Devolatilization of high viscous fluids with high gravity technology

Volatile organic compounds(VOCs)are generally toxic and harmful substances that can cause health and environmental problems.The removal of VOCs from polymers has become a key problem.The effective devolatilization to remove VOCs from high viscous fluids such as polymer is necessary and is of great importance.In this study,the devolatilization effect of a rotating packed bed(RPB)was studied by using polydimethylsiloxane as the viscous fluid and acetone as the VOC.The devolatilization rate and liquid phase volume(KLa)have been evaluated.The results indicated that the optimum conditions were the high-gravity factor of 60,liquid flow rate of 10 L·h^(-1),and vacuum degree of 0.077 MPa.The dimensionless correlation of KLa was established,and the deviations between predicted and experimental values were less than±28%.The high-gravity technology will result in lower mass transfer resistance in the devolatilization process,enhance the mass transfer process of acetone,and improve the removal effect of acetone.This work provides a promising path for the removal of volatiles from polymers in combination with high-gravity technology.It can provide the basis for the application of RPB in viscous fluids.

Vibration of a Two-Layer“Metal+PZT”Plate Contacting with Viscous Fluid

The present work investigates the mechanically forced vibration of the hydro-elasto-piezoelectric system consisting of a two-layer plate“elastic+PZT”,a compressible viscous fluid,and a rigid wall.It is assumed that the PZT(piezoelectric)layer of the plate is in contact with the fluid and time-harmonic linear forces act on the free surface of the elastic-metallic layer.This study is valuable because it considers for the first time the mechanical vibration of the metal+piezoelectric bilayer plate in contact with a fluid.It is also the first time that the influence of the volumetric concentration of the constituents on the vibration of the hydro-elasto-piezoelectric system is studied.Another value of the present work is the use of the exact equations and relations of elasto-electrodynamics for elastic and piezoelectric materials to describe the motion of the plate layers within the framework of the piecewise homogeneous body model and the use of the linearized Navier-Stokes equations to describe the flow of the compressible viscous fluid.The plane-strain state in the plate and the plane flow in the fluid take place.For the solution of the corresponding boundary-value problem,the Fourier transform is used with respect to the spatial coordinate on the axis along the laying direction of the plate.The analytical expressions of the Fourier transform of all the sought values of each component of the system are determined.The origins of the searched values are determined numerically,after which numerical results on the stress on the fluid and plate interface planes are presented and discussed.These results are obtained for the case where PZT-2 is chosen as the piezoelectric material,steel and aluminum as the elastic metal materials,and Glycerin as the fluid.Analysis of these results allows conclusions to be drawn about the character of the problem parameters on the frequency response of the interfacial stress.In particular,it was found that after a certain value of the vibration frequency,the presence of the metal layer in the two-layer plate led to an increase in the absolute values of the above interfacial stress.

Analysis of a Propeller Wake Flow Field Using Viscous Fluid Mechanics

The computational fluid dynamics （CFD） method is used to numerically simulate a propeller wake flow field in open water. A sub-domain hybrid mesh method was adopted in this paper. The computation domain was separated into two sub-domains, in which tetrahedral elements were used in the inner domain to match the complicated geometry of the propeller, while hexahedral elements were used in the outer domain. The mesh was locally refined on the propeller surface and near the wake flow field, and a size function was used to control the growth rate of the grid. Sections at different axial location were used to study the spatial evolution of the propeller wake in the region ranging from the disc to one propeller diameter （D） downstream. The numerical results show that the axial velocity fluctuates along the wake flow; radial velocity, which is closely related to vortices, attenuates strongly. The trailing vortices interact with the tip vortex at the blades＇ trailing edge and then separate. The strength of the vortex shrinks rapidly, and the radius decreases 20% at one diameter downstream.

Reflection and refraction of attenuated waves at boundary of elastic solid and porous solid saturated with two immiscible viscous fluids

The propagation of elastic waves is studied in a porous solid saturated with two immiscible viscous fluids. The propagation of three longitudinal waves is represented through three scalar potential functions. The lone transverse wave is presented by a vector potential function. The displacements of particles in different phases of the aggregate are defined in terms of these potential functions. It is shown that there exist three longitudinal waves and one transverse wave. The phenomena of reflection and refraction due to longitudinal and transverse waves at a plane interface between an elastic solid half-space and a porous solid half-space saturated with two immiscible viscous fluids are investigated. For the presence of viscosity in pore-fluids, the waves refracted to the porous medium attenuate in the direction normal to the interface. The ratios of the amplitudes of the reflected and refracted waves to that of the incident wave are calculated as a non- singular system of linear algebraic equations. These amplitude ratios are used to further calculate the shares of different scattered waves in the energy of the incident wave. The modulus of the amplitude and the energy ratios with the angle of incidence are computed for a particular numerical model. The conservation of the energy across the interface is verified. The effects of variations in non-wet saturation of pores and frequencies on the energy partition are depicted graphically and discussed,

On the pressure and stress singularities induced by steady flows of incompressible viscous fluids

Design for structural integrity requires an appreciation of where stress singularities can occur in structural configurations. While there is a rich literature devoted to the identification of such singular behavior in solid mechanics, to date there has been relatively little explicit identification of stress singularities caused by fluid flows. In this study, stress and pressure singularities induced by steady flows of viscous incompressible fluids are asymptotically identified. This is done by taking advantage of an earlier result that the Navier-Stokes equations are locally governed by Stokes flow in angular corners. Findings for power singularities are confirmed by developing and using an analogy with solid mechanics. This analogy also facilitates the identification of flow-induced log singularities. Both types of singularity are further confirmed for two global configurations by applying convergence-divergence checks to numerical results. Even though these flow-induced stress singularities are analogous to singularities in solid mechanics, they nonetheless render a number of structural configurations singular that were not previously appreciated as such from identifications within solid mechanics alone.

Performance of viscous fluid dampers coupling adjacent inelastic structures under near-fault earthquakes

The behavior of viscous fluid damper applied in coupling structures subjected to near-fault earthquake was studied.The structural nonlinearity was characterized by Bouc-Wen model and several near-fault ground motions were simulated by the combination of a recorded earthquake(background ground motion) with equivalent velocity pulses that possess near-fault features.Extensive parametric studies were carried out to find the appropriate damping coefficient.Performances of viscous fluid dampers were demonstrated by the relationship between the force and displacement,the maximal damper force and stroke.The control performances were demonstrated in terms of the response reductions of adjacent structures.The results show that the dynamic responses of adjacent structures are mitigated greatly.Proper damping coefficients of connecting fluid dampers have a small difference,while adjacent structures under different near-fault ground motions with the same peak acceleration.The maximum force of damper is about 0.8 MN,and the maximum damper stroke is about ±550 mm.Satisfied viscous fluid dampers can be produced according to the current manufacturing skills.

Acoustic radiation force on a rigid cylinder between two impedance boundaries in a viscous fluid

Acoustofluidic technology combines acoustic and microfluidic technologies to realize particle manipulation in microchannels driven by acoustic waves,and the acoustic radiation force(ARF)with boundaries is important for particle manipulation in an acoustofluidic device.In the work reported here,the ARF on a free cylinder immersed in a viscous fluid with an incident plane wave between two impedance boundaries is derived analytically and calculated numerically.The influence of multiple scattering between the particle and the impedance boundaries is described by means of image theory,the finite-series method,and the translational addition theorem,and multiple scattering is included partly in image theory.The ARF on a free rigid cylinder in a viscous fluid is analyzed by numerical calculation,with consideration given to the effects of the distances from cylinder edge to boundaries,fluid viscosity,cylinder size,and boundary reflectivity.The results show that the interaction between the two boundaries and the cylinder makes the ARF change more violently with different frequencies,while increasing the viscosity can reduce the amplitude of the ARF in boundary space.This study provides a theoretical basis for particle manipulation by the ARF in acoustofluidics.

On the pressure and stress singularities induced by steady flows of a pair of nonmiscible,incompressible,viscous fluids in contact with a wall

Design for structural integrity requires an appreciation of where stress singularities can occur in structural configurations. While there is a rich literature devoted to the identification of such singular behavior in solid mechanics, only of late has there been much in the way of corresponding identifications of flow-induced stress singularities in fluid mechanics. These recent asymptotic identifications are for a single incompressible viscous fluid： Here the asymptotic approach is extended to apply to a configuration entailing two such fluids, For this configuration, various specifications leading to power or log singularities are determined. These results demonstrate that flow-induced stress singularities can occur in a structural container at a location where no singularities are identified within solid mechanics alone.

VARIATIONAL PRINCIPLES AND GENERALIZED VARIATIONAL PRINCIPLES IN HYDRODYNAMICS OF VISCOUS FLUIDS

In this paper, the variational principles of hydrodynamic problems for the incompressible and compressible viscous fluids are established. These principles are principles of maximum power losses. Their generalized variational principles are also discussed on the basis of Lagrangian multiplier methods.

FLOW OF A VISCOUS FLUID PAST A FLEXIBLE MEMBRANE

This paper treats the numerical calculation of a steady two-dimensional viscous flow past a flexible membrane. Both edges of the membrane are fixed in the flow and its chord is set normal to the flow. The numerical calculations of the Navier-Stokes equation based on a finite difference method and a relaxation method are carried out for several values of the membrane tension in cases when the Reynolds numbers are 5, 10 and 20. It is found that the membrane tension has a minimum value below which there is no steady shape of the membrane. Two different shapes of the membrane are possible at a given value of tension: the one is of small deformation, while the other a large deformation. There appear twin vortices in the concave region of the membrane shape if its deformation increases to a certain extent.

Slip effects on streamline topologies and their bifurcations for peristaltic flows of a viscous fluid

We discuss the effects of the surface slip on streamline patterns and their bifurcations for the peristaltic transport of a Newtonian fluid. The flow is in a two-dimensional symmetric channel or an axisymmetric tube. An exact expression for the stream function is obtained in the wave frame under the assumptions of long wavelength and low Reynolds number for both cases. For the discussion of the particle path in the wave frame, a system of nonlinear autonomous differential equations is established and the methods of dynamical systems are used to discuss the local bifurcations and their topological changes. Moreover, all types of bifurcations and their topological changes are discussed graphically. Finally, the global bifurcation diagram is used to summarize the bifurcations.

Numerical Comparison for Focused Wave Propagation Between the Fully Nonlinear Potential Flow and the Viscous Fluid Flow Models

Numerical simulations on focused wave propagation are carried out by using three types of numerical models,including the linear potential flow,the nonlinear potential flow and the viscous fluid flow models.The wave-wave interaction of the focused wave group with different frequency bands and input wave amplitudes is examined,by which the influence of free surface nonlinearity and fluid viscosity on the related phenomenon of focused wave is investigated.The significant influence of free surface nonlinearity on the characteristics of focused wave can be observed,including the increased focused wave crest,delayed focused time and downstream shift of focused position with the increase of input amplitude.It can plot the evident difference between the results of the nonlinear potential flow and linear potential flow models.However,only a little discrepancy between the nonlinear potential flow and viscous fluid flow models can be observed,implying the insignificant effect of fluid viscosity on focused wave behavior.Therefore,the nonlinear potential flow model is recommended for simulating the non-breaking focused wave problem in this study.

WEAK SOLUTION TO THE INCOMPRESSIBLE VISCOUS FLUID AND A THERMOELASTIC PLATE INTERACTION PROBLEM IN 3D

In this paper we deal with a nonlinear interaction problem between an incompressible viscous fluid and a nonlinear thermoelastic plate.The nonlinearity in the plate equation corresponds to nonlinear elastic force in various physically relevant semilinear and quasilinear plate models.We prove the existence of a weak solution for this problem by constructing a hybrid approximation scheme that,via operator splitting,decouples the system into two sub-problems,one piece-wise stationary for the fluid and one time-continuous and in a finite basis for the structure.To prove the convergence of the approximate quasilinear elastic force,we develop a compensated compactness method that relies on the maximal monotonicity property of this nonlinear function.

PENALTY FINITE ELEMENT METHOD FOR NONLINEAR DYNAMIC RESPONSE OF VISCOUS FLUID-SATURATED BIPHASE POROUS MEDIA

The governing equations as well as boundary land initial conditions for nonlinear dynamic response problems of viscous fluid-saturated biphase porous medium model, based on mixture theory, are presented. With Galerkin weighted residual method the corresponding nonlinear dynamic penalty finite element equation, in which the dependencies of volume fraction and permeation coefficients an deformation are included, is obtained. The iteration solution method of the nonlinear system equation is also discussed. As a numerical example, the dynamic response of a porous medium column under impulsive loading action is analyzed with the developed finite element program. The numerical results demonstrate the efficiency and correctness of the method.

Fallopian tube assessment of the peristaltic-ciliary flow of a linearly viscous fluid in a finite narrow tube

The present theoretical assessment deals with the peristaltic-ciliary trans- port of a developing embryo within a fallopian tubal fluid in the human fallopian tube. A mathematical model of peristalsis-cilia induced flow of a linearly viscous fluid within a fallopian tubal fluid in a finite two-dimensional narrow tube is developed. The lubrica- tion approximation theory is used to solve the resulting partial differential equation. The expressions for axial and radial velocities, pressure gradient, stream function, volume flow rate, and time mean volume flow rate are derived. Numerical integration is performed for the appropriate residue time over the wavelength and the pressure difference over the wavelength. Moreover, the plots of axial velocity, the appropriate residue time over wavelength, the vector, the pressure difference over wavelength, and the streamlines are displayed and discussed for emerging parameters and constants. Salient features of the pumping characteristics and the trapping phenomenon are discussed in detail. Yhrther- more, a comparison between the peristaltic flow and the peristaltic-ciliary flow is made as the special case. Relevance of the current results to the transport of a developing embryo within a fallopian tubal fluid from ampulla to the intramural in the fallopian tube is also explored. It reveals the fact that cilia along with peristalsis helps to complete the required mitotic divisions while transporting the developing embryo within a fallopian tubal fluid in the human fallopian tube.

Elastodynamic analysis at an interface of viscous fluid/thermoelastic micropolar honeycomb medium due to inclined load

In this paper, the effect of angle inclination at the interface of a viscous fluid and thermoelastic micropolar honeycomb solid due to inclined load is investigated. The inclined load is assumed to be a linear combination of normal load and tangential load. Laplace transform with respect to time variable and Fourier transform with respect to space variable are applied to solve the problem. Expressions of stresses, temperature distribution, and pressures in the transformed domain are obtained by introducing potential functions. The numerical inversion technique is used to obtain the solution in the physical domain. The frequency domain expressions for steady state are also obtained with appropriate change of variables. Graphic representations due to the response of different sources and changes of angle inclination are shown. Some particular cases are also discussed.

DAMPING OF VERTICALLY EXCITED SURFACE WAVE IN WEAKLY VISCOUS FLUID

In a vertically oscillating circular cylindrical container, singular perturbation theory of two-time scale expansions is developed in weakly viscous fluids to investigate the motion of single free surface standing wave by linearizing the Navier-Stokes equation. The fluid field is divided into an outer potential flow region and an inner boundary layer region. The solutions of both two regions are obtained and a linear amplitude equation incorporating damping term and external excitation is derived. The condition to appear stable surface wave is obtained and the critical curve is determined. In addition, an analytical expression of damping coefficient is determined. Finally, the dispersion relation, which has been derived from the inviscid fluid approximation, is modified by adding linear damping. It is found that the modified results are reasonably closer to experimental results than former theory. Result shows that when forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when forcing frequency is high, the surface tension of the fluid is prominent.

VELOCITY FIELD IN SHIP WAVES ON THE VISCOUS FLUID

From the Navier-Stokes equations, the integral expressions of the free-surface elevation and the velocity field in ship waves of a moving waterborne body are obtained. Next, Lighthill' s two-stage scheme is employed to change the above-mentioned integral expressions to algebraic expressions. Compared with the results obtained when the seawater is idealized to an inviscid fluid, the singularities are dispelled or weakened, and the accuracy of the digit information of ship waves is improved.

Viscous Fluid Flowing around the Plate: Turbulence

Diffusion of momentum gives rise to viscosity. This article presents a solution in the explicit form of the equation of the momentum diffusion for a viscous fluid flowing around a plate taking into account deceleration. Three characteristic regions of a viscous flow have been described: the mantle, the body of the boundary layer, the viscous sublayer. In the mantle, the effect of viscosity is significant at a considerable distance from the plate. The momentum diffusion is focused in the body of the boundary layer. The diffusion force that produces the momentum of force giving rise to eddies is localized in the viscous sublayer. At the beginning of the plate, a moment of force twists the liquid along the flow, creating eddies that roll along the plate. For this reason, they are pressed against the surface of the plate. But at some distance from the beginning of the plate, the moment of force changes its orientation to the opposite and twists the vortices in the opposite direction, causing the vortices to roll along the plate against the flow. This causes the liquid to detach from the surface of the plate. This is the beginning of turbulence. The diameter of the vortex produced in the viscous sublayer is small being of the order of the thickness of the viscous sublayer. The vortex possesses a large angular velocity. Due to the momentum diffusion and the effect of the eddies combined in passing along the plate, its diameter increases up to the size of the thickness of the boundary layer and even more, whereas its angular velocity decreases down to the values really observed. The value of the critical Reynolds number of the transition from the laminar flow to the turbulent one has been found, and it agrees with the experimental data. The value of the shear stress produced by the viscous fluid on the plate surface has also been obtained. The way of measurement of the friction coefficient characterizing the effect of the plate on the flow has been proposed. It has been shown that the boundary condition of adhesion to the surface of a body flown around, that is applied in the estimation of viscous flows, contradicts the real processes of the flow.

Viscous fluid damping in a laterally oscillating finger of a comb-drive micro-resonator based on micro-polar fluid theory

Viscous damping is a dominant source of energy dissipation in laterally oscillating micro-structures. In microresonators in which the characteristic dimensions are comparable to the dimensions of the fluid molecules, the assumption of the continuum fluid theory is no longer justified and the use of micro-polar fluid theory is indispensable. In this paper a mathematical model was presented in order to predict the viscous fluid damping in a laterally oscillating finger of a micro-resonator considering micro-polar fluid theory. The coupled governing partial differential equations of motion for the vibration of the finger and the micro-polar fluid field have been derived. Considering spin and no-spin boundary conditions, the related shape functions for the fluid field were presented. The obtained governing differential equations with time varying boundary conditions have been transformed to an enhanced form with homogenous boundary conditions and have been discretized using a Galerkin-based reduced order model. The effects of physical properties of the micro-polar fluid and geometrical parameters of the oscillating structure on the damping ratio of the system have been investigated.