Contraction/expansion flows: The pressure drop and related issues

Binding, David; Phillips, P.M.; Philips, T.N., (2006) 'Contraction/expansion flows: The pressure drop and related issues', Journal of Non-Newtonian Fluid Mechanics 137 pp.31-38 RAE2008

An Experimental Investigation into the Pressure Drop for Turbulent 90o Elbow Bends

The prediction of the pressure drop for turbulent single-phase fluid flow around sharp 90° bends is difficult owing to the complexity of the flow arising from frictional and separation effects. Several empirical equations exist, which accurately predict the pressure loss due to frictional effects. More recently, Crawford et al. [1] proposed an equation for the prediction of pressure loss due to separation of the flow. This work proposes a new composite equation for the prediction of pressure drop due to separation of the flow, which incorporates bends with ratio R/r <2. A new composite equation is proposed to predict pressure losses over the Reynolds number range 4 x 103-3 x 105. The predictions from the new equation are within a range of -4 to +6 per cent of existing experimental data.

2D-drop model applied to the calculation of step formation energies on a (111) substrate

A model is presented for obtaining the step formation energy for metallic islands on (1 1 1) surfaces from Monte Carlo simulations. This model is applied to homo (Cu/Cu(1 1 1), Ag/Ag(1 1 1)) and heteroepitaxy (Ag/Pt(1 1 1)) systems. The embedded atom method is used to represent the interaction between the particles of the system, but any other type of potential could be used as well. The formulation can also be employed to consider the case of other single crystal surfaces, since the higher barriers for atom motion on other surfaces are not a hindrance for the simulation scheme proposed.

Investigation on drop penetration and wetting characteristics of powder-liquid systems in relation to the mixing of acrylic bone cement

This study investigated methyl methacrylate – polymethyl methacrylate powder bed interactions through droplet analyses, using model fluids and commercially available bone cement. The effects of storage temperature of liquid monomer and powder packing configuration on drop penetration time were investigated. Methyl methacrylate showed much more rapid imbibition than caprolactone due to decrease in both contact angle and fluid viscosity. Drop penetration of caprolactone through polymethyl methacrylate increased with decrease in bed macro-voids and increase in bulk density as predicted by the modified constant drawing area penetration model and confirmed by drop penetration images. Linear relationships were found between droplet mass and drawing area with imbibition time. Further experiments showed gravimetric analysis of the polymerised methyl methacrylate – polymethyl methacrylate matrix under various storage temperatures correlated with Reynolds number and Washburn analyses. These observations have direct implications for the design of mixing and delivery systems for acrylic bone cements used in orthopaedic surgery.

Pressure drop of gas–liquid Taylor flow in round micro-capillaries for low to intermediate Reynolds numbers

In this paper, a model is presented that describes the pressure drop of gas-liquid Taylor flow in round capillaries with a channel diameter typically less than 1 mm. The analysis of Bretherton (J Fluid Mech 10:166-188, 1961) for the pressure drop over a single gas bubble for vanishing liquid film thickness is extended to include a non-negligible liquid film thickness using the analysis of Aussillous and Qu,r, (Phys Fluids 12(10):2367-2371, 2000). This result is combined with the Hagen-Poiseuille equation for liquid flow using a mass balance-based Taylor flow model previously developed by the authors (Warnier et al. in Chem Eng J 135S:S153-S158, 2007). The model presented in this paper includes the effect of the liquid slug length on the pressure drop similar to the model of Kreutzer et al. (AIChE J 51(9):2428-2440, 2005). Additionally, the gas bubble velocity is taken into account, thereby increasing the accuracy of the pressure drop predictions compared to those of the model of Kreutzer et al. Experimental data were obtained for nitrogen-water Taylor flow in a round glass channel with an inner diameter of 250 mu m. The capillary number Ca (gl) varied between 2.3 x 10(-3) and 8.8 x 10(-3) and the Reynolds number Re (gl) varied between 41 and 159. The presented model describes the experimental results with an accuracy of +/- 4% of the measured values.

Verification of McCabe's Delta L Law for Growth of Lysozyme Crystals by Hanging Drop Method

Lysozyme is a naturally occurring enzyme in egg white and has high commercial importance due to its antimicrobial properties. The main objective of this work was to study the growth rate of lysozyme crystals isolated from egg for the first 72 hours and verify the results with McCabe’s constant crystal growth theory. Hanging drop crystallization method was used to form high purity lysozyme crystals from the embryonic stage. To this end, this work differs from an earlier work of Forsythe et al., who used seed crystals in the size range of 10 µm - 40 µm for face growth measurements at different pH values. The maximum crystal size recorded in the present work was 392.86 µm, which is within the typical size range of 50 µm - 500 µm for which constant crystal growth is expected to hold according to McCabe’s ?L law. Electron micrographs (SEM) revealed the structure and dimensions of the crystals while SDS-Page was used to measure the purity of the crystals. The SEM results showed that that lysozyme growth rate was linear and agreed with McCabe’s constant growth theory, producing a growth rate of 1.77 x 10-3 µm .s-1

Liquid-liquid slug flow: Hydrodynamics and pressure drop

In this paper, the hydrodynamics and the pressure drop of liquid-liquid slug flow in round microcapillaries are presented. Two liquid-liquid flow systems are considered, viz. water-toluene and ethylene glycol/water-toluene. The slug lengths of the alternating continuous and dispersed phases were measured as a function of the slug velocity (0.03-0.5 m/s), the organic-to-aqueous flow ratio (0.1-4.0), and the microcapillary internal diameter (248 and 498 mu m). The pressure drop is modeled as the sum of two contributions: the frictional and the interface pressure drop. Two models are presented, viz, the stagnant film model and the moving film model. Both models account for the presence of a thin liquid film between the dispersed phase slug and the capillary wall. It is found that the film velocity is of negligible influence on the pressure drop. Therefore, the stagnant film model is adequate to accurately predict the liquid-liquid slug flow pressure drop. The influence of inertia and the consequent change of the slug cap curvature are accounted for by modifying Bretherton's curvature parameter in the interface pressure drop equation. The stagnant film model is in good agreement with experimental data with a mean relative error of less than 7%.