Rheological characterization of a solder paste for surface mount applications

Solder pastes used in surface mount soldering techniques (SMT) are very complex suspensions containing high volumes of metallic powder in a carrier fluid. The rheological complexity results largely from the carrier fluid itself, which is a suspension of colloidal particles. In this work, we have characterized the rheological properties of a typical carrier fluid and its solder paste containing 64 vol.% metallic powder. A six-blade vane geometry was used to avoid wall slip and sample fracture. All measurements were carried out following pre-shearing and rest time in order to obtain reproducible results. Steady shear experiments showed that the solder paste was highly shear-thinning and thixotropic. In oscillatory shear, the linear viscoelastic domain was found to be very narrow for both the suspending fluid and the paste. Frequency sweep tests in the linear domain revealed a gel-like structure with a nearly constant G′ for the suspending fluid and a slightly increasing G′ for the solder paste. From creep experiments, a yield stress of about 40 Pa was determined for the suspending fluid at temperatures between 25 and 40°C, and of 100 Pa at 4°C. A much larger yield stress, 480 Pa, was determined for the solder paste at 25°C.     

Viscoelastic behaviour of wheat starch pastes

Summary The dynamic mechanical behaviour of starch pastes has been investigated over a frequency range of 0.02 to 5.0 radian sec^–1. The influence of concentration of starch, source of starch and method of paste preparation on rheological properties have been studied. The results suggest that under the conditions examined differences in the dynamic rigidity and viscosity of pastes may be attributed to differences in the number fraction of large granules and the volume fraction of swollen starch particles they contain.With 4 figures and 4 tables     

The use of the capillary rheometer for the rheological evaluation of extrudable cement-based materials

In this paper, the rheological properties of an extrudable cement-based paste are investigated by means of an original ram extrusion apparatus (capillary rheometer). The experimental results indicate that a careful measurement of the die pressure is necessary to obtain a realistic viscosity vs shear rate curve, as required in extrusion technology. In particular, it is shown that the optimal test configuration is when the pressure measurement is made directly inside the rheometer die. By applying this rheological methodology in steady-state conditions, it has been observed that the extrudable cement-based material here evaluated obeys to a simple power–law equation, in the range of shear rates investigated, which are suitable for an industrial extrusion process. This paper was presented at the third Annual European Rheology Conference (AERC) held in Hersonissos, Crete, Greece, April 24–27, 2006.     

Rheology of milled black cumin (Nigella sativa L.)

Black cumin (Nigella sativa L.) paste is a local food in the Middle East, which is produced from dehulled black cumin seeds. The rheological properties of a commercial black cumin paste in the temperature range of 5-40 °C have been studied. Shear-thinning flow behavior with a yield stress was observed for the samples tested. The Herschel-Bulkley model described well the flow curves of the black cumin pastes at different temperatures. It was found that the yield stress, the consistency coefficient, and the flow behavior index decrease with temperature. As far as the effect of steady shearing on the rheological properties of black cumin paste is concerned, the structural kinetic approach was used to predict the thixotropic behavior. It was found that the thixotropic behavior of black cumin paste increases with increasing shear rate and is mitigated by increasing temperature. The completely destructed black cumin paste flow curves were also measured after subjecting the samples to a high shear rate for 2 h. The flow curves of the completely destructed samples were modeled well by the Herschel-Bulkley model. A comparison between the fresh and the completely destructed black cumin paste results at different temperatures revealed that there was a systematic difference, such that the completely destructed paste showed lower yield stress and flow behavior index, and showed a greater consistency coefficient.     

Rheological properties of disperse systems at low shear stresses

Three-dimensional network structures can be built up in disperse systems due to long-range colloidal interactions between the dispersed particles. The rheological behaviour of such coagulation structures has been studied by means of creep and recovery experiments at low shear stresses, i.e. by measuring the shear strain as a function of time under constant stress and after removal of stress. Measurements of this type give insight into the elastic and viscous deformations and the retardation times necessary to reach equilibrium or steady-state conditions.Results obtained with dispersions of pigments in polymer solutions and with monodisperse polymer latexes indicate the existence of an equilibrium state at low shear stresses with a predominant elastic deformation and a high viscosity suggesting that the disperse systems investigated do not behave exactly as rigid gels but apparently exhibit a dynamic equilibrium of structural break-down and formation under applied stress. This behaviour is approximately described by a 4-parameter-model with an instantaneous and a steady-state compliance, one retardation time, and a viscosity.At higher shear stresses thixotropic structural break-down occurs resulting in a transition from the rheological behaviour described here to a liquid-like state with a comparatively low viscosity. In this stress range the viscoelastic properties become strongly time-dependent.These measurements give evidence of the presence of two types of deformation: an instantaneous, purely elastic deformation attributable to the unperturbed coagulation structure and the creep-recovery behaviour of an elastic liquid apparently related to the breaking and re-forming of bonds.     

Rheological behaviour of nano-composites based on polyamide 6 under shear and elongational flow at high strain rates

In this work, the rheological behaviour of high molecular mass polyamide 6 (PA6)/organo-montmorillonite nano-composites, obtained via melt blending, was investigated under shear and extensional flow. Capillary rheometry was used for the measurement of high shear rate steady state shear viscosity and die entrance pressure losses; further, by the application of a converging flow method (Cogswell model) to these experimental results, elongational viscosity data were indirectly calculated. The extensional behaviour was directly investigated by means of melt spinning experiments, and data of apparent elongational viscosity were determined. The results evidenced that the presence of the organo-clay in filled PA6 melts modifies the rheological behaviour of the material, with respect to the unfilled polymer, in dependence on the type of flow experienced by the fluid. In shear flow, the nano-composites showed a slightly lower viscosity than neat PA6, whereas in elongation, they appeared much more viscous, in dependence on the organo-clay content.     

Rheological properties of poly(dimethylsiloxane) filled with fumed silica: I. Hysteresis behaviour

The apparent viscosity and primary normal stress difference were measured for dispersions of fumed silica in poly(dimethylsiloxane). Dispersions with less than 4.75% by weight of filler exhibit hysteresis in both the viscosity and normal stress, when the shear rate was increased and then decreased in discrete steps. The shape of the hysteresis loops were sensitive to the details of the deformation history. By using the appropriate deformation history, the material properties determined during the increasing shear rate part of the hysteresis experiment compare favourably with the steady-state rheological properties. The rheological properties of the dispersion were quite sensitive to the age of the fluid with no hysteresis behaviou exhibited by dispersions less than three days old. For dispersions with at least 4.75% by weight of fumed silica, neither the apparent viscosity nor the primary normal stress coefficient exhibited significant hysteresis behaviour. The relationship between the observed rheological behaviour and the dispersion's microstructure is discussed.     

Modeling of blood rheological behavior in unsteady-state shearing flows

Issues of blood flow modeling under unsteady-state conditions at moderate shear rates are considered using a blood rheological model accounting both for the viscoelastic properties and the thixotropy caused by erythrocyte aggregation. The resulting shear stress versus time relations for single shear rate steps and the dependence of the complex viscosity components on the shear rate amplitude in oscillating shear flow show good qualitative correspondence with the experimental data reported in the literature.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 26–30, November–December, 1995.     

Rheological behaviour of vitreous humour

The vitreous humour (VH) is a complex biofluid that occupies a large portion of the eyeball between the lens and the retina, and exhibits non-Newtonian rheological properties that are key for its function in the eye. It is often possible to distinguish two different phases in VH, known as liquid and gel phases (Sebag J Eye 1: 254–262, 1987). In this work, we present a detailed rheological characterisation of the two phases of the VH under shear and extensional flow conditions. Healthy New Zealand rabbit eyes were used to measure the surface tension and the shear and extensional rheological properties of VH in different phase conformations and at different times after dissection. The results show that VH liquid phase exhibits a surface tension of 47.8 mN/m, a shear thinning behaviour reaching a viscosity plateau around 10^?3 Pa s for shear rates above ~1000 s^?1, and an average relaxation time of 9.7 ms in extensional flow. Interestingly, both VH phases present higher storage modulus than loss modulus, and the measurements performed with VH gel phase 4?±?1 h after dissection exhibit the highest moduli values. The compliance measurements for the gel phase show a viscoelastic gel behaviour and that compliance values decrease substantially with time after dissection. Our results show that the two VH phases exhibit viscoelastic behaviour, but with distinct rheological characteristics, consistent with a gel phase mostly composed of collagen entangled by hyaluronan and a second phase mainly composed of hyaluronan in aqueous solution.     

Rheological properties of fresh cement pastes and clinker reactivity

This paper presents research results concerning the influence of clinker reactivity on rheological properties of cement pastes at early stages of hydration (lasting less than one hour). The research was carried out on clinkers synthesized in a laboratory, on non-alkaline cements and cements containing in-built alkalis (sodium, potassium) in the clinker phase.The clinker reactivity was estimated from the flow curves and stress changes in time occurring in clinker pastes while maintaining constant measurement parameters. It was found that the effectiveness of gypsum as a setting controller depends on clinker reactivity. Increased clinker reactivity is accompanied by a decreased consistency of a cement paste.The research results indicate that decreased reactivity of clinkers containing inbuilt alkalis is connected with decreased setting controlling effectiveness of added gypsum. This is manifested by a consistency increase of such system at early stages of hydration.     

Rheology of gel-like materials in textile printing

Printing of fabrics made of cellulose fibres involves printing pastes mainly containing the dyer and thickeners which are generally polysaccharides. The process is a sequence of several operations in order to obtain the penetration and the fixation of the dyer molecule in the fibre. Firstly, the paste is deposited on the fabric and dried. Then, there is a gelation phase by means of a cross-linking agent. This paper presents experimental results obtained with thickeners used in textile industry. The rheological properties of the thickeners and of the gels are characterised by oscillatory measurements. The influence of the pH and of the presence of salt is discussed.     

Study on the rheological properties of Portland cement pastes with polycarboxylate superplasticizers

The coupling effects of temperature and time on the fluidity of fresh cement mixtures were investigated. Mini-cone tests on cement mortars and rheological tests on cement pastes under different temperatures (0 to 60 °C) were conducted to characterize the development of the fluidity of fresh cement mixtures over time. In addition, total organic carbon tests were performed to quantify the adsorption amount of superplasticizers on the cement surface. The amount of free water in cement pastes was determined via centrifugation. Isothermal calorimetry was employed to characterize the hydration kinetics of cement under different temperatures. Results show that the spread diameter of mortars decreases in a roughly linear fashion over elapsed time. Higher temperature facilitates a sharper decrease in fluidity with time, although the initial fluidity of fresh mortars is not significantly affected by temperature. Higher temperature results in a greater amount of adsorbed polycarboxylate ester/ether on the cement surface and a lower amount of free water in fresh cement pastes, which is believed to result from the higher hydration rate of cement. The evolution of rheological properties over time can be attributed to the development of hydration degree. Relative hydration degree is introduced to indicate the development of rheological properties with time. Two models to describe the evolution of yield stress and plastic viscosity for fresh cement pastes were developed.     

Numerical simulation of blade coating with short dwell and roll application coaters

Paper and board are often coated at high speeds with a mineral-based aqueous suspension in order to improve their printing properties. This suspension is usually called coating colour. The flow behaviour of the coating colour in the cavity of the short dwell coater (SDC) and in the vicinity of the blade tip when paper is coated with a stiff blade has been analysed using the finite element method. The models used to simulate the flow incorporated free surfaces and shear-thinning colours. The Newtonian case was in some cases also included in the modelling. The viscosity level and the shear-thinning character of the coating colour had a significant influence on the flow in the SDC cavity, although the overall behaviour was to a large extent governed by the speed of the coater. The pressure distribution along the paper surface in the SDC cavity was also analysed.In agreement with earlier reported results, increasing the machine speed raised the pressure level in the colour close to the blade tip. The rheological properties of the coating colour also affected the flow field and the pressure distribution in this region; e.g. it was found here that a colour with a high viscosity level at low shear rates developed a high pressure level close to the blade tip. The most interesting result revealed by the analysis was that changes in the configuration close to the blade tip (converging flow between the blade tip and the paper and compression of the substrate under the blade tip) and boundary conditions at the blade tip surface had a very significant effect on the pressure distribution. The predictions of the numerical simulation were to some extent compared with experience from practical coating trials.     

The phenomenological description of the thixotropic behaviour of fresh cement pastes

The present work reports an investigation on the rheological behaviour of fresh cement pastes. Three types of Portland cement were used. The water/cement ratio was varied in the range 0.35 ÷ 0.40. The rheological tests were performed using the coaxial-cylinder viscometer Rotovisko-Haake RV 11. The material to be tested was subjected immediately after mixing to a constant shear rate until a steady value of shear stress (equilibrium value) was attained. All the pastes tested exhibited a flow behaviour of the partially thixotropic type. A rheological model consisting of a sole constitutive equation \(\tau = \tau (\dot \gamma ,t)\) was defined according to the Cheng and Evans approach. The parameters of the constitutive equation were correlated with the cement specific surface and the water/cement ratio.     

The instron rheometer

It was shown some years ago by one of the authors (R. S. Higginbotham) that measurements of viscosity at a shearing stress of about 4500 dynes/cm² were especially useful for predicting the behaviour of colour pastes used for printing textile fabrics on engraved-roller machines. Such measurements could be made with various types of equipment, the most convenient to use being theFerranti-Shirley cone and plate viscometer, but it was felt that there was a need for a viscometer specifically designed for this purpose, and as cheap, simple, robust and easy to use as possible. A first attempt to produce such a viscometer (Higginbotham andBenbow, J. Sci. Instr.29, 221, 1952) was not entirely successful but a satisfactory, direct reading, cone and plate instrument has now been produced. It employs a permanentmagnet motor driven under conditions of constant torque to provide a constant shearing stress. The cone speed is then inversely proportional to the viscosity of the fluid under examination. A photoelectric tachometer with an associated electronic circuit generates a voltage proportional to the viscosity and the result is displayed on a linearly calibrated meter. The instrument has been tested in two printworks over a period of several months, and it has been shown to be suitable for the control of screen printing, as well as roller printing, pastes.     

Flow properties of oven-curing high solids white enamels

For the characterization of the rheological behaviour of a white, high solids, oven-curing enamel for household equipment with regard to its industrial application, attention was focused on the flow aspects involved in laying down process and film formation phenomena, i.e. viscosity at very high and very low shear rate, structural build-up in rest conditions, presence and magnitude of elastic components. Hence, investigations were aimed at (1) the determination of the equilibrium flow curve; the application of the Shangraw-Grim-Mattocks model led to the evaluation of parameters to describe infinite shear-rate viscosity and yield stress; (2) obtaining information about particle aggregation state in shear conditions. Quemada model gave indication that, even at very high shear, particle aggregates are stable; (3) the determination of time-dependent behaviour: elastic components were found to be almost negligible; the Trapeznikov-Fedotova procedure allowed thixotropic build-up in rest conditions to be evaluated, as concerns both amount and kinetics. Remarkable flow features found were: differences in the temperature dependence of viscosity at low shear rate and of yield value for enamels formulated with different pigment volume concentrations and the strong effect of the pigment volume concentration on the initial rate of thixotropic build-up in rest conditions.     

Rheological properties of suspensions of TiO2 particles in polymer solutions. 1. Shear viscosity

This paper presents results on the rheological behaviour of suspensions of two kinds of TiO₂ particles in two different polymer solutions. The particles differ in their hydrophilic or hydrophobic properties. The dispersing media are a solution of high molecular weight polyisobutylene in decalin and a solution of a low molecular weight polybutene in decalin. The concentrations of polymer are adjusted in order to get the same zero shear viscosity. The shear viscosity measurements display an apparent yield stress in some cases. The existence and the values of the yield stress depend on the volume fraction of solid particles and on the type of particles. The evolution of the intrinsic viscosity and of the maximum packing fraction vs the shear rate is interpreted in terms of evolution of the size and of the shape of aggregates of particles under shear. The effect of temperature on the development of the yield stress is also discussed. The results are completed by microscopic observations.     

Rheological properties of suspensions of the green microalga Chlorella vulgaris at various volume fractions

A systematic study of the rheological properties of solutions of non-motile microalgae (Chlorella vulgaris CCAP 211-19) in a wide range of volume fractions is presented. As the volume fraction is gradually increased, several rheological regimes are observed. At low volume fractions (but yet beyond the Einstein diluted limit), the suspensions display a Newtonian rheological behaviour and the volume fraction dependence of the viscosity can be well described by the Quemada model (Quemada, Eur Phys J Appl Phys 1:119–127, 1997). For intermediate values of the volume fraction, a shear thinning behaviour is observed and the volume fraction dependence of the viscosity can be described by the Simha model (Simha, J Appl Phys 23:1020–1024, 1952). For the largest values of the volume fraction investigated, an apparent yield stress behaviour is observed. Increasing and decreasing stress ramps within this range of volume fractions indicate a thixotropic behaviour as well. The rheological behaviour observed within the high concentration regime bears similarities with the measurements performed by Heymann and Aksel (Phys Rev E 75:021505, 2007) on polymethyl methacrylate suspensions: irreversible flow behaviour (upon increasing/decreasing stresses) and dependence of the flow curve on the characteristic time of forcing (the averaging time per stress values). All these findings indicate a behaviour of the microalgae suspensions similar to that of suspensions of rigid particles. A deeper insight into the physical mechanisms underlying the shear thinning and the apparent yield stress regime is obtained by an in situ analysis of the microscopic flow of the suspension under shear. The shear thinning regime is associated to the formation of cell aggregates (flocs). Based on the Voronoi analysis of the correlation between the cell distribution and cell sizes, we suggest that the repulsive electrostatic interactions are responsible for this microscale organisation. The apparent yield stress regime originates in the formation of large-scale cell aggregates which behave as rigid plugs leading to a maximally random jammed state.     

Small and large strain rheology of wheat gluten

 The rheological properties of wheat gluten were studied under both small and large deformation and compared with those of the parent flours. The limiting strain of linear viscoelastic behaviour of gluten doughs, 3 × 10⁻², was an order of magnitude larger than that of the flour doughs, 10⁻³. The role of starch in the lower limiting strain of flour doughs was indicated by the exponential decrease in the limiting strain of gluten-starch mixtures with greater quantities of starch. Large strain measurements showed gluten doughs possessed greater shear and elongational viscosities than flour doughs and these differences were greatest at lower shear and elongation rates (0.01 and 0.1 s⁻¹). The larger viscosities of flour and gluten doughs at the low strain rates help to stabilise and prevent the collapse of gas bubbles during bread fermentation and baking. Increasing starch levels in gluten-starch mixtures, at either constant or optimal water levels, lowered the elongational viscosity. Dynamic measurements were, however, more sensitive to the level of water added to the gluten-starch mixtures. The storage modulus decreased with increasing starch levels when constant water levels were used to prepare the mixtures, but when optimal water levels were used the storage modulus increased. Gluten and starch are major contributors to the large and small strain rheological properties of flour doughs; however, gluten-starch mixtures were unable to duplicate exactly the rheological properties of flour doughs, indicating that other flour components such as pentosans, lipids and water soluble proteins also influence dough rheology. Received: 20 March 2001 Accepted: 11 July 2001     

Study of magnetorheological fluids at high shear rates

The tunable rheological properties of magnetorheological (MR) materials at high shear rates are studied using a piston-driven flow-mode-type rheometer. The proposed method provides measurement of the apparent viscosity and yield stress of MR fluids for a shear rate range of 50 to 40,000 s⁻¹. The rheological properties of a commercial MR fluid, as well as a newly developed MR polymeric gel, and a ferrofluid-based MR fluid are investigated. The results for apparent viscosity and dynamic and static shear stresses under different applied magnetic fields are reported.