, containing a circular rod, and mass- and rigidity less circular "air columns". In the analysis for motions of these circular columns in the liquid, damping matrix is assumed to be diagonal, and the damping ratio is evaluated. The theoretical values are compared with the experimental ones, giving a good agreement.