Improvements of an oscillatory squeezing flow rheometer for small elasticity measurements of liquids

Dilute dispersions and polymer solutions used as functional fluids or operation fluids are required to be controlled in an extremely high quality level in the semiconductor industry or MEMS (Micro Mechanical Electric System) devices, such as inkjet print heads and micro pumps. Many of the quality items depend on microscopic state of dispersion or solution stem from mutual interactions among the dispersed particles and solved polymers; hence, close investigations of these complex interactions are of great concern for developments of highly functional fluids and micro fluidic devices. Here, some great improvements are presented on a random oscillatory squeezing flow rheometer to detect subtle rheological properties arise as results of interactions between micro solid particles dispersed in liquids. To detect subtle elasticity within fundamentally viscous liquids, very small phase difference from the viscous response has to be measured, and for this reason effects from three major sources (sensor nonlinearity, nonlinear squeeze flow response, and instrument compliance) that give phase errors and noises as well as fluid inertia are completely compensated by data processing, achieving sensitivity for subtle dynamic modulus G to the extent of G/G 0.001. As examples of the dilute dispersions, water dispersions of monodisperse acrylic latex were measured and detections of dynamic modulus G of 10^–3 Pa at 100 Hz were demonstrated.     

Field dependence of the response of a magnetorheological suspension under steady shear flow and squeezing flow

A comparison was made of the behaviour of a magnetorheological suspension under steady shear flow and constant velocity squeezing flow. The strain rates and sample dimensions were chosen to be comparable in the two deformation modes, and the dependence of the mechanical properties on the magnetic flux density B was investigated. The measurements found that the mechanical response under squeezing flow scaled as B^0.91, whereas the response under shearing scaled as B^1.4, close to theoretical predictions. This difference of the field dependence between the shearing and squeezing flows was possibly due to the different microstructural rearrangement processes which occur in the two deformation modes.     

Oscillatory Couette flow of rotating Sisko fluid

The oscillatory Couette flow of a magnetohydrodynamic （MHD） Sisko fluid between two infinite non-conducting parallel plates is explored in a rotating frame. The lower plate is fixed, and the upper plate is oscillating in its own plane. Using MATLAB, a numerical solution to the resulting nonlinear system is presented. The influence of the physical parameters on the velocity components is analyzed. It is found that the effect of rotation on the primary velocity is more significant than that on the secondary velocity. Further, the oscillatory character in the flow is also induced by rotation. The considered flow situation behaves inertialess when the Reynolds number is small.     

Three-dimensional mixed convection squeezing flow

The unsteady mixed convection squeezing flow of an incompressible Newtonian fluid between two vertical parallel planes is discussed. The fluid is electrically conducting. The governing equations are transformed into ordinary differential equations (ODEs) by appropriate transformations. The transformed equations are solved successfully by a modern and powerful technique. The effects of the emerging parameters on the flow and heat transfer characteristics are studied and examined. The values of the skin friction coefficient and the local Nusselt number are tabulated and analyzed.     

土体颗粒物流动物质点法模拟的弹塑性和非牛顿流体本构模型比较研究

土体颗粒物流动是一种典型的大变形破坏,具有非牛顿流体的流动特征。准确模拟土体颗粒物的流动及冲击过程,对滑坡和泥石流等地质灾害的防治具有重要意义。物质点法是一种无网格粒子类方法,已在各类大变形问题中得到了广泛应用。以往土体颗粒物流动的模拟,通常采用弹塑性本构模型,但缺乏对非牛顿本构模型的模拟分析。本文引入非牛顿本构模型的模拟分析,旨在为土体颗粒物流动模拟提供一种新的方法与思路。非牛顿本构模型的模拟分析是将非牛顿广义Cross模型引入三维物质点法,通过人工阻尼力模拟颗粒间的摩擦力,对土体颗粒物的坍塌、沿斜面滑动以及冲击障碍物等问题进行了动态模拟,研究了其运动全过程,并与弹塑性本构模型的模拟结果进行了对比验证。结果表明,基于非牛顿流体本构模型的物质点法可以较好地模拟土体颗粒物加速、减速到再次稳定的流动全过程及其对障碍物的冲击效应。     

Analysis of the squeezing flow of dusty fluids

The current investigation deals with the study of the effect of introducing a small fraction of dust, by volume, to the fluid in a squeeze film on the viscous resistance to a steady moving disc. Expressions are obtained for the fluid-phase and the dust-phase velocity distributions and the dust particle number density. Analysis based on an iterative procedure indicates that the resistance to motion experienced by the moving disc increases due to the presence of dust.Nomenclature A arbitrary function of integration - B bulk concentration - F resistance to motion experienced by the disc (dusty fluid case) - F _c resistance to motion experienced by the disc (clean fluid case) - F* difference in resistance between the clean fluid and dusty fluid films - f mass concentration - h thickness of the squeeze film - K Stokes coefficient of resistance - m mass of a single dust particle - fluid viscosity coefficient - N dust particles number density - N ₀ dust particles number density at r=R - n iteration level - p fluid pressure in the squeeze film - P pressure in the surrounding - R radius of the disc - fluid density - (r, , y) cylindrical coordinates - t time - U fluid-phase velocity vector - V dust-phase velocity vector - ₁ fluid-phase radial velocity component - U ₂ dust-phase radial velocity component     

Slip and no-slip squeezing flow of liquid food in a wedge

Squeezing flow in a wedge simulates a number of practical processes, e.g. lubrication, coating and the sensory evaluation of liquid foods. This paper reports analytical approximate solutions for both slip (or lubricated) and no-slip squeezing flow of liquid food in a wedge, in which the power law fluid model was used. The solutions do not seem to be more complex than that for squeezing flow between two parallel disks and may be used as a variation of the psycho-physical models of in-mouth viscosity and food spreadability. Alternatively, a rheometer for testing liquid foods may be developed according to the equations described in this paper.     

Oscillatory flow in microchannels

Commonly used, lumped-parameter expressions for the impedance of an incompressible viscous fluid subjected to harmonic oscillations in a channel were compared with exact expressions, based on solutions of the Navier-Stokes equations for slots and channels of circular and rectangular cross-section, and were found to differ by as much as 30% in amplitude. These differences resulted in predicted discrepancies by as much as 400% in frequency response amplitude for simple second-order systems based on size scales and frequencies encountered in microfluidic devices. These predictions were verified experimentally for rectangular microchannels and indicate that underdamped fluidic systems operating near the corner frequency of any included flow channel should be modeled with exact expressions for impedance to avoid potentially large errors in predicted behavior.List of symbols A Channel cross-sectional area (m²) - A_c Membrane area (m²) - a Rectangular duct and slot half-width or radius (m) - b Rectangular duct half-depth and slot depth (m) - C Capacitance (m³/Pa) - C - D_h Channel hydraulic diameter (m) - E Voltage (V) - f Darcy friction factor - F Force (N) - I Channel inertance (Pa s²/m³) - i - Imaginary part of a complex number - J_k Bessel function of the first kind of order k - System transfer function - K Sum of minor loss factors - k Membrane stiffness (N/m) - L Channel length (m) - n Outward unit normal vector - P Fluid pressure (Pa) - p_n - Q Volumetric flow rate (m³/s) - R Channel resistance (Pa s/m³) - Real part of a complex number - Re Reynolds number, - V Velocity (m/s) - _V Volume (m³) - w Axial component of velocity (m/s) - Harmonic amplitude of membrane centerline displacement - Fluid impedance (kg/m⁴ s) - Duct aspect ratio, b/a - ² Nondimensional frequency parameter, - Nondimensional corner frequency, - Membrane shape factor - C/C - µ Fluid dynamic viscosity (Pa s) - Fluid kinematic viscosity (m²/s) - Mass density (kg/m³) - Radian frequency - _c R_s/I_s cutoff or corner frequency - _n Undamped natural frequency - Channel shape parameter in Eqs. 29 and 30 - Damping ratio - ( )_e Exact property - ( )_s Simplified property - (^–) Spatial average - Complex quantity     

Imperfect lubricated squeezing flow viscometry for foods

Commercial mayonnaise and mustard samples placed in a wide, shallow Teflon container were compressed by a wide Teflon plate to induce an imperfect lubricated squeezing flow. A dominant squeezing flow regime could be clearly identified as a linear region in the log F(t) vs log H(t) relationship, F(t) and H(t) being the momentary force and specimen height respectively. The slope of the relationship enabled the estimation of the flow index, n, and the consistency coefficient K. The n values of the mayonnaise were on the order of 0.6–0.85 and those of the mustard about 0.7. The corresponding K values were on the order of 6–13 and 4–5 kPasⁿ respectively. Considering the crudeness of the array the measurements were highly reproducible and sensitive enough to detect differences (mayonnaise) or establish similarities (mustard) in products of different brands. The calculated flow index was practically independent of the plate's radius and of the consistency coefficient, which had a weak dependency on the latter. The calculated elongational viscosity vs biaxial strain rate relationship could also be used to compare the different products and brands. At 0.01 s^–1 the elongational viscosity of the maynonnaise was on the order of 150 kPas, and of the mustard 60 kPas.     

On the continuous squeezing flow in a wedge

The paper is concerned with the continuous squeezing flow of Oldroyd-type fluids in a two-dimensional wedge. The flow mimics the lubrication action in a squeezing flow and is important in that there exists a similarity solution for any simple fluid. We are only concerned with Oldroyd-type fluids, however. It is shown by using a parameter continuation method that the Oldroyd-B model has a limiting Weissenberg number. The Phan Thien/Tanner model does not have this limiting Weissenberg number.     

Oscillatory flow of second grade fluid in cylindrical tube

The unsteady oscillatory flow of an incompressible second grade fluid in a cylindrical tube with large wall suction is studied analytically. Flow in the tube is due to uniform suction at the permeable walls, and the oscillations in the velocity field are due to small amplitude time harmonic pressure waves. The physical quantities of interest are the velocity field, the amplitude of oscillation, and the penetration depth of the oscillatory wave. The analytical solution of the governing boundary value problem is obtained, and the effects of second grade fluid parameters are analyzed and discussed.     

An investigation of squeeze flow as a viable technique for determining the yield stress

A systematic study of squeeze flow (SF) was performed on different concentrations of Carbopol with varying yield stresses. A sample of constant volume was placed between two parallel plates and a series of constant force steps applied, following the plate separation as a function of time. Precise rheological measurements of the model yield stress fluids were performed in addition to the well-controlled SF tests. These rheological measurements were used in conjunction with the SF equations to determine the time-dependent plate separation, allowing a direct comparison of theory and experiment throughout the entire test. The limiting height achieved during constant force SF reveals information about the yield stress of the fluid as predicted by the theory. It appears that by carefully controlling the experimental conditions of the squeeze test one can obtain yield stress values that agree with the rheological measurements within 10%. Additionally, the validity of the lubricational theory was tested; not only for the determination of the yield stress but throughout the flow as well.     

A relation between shear flow material functions for a single-integral constitutive equation

This contribution suggests some relations between normal-stress differences and shear stress, both in the steady state and in the transient regimes. It shows that the general form of the BKZ-type equation can be used for the discussion of the relations between several material functions. In addition, a geometric interpretation is offered and some examples are discussed.     

MHD squeezing flow of second‐grade fluid between two parallel disks

This paper examines the unsteady two‐dimensional flow of a second‐grade fluid between parallel disks in the presence of an applied magnetic field. The continuity and momentum equations governing the unsteady two‐dimensional flow of a second‐grade fluid are reduced to a single differential equation through similarity transformations. The resulting differential system is computed by a homotopy analysis method. Graphical results are discussed for both suction and blowing cases. In addition, the derived results are compared with the homotopy perturbation solution in a viscous fluid (Math. Probl. Eng., DOI: 10.1155/2009/603916 ). Copyright © 2011 John Wiley & Sons, Ltd.     

Oscillatory line source for water waves in shear flow

The linearized water-wave radiation problem for the oscillating 2D submerged source in an inviscid shear flow with a free surface is investigated analytically. The vorticity is uniform, with zero velocity at the free surface. Then there will be at most two emitted waves, and no Doppler effects. Exact far-field waves are derived, with radiation conditions applied at infinity. An upstream wave will always exist, whereas the downstream wave exists only when the angular frequency of oscillation exceeds the vorticity. The wave radiation problem is solved also for oscillating vortex and dipoles. The amplitudes and energy fluxes are calculated.     

The squeezing flow of a model suspension fluid

The paper is concerned with the squeezing flow of a model suspension fluid. The numerical solution obtained by a time-dependent Boundary Element Method is compared to an asymptotic solution at large radius. It is found that the kinematics are Newtonian in character, and the fibres quickly align themselves radially. Consequently, the squeezing force is only weakly dependent on the initial orientations of the fibres and the device can be used for measuring the effective viscosity of the suspension. The effective viscosity found from the squeezing flow agrees surprisingly well with experimental data and numerical data derived from the falling sphere geometry at low volume fractions ( < 0.1).     

Analysis of lubricated squeezing flow

A thin film of low-viscosity lubricating liquid between a solid wall and a viscous material reduces shear stress on the latter and tends to make it flow as though it were slipping along the wall. The result when the lubricated material is being squeezed out of the gap between approaching parallel plates is flow more nearly irrotational, or extensional, the more effective the lubricating film on the plates. Two Newtonian analyses of this flow situation are reported. One is an approximate, asymptotic analytical solution for Newtonian lubricating flow in the films and combined mixed flow, shear and extension, in the viscous layer. The second is a full two-dimensional axisymmetric solution of the momentum and continuity equations along with the kinematic condition which governs the motion of the interface. Both analyses indicate that there are two limiting flow regimes, depending on the ratio of the thickness of each of the two phases to radius and on the viscosity ratio of the two liquids. In one limit the flow is parallel squeezing and the lubricant layer slowly thins and persists a long time. In the other the lubricant is expelled preferentially. Implications of the results are discussed for rheological characterization of viscoelastic liquids and for prediction of lubricated or autolubricated flows in processing situations.     

Lubricated squeezing flow of a Newtonian liquid between elastic and rigid plates

Theoretical force-time relationships were derived for squeezing flow of a Newtonian liquid between lubricated rigid and elastic plates. It is shown how the elastic number, representing the ratio between the elastic plate's rigidity and the specimen's viscosity, affects the force-time curve and under what circumstances the fluid specimen's thickness becomes a significant factor. Potential implications of the analysis in oral sensory evaluations of viscous foods are also considered.