Self-oscillational motion of a cylinder towed in weak aqueous polymer solution

A study is made of the effect of polymer additions on the nonstationary vibrational motion of a cylinder towed in a weak aqueous solution of the polymer and capable of making transverse displacements under the action of the force arising from asymmetry of the periodic detachment of the boundary layer. The Reynolds number was 3·10³–10⁴.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 162–164, 1973.The authors wish to thank V. P. Borovikov for his assistance in organizing the experiments.     

Convective heat transfer of aqueous alumina nanosuspensions in a horizontal mini-channel

This work reports an experimental study of convective heat transfer of aqueous alumina nanofluids in a horizontal mini-channel under laminar flow condition 40 < Re < 1,000. The variation of local heat transfer coefficients, in both entrance and developed flow regimes, was obtained as a function of axial distance. The heat transfer coefficient of nanofluids was found to be dependent on not only nanoparticle concentration but also mass flow rate. Different to the behavior in conventional-sized channels, the major heat transfer coefficient enhancement is shown in the fully developed regime in the minichannel where up to 40% increase is observed. Discussions of the results suggest that apart from the need of a careful assessment of different thermo-physical properties of nanofluids, i.e., viscosity, specific heat and thermal conductivity, the heterogeneous nature of nanoparticle flow should be considered especially under high flow rate conditions.     

A rising bubble in a polymer solution

We propose a boundary integral method to study the shape of a bubble rising under gravity in a dilute polymer solution. Constitutive properties are modelled using a FENE model [M.D. Chilcott, J.M. Rallison, J. Non-Newtonian Fluid Mech. 29 (1988) 381] with a pure surface tension interface. We employ a birefringent strand representation [O.G. Harlen, J.M. Rallison, M.D. Chilcott, High-Deborah-number flows of dilute polymer, J. Non-Newtonian Fluid Mech.34 (1990) 319–349] of the wake to simulate the shape and the time-dependent motion of the bubble. Steady and non-steady solutions reproduce qualitatively the bubble deformation seen in experiment with a small region of very high curvature near the rear stagnation point of the bubble. We find a limit point for steady axisymmetric solutions if the polymer concentration is increased or the surface tension is decreased. Rise speed jump discontinuities were not found.     

Divergent channel flow of a liquid crystalline polymer solution

 The flow of a `model' lyotropic liquid crystal polymer, (hydroxypropyl)cellulose in water, through a rectangular channel with a divergence in the channel width, is studied by in situ light microscopy. Microscopic texture observations are related to measurements of the flow velocity field, in order to characterize the shear and elongational aspects of the flow and to examine the effects of the divergence from a narrow channel to a wide channel. A strong dependence of flow-induced texture on position in the channel is observed and is related to the interplay of shear and elongational strain. The divergence generates both a perpendicular elongational strain due to the widening of the channel, and subsequently an elongational strain along the flow direction due to the change in flow pattern from quasi-radial to unidirectional down the wide channel. Additionally side wall structure is observed to be more complex than a simple strong alignment, displaying a fine birefringent texture. Finally there is a marked dependence of the macroscopic structure on the strain history of the fluid prior to entry into the channel, indicating that very different structures of, for instance, moulded parts, can result from differences in geometry and fluid treatment prior to entry into the mould itself. Received: 12 October 1999/Accepted: 29 October 1999     

Unstable slit flow of a liquid crystalline polymer solution

A lyotopic solution of 27 wt% hydroxypropylcellulose [HPC] in m-cresol has been studied in pressure-driven slit flow. At high flow rates an instability leads to large wavelength disturbances in fluid structure. A combination of image analysis and time signal processing is used to determine the velocity at which the structural disturbances are convected downstream, which is shown to be equal to the independently measured and predicted centerline velocity. This implies that the disturbance structure is confined near the midplane of the slit flow. Upstream of the onset point of the wavy fluid structures, the fluid exhibits unusual optical properties when viewed between crossed polarizers that are rotated relative to the flow direction. Specifically, the optical properties indicate that there must be some variation in the macroscopic optical axis of the sample as light passes through the slit flow. A discrete optical model consisting of birefringent elements twisted away from and back to the flow direction as a function of depth in the sample is able to predict the essential optical characteristics; however, independent x-ray scattering measurements show that the macroscopic molecular alignment is along the flow direction. The wavy textures apparently emerge as a result of an inhomogeneous transition of orientation back to the flow direction, trapping thin bands of fluid in the twisted configuration.     

Convective drying analysis of three-dimensional porous solid by mass lumping finite element technique

A numerical analysis of convective drying of a 3D porous solid of brick material is carried out using the finite element method and mass lumping technique. The energy equation and moisture transport equations for the porous solid are derived based on continuum approach following Whitaker’s theory of drying. The governing equations are solved using the Galerkin’s weighted residual method, which convert the governing equations into discretized form of matrix equations. The resulting capacitance matrices are made diagonal matrices by following the classical row-sum mass lumping technique. Hence with the use of the Eulerian time marching scheme, the final equations are reduced to simple algebraic equations, which can be solved directly without using an equation solver. The proposed numerical scheme is initially validated with experimental results for 1D drying problem and then tested by application to convective drying of 3D porous solid of brick material for four different aspect ratios obtained by varying the cross section of the solid. The mass lumping technique could correctly predict the wet bulb temperature of the solid under evaporative drying conditions. A parametric study carried out for three different values of convective heat transfer coefficients, 15, 30 and 45 W/m² K shows an increased drying rate with increase in area of cross section and convective heat transfer coefficient. The proposed numerical scheme could correctly predict the drying behavior shown in the form of temperature and moisture evolutions.     

Surface tension measurement of aqueous polymer solutions

The surface tension of aqueous polymer solutions of polyacrylamide (PAM), polyacrylic acid (PAA), carboxymethyl cellulose (CMC), and hydroxyethyl cellulose (HEC) was studied over a range of polymer concentrations by using the maximum bubble pressure method at temperatures ranging from 20 to 65°C. The surface tension of water was also measured by the maximum bubble pressure method as well as by the DuNoüy ring method over the same temperature range. The experimental water data are in excellent agreement with the well-established tabulated data in the literature.

For a fixed concentration, all of the polymer solutions exhibited a decrease in surface tension with increasing temperature level. When compared with water at a fixed temperature level, the PAM and CMC solutions showed slightly higher surface tension values, whereas the PAA solutions yielded values equal to those found for water. In the case of the HEC solutions, the measured surface tensions decreased with concentration at a fixed temperature level and were lower than the values found for water. For a concentration of 2000 wppm the surface tension values for the hydroxyethyl cellulose were of the order of 10% lower than those for water at a fixed temperature level.

A comparison of the new measurements with the relatively limited previously published studies showed good agreement.     

A rheological and structural study of a discotic side chain polymer solution

The structural and dynamical properties of a physical network in a discotic side-chain polymer solution have been studied. For that purpose, use has been made of rheological measurements and a statistical network model for the crosslinking of polymer. The goal of the investigation was to gain more insight into processes playing important roles in the subtle interactions between discotic side-chain polymers. A relatively simple mechanical model is presented to describe the mechanical behaviour of the solutions. Moreover, results are shown for the specific dynamic as well as structural properties of the physical networks in these solutions.     

Structure and dynamics of a polymer solution subject to flow-induced phase separation

Experiments combining mechanical rheometry with polarimetry (birefringence and scattering dichroism) have been conducted on a 6% solution of polystyrene (1.86x10⁶ molecular weight) in dioctyl phthalate. Birefringence is used to measure the extent of segmental orientation, whereas the dichroism is sensitive to orientation and deformation of concentration fluctuations associated with the process of flow-induced phase separation. The results indicate that these fluctuations grow predominately along the neutral (or vorticity axis) of a simple shear flow. At higher rates of shear, orientation in the flow direction is favored. The transition in orientation direction is accompanied by time-dependent behavior in the optical properties of the solution during shear and the onset of shear thickening of the viscosity and the first normal stress difference coefficient.     

Boundary layer of a body of revolution in a drag-reducing polymer solution

A possible method is presented for calculating an axisymmetric boundary layer when a body moves in weak polymer solutions with constant concentration. The method is based on the use of a velocity profile and system of integral equations which take into account most fully the effects of the transverse curvature of the body's surface. The computational scheme makes it possible to take into account the change in the flow regimes in the boundary layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 40–48, May–June, 1981.     

Shear stress and normal stress measurements of aqueous polymer solutions in a cone-and-plate rheogoniometer

Summary The rheological behaviour of aqueous solutions of Separan AP-30 and Polyox WSR-301 in a concentration range of 10–10000 wppm is investigated by means of a cone-and-plate rheogoniometer. The relation between the shear stress and the shear rate is for lower shear rates characterized by a timet ₀, which is concentration dependent. Both polymers show for 4000 s^–1 < < 10000 s^–1 a behaviour similar to that of a Bingham material, characterized by a dynamic viscosity ₀ and an apparent yield stress ₀, which also depend on the concentration. The inertial forces are measured for water and some other Newtonian liquids. An explanation is given why the theoretical model developed for these forces does not match the experimental values; the shape of the liquid surface is shear rate dependent. To obtain the first normal stress difference, we have to correct for these inertial forces, the surface tension and the buoyancy. The normal forces, measured for Separan AP-30, appear to be a linear function of the shear rate for 350 s^–1 < < 3300 s^–1.

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Zusammenfassung Das rheologische Verhalten wäßriger Polymerlösungen von Separan AP-30 und Polyox WSR-301 wird in einem Konzentrationsgebiet von 10–10000 wppm in einem Kegel-Platte-Rheogoniometer untersucht. Der Zusammenhang zwischen Schubspannung und Schergeschwindigkeit wird für niedrige Schergeschwindigkeiten durch eine konzentrationsabhängige Zeitt ₀ gekennzeichnet. Für Schergeschwindigkeiten 4000 s^–1 < < 10000 s^–1 zeigen beide Polymere ein genähert binghamsches Verhalten, gekennzeichnet durch eine dynamische Viskosität ₀ und eine scheinbare Fließgrenze ₀, welche ebenfalls konzentrationsabhängig sind. Die Trägheitskräfte werden für Wasser und einige newtonsche Öle bestimmt. Die Abweichung der experimentellen Ergebnisse vom theoretischen Modell wird durch die Abhängigkeit der Gestalt der Flüssigkeitsoberfläche von der Schergeschwindigkeit erklärt. Um die Werte der ersten Normalspannungsdifferenz zu erhalten, muß man bezüglich der Trägheitskräfte, der Oberflächenspannung und der Auftriebskräfte korrigieren. Die Normalspannungen für Separan AP-30, gemessen für 350 s^–1 < < 3300 s^–1, zeigen eine lineare Abhängigkeit von der Schergeschwindigkeit.

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c concentration (wppm) - g acceleration of gravity (ms^–2) - K force (N) - K _b buoyant force (N) - K _c force, acting on the cone (N) - K ₀ dimensional constant def. by eq. [24] (N) - K _s force, def. by eq. [22] (N) - M dimensional constant def. by eq. [24] (Ns) - P _s pressure def. by eq. [17] (Nm^–2) - P ₀ average pressure in the liquid atr = 0 (Nm^–2) - P _R average pressure in the liquid atr = R (Nm^–2) - r ₁,r ₂ radii of curved liquid surface (m) - R platen radius (m) - R _w radius of wetted platen area (m) - S _x standard deviation ofx - t ₀ characteristic time def. by eq. [1] (s) - T temperature (°C) - V volume of the submerged part of the cone (m³) - v tangential velocity of liquid (ms^–1) - x distance (m) - angle (rad) - ₀ cone angle (rad) - calibration constant (Nm^–3) - shear rate (s^–1) - dynamic viscosity (mPa · s) - ₀ viscosity def. by eq. [1] (mPa · s) - contact angle (rad) - density (kgm^–3) - static surface tension (Nm^–1) - shear stress (Nm^–2) - ₀ yield stress def. by eq. [1] (Nm^–2) - _c, _p angular velocity (c = cone,p = plate) (s^–1) With 8 figures and 3 tables     

Viscoelastic stresses in the stagnation flow of a dilute polymer solution

In this paper, we consider viscoelastic stresses T₁₁, T₁₂ and T₂₂ arising in the stagnation flow of a dilute polymer solution; in particular, we consider an upper convected Maxwell (UCM) fluid. We present exact solutions to the coupled partial differential equations describing the viscoelastic stresses and deduce the results for the stress T₂₂ of Becherer et al. [P. Becherer, A.N. Morozov, W. van Saarloos, Scaling of singular structures in extensional flow of dilute polymer solutions, J. Non-Newtonian Fluid Mech. 153 (2008) 183–190]. As we considered the viscoelastic stresses over two spatial variables, we are able to study the effect of variable boundary data at the inflow. As such, our results are applicable to a wider range of fluid flow problems.     

Rheological characterization in shear of a model dumbbell polymer concentrated solution

We investigate the linear and non-linear rheological behavior in shear of a concentrated solution of ??dumbbell?? polystyrene with long linear backbone and dense short brushes at both ends and compare it with corresponding linear polymers. This type of dumbbells has never been rheologically characterized before. In linear viscoelasticity, the dumbbell polymers show significant differences with conventional linear polymers. In particular, the reptation relaxation of the dumbbell is strongly slowed down. Furthermore, the addition of the side chains increases the friction so that the dumbbell lies above the ?? ₀ vs. number of entanglements relation of linear samples. Transient shear rheology experiments on weakly entangled solutions show a retardation of the chain stretch relaxation of the dumbbell by a factor 2.5 vs. a linear polymer with the same Rouse time. Additionally, a second peak in the transient viscosity is observed at high shear rates.     

Change in the structure of a polymer solution in a longitudinal hydrodynamic field

There are two qualitatively different conditions for the stretching of liquid fibers formed by moderately concentrated polymer solutions [1]. If the longitudinal gradient of the drawing rate is rather small the structure of the solution remains unchanged. If this gradient exceeds a certain critical value, some of the solvent is expressed from the solution in and the liquid filament is converted into a slightly swollen fiber. The solvent released settles as droplets on the filament surface. This effect is of very great importance for a number of industrial processes pertaining to the production of filaments and films from polymer solutions. In addition, as was reported in [1], the drawing of a liquid filament, accomapnied by orientational formation of the solid phase, can serve as a most simple imitation of the formation of silk and gossamer filaments in nature.This paper presents a qualitative theory for this phenomenon, based on investigation of the thermodynamic stability of a polymer solution in a longitudinal hydrodynamic field.In conclusion the author thanks S. Ya. Frenkel for kindly providing information about the experiments conducted in his laboratory.     

Determination of properties for the calculation of aqueous thin film drying

 This paper deals with the determination of various properties required for the numerical calculation of the thin film drying of a water based varnish applied on paper. Experimental and analytical methods which provide the activity of water in paper and in a water based varnish, and the diffusion coefficient of water in this varnish are presented. Received on 23 March 2001     

Viscosity of a liquid crystalline polymer solution with a polydomain or a band texture

The viscosity of a main-chain liquid crystalline polymer (anisotropic aqueous solution of hydroxypropylcellulose) is measured in the case where the liquid crystalline polymer presents a band texture and is compared to the case of a polydomain texture.     

Convective instability of a ferrofluid

We clarify the conditions under which instability arises in the equilibrium of a nonuniformly heated ferrofluid in a gravitational field and a nonuniform magnetic field. The latter is, in the first place, responsible for the Archimedean buoyant forces, and in the second, gradients in the magnetic intensity result in the appearance of internal heat sources (magnetocaloric effect). As a rule, this effect is extremely weak and to take correct account of it requires that at the same time the compressibility of the fluid be taken into account in the equation of heat conduction. We show that it is precisely the neglect of compressibility that explains the erroneous conclusion, contradictory to the laws of thermodynamics, concerning the convective instability of an isothermal ferrofluid that was arrived at in a series of papers by B. M. Berkovskii. We formulate a dimensionless criterion that characterizes the stability of the equilibrium of a ferrofluid. In limiting cases of large or small cavities this criterion passes over to the ferrohydrodynamic analog of the usual Schwartzschild or Rayleigh criteria.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No, 6, pp. 130–135, November–December, 1973.The author thanks members of seminars conducted by G. A. Lyubimov and G. I. Petrov for discussion of the questions considered here.