The flow field induced by the torsional oscillations of a spherical cell containing a fluid drop

The flow field induced by the torsional oscillations of a spherical cell containing a fluid drop is examined. It has been found that in addition to the oscillating motion of each fluid particle there exist three standing vortices in every quadrant between the drop and the container. The steady streaming into the drop can be directed either clockwise or counterclockwise, depending on the values of the parameter of the fluids inside and outside the drop. Typical flow fields are shown graphically.     

Newtonian drop in a Newtonian matrix subjected to large amplitude oscillatory shear flows

The dynamics of a single Newtonian drop immersed in a Newtonian matrix subjected to large-amplitude oscillatory shear flow is investigated. The ratio of the drop and matrix viscosity is above criticality, and thus break-up is absent under constant shear flow. At small forcing amplitudes the drop shape follows a regular oscillation. As the forcing amplitude increases, multipeaked oscillations of drop shape and orientation are observed. Experimental results are compared with predictions obtained with a phenomenological model. Model predictions are in qualitative good agreement with experimental data. The model suggests that the appearance of higher harmonics in the drop response is mainly due to flow nonaffinity.     

Stokes flow inside and around a fluid drop distorted by the presence of a tube wall

Using a quadratic optimisation process to satisfy the boundary conditions, the drag coefficient and the flow patterns inside and outside a fluid drop translating axially in a tube have been determined accurately even when the drop is clearly elongated. Convincing comparisons with experimental results (flow visualizations, velocity and drag measurements) are presented. The effects of the viscosity and density ratios are examined.     

Gravity-induced spreading of a drop of a viscous fluid over a surface

The unsteady-state nonlinear problem of spreading of a drop of a viscous fluid on the horizontal surface of a solid under the action of gravity and capillary forces is considered for small Reynolds numbers. The method of asymptotic matching is applied to solve the axisymmetrical problem of spreading when the gravity exerts a significant effect on the dynamics of the drop. The flow structure in the drop is determined at large times in the neighborhood of a self-similar solution. The ranges of applicability of the quasiequilibrium model of drop spreading with a dynamic edge angle and a self-similar solution are found. It is shown that the transition from one flow model to another occurs at very large Bond numbers. Institute of Mechanics of Multiphase Systems, Siberian Division, Russian Academy of Sciences, Tyumen’ 625000. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 3, pp. 59–67, May–June, 1999.     

Evaporation and explosion of liquid drops on a heated surface

The literature pertinent to various aspects of drop evaporation on a heated surface is reviewed. Both the laser shadowgraphic and direct photographic methods are employed to study thermal stability and flow structures in evaporating drops in all heating regimes. It is revealed that four flow regions exist in stable and unstable type drops at low liquid-film type vaporization regime. As the surface temperature is raised, the flow regions reduce to two. In the nucleate-boiling type vaporization regime, the interfacial flow structure changes due to a reduction in the Marangoni number as well as the dielectric constant of the liquid. An evidence of bubble growth in the drops is disclosed. The micro explosion of drops is found to occur in the transition-boiling type heating range. No drop explosion takes place in the spheriodal vaporization regime except when the drop rolls on to a microscratch on the heating surface. It is concluded that the mechanisms for triggering drop explosion include the spontaneous nucleation and growth phenomena and the destabilization of film boiling.     

Effect of void fraction and friction factor models on the prediction of pressure drop of R134a during downward condensation in a vertical tube

The theoretical flow models of homogeneous and separated flow are applied to in-tube condensation to predict the pressure drop characteristics of R134a. The homogeneous flow model is modified by ten different dynamic viscosity correlations and various alternative correlations of total, frictional and momentum pressure drops to take account of the partial condensation inside the tube. Numerical analyses were performed to determine the average and local homogeneous wall shear stresses and friction factors by means of a CFD program. The equivalent Reynolds number model is modified by six different two-phase friction factors to determine the total condensation pressure drop in the separated flow model. The refrigerant side total pressure drops, frictional pressure drops, friction factors and wall shear stresses are determined within a ±30% error band. The importance of using the alternative total, momentum and frictional pressure drop correlations for the homogeneous flow model is also shown.     

A Taylor drop rising in a liquid co-current flow

The present work presents a numerical study on the behavior of isolated liquid Taylor drops rising in vertical tubes with co-current heavier continuous phase. Numerical simulations were performed with a previously validated model, implementing Volume of Fluid method in an axisymmetric geometry. Detailed flow patterns and drop shapes are provided and discussed for several conditions. The balance between gravity effect and velocity of the continuous phase flow was found to have a great influence in the flow patterns observed. The increase of inertial effects, due to the increase of Eo number and the co-current velocity, leads to the occurrence of closed recirculations below the drops. Furthermore, the continuous phase stabilization distance below the drop is a function of the drop Reynolds number. Drop and continuous phase velocities relationship was studied. A viscosity ratio related term was appended to a pre-existing correlation. The flow in the absence of gravity was also studied. Results demonstrate that micro-scale flow is a lower limit to the cases studied in the present work and suggest that the viscosity ratio affects mainly the inertial part of the drop velocity.     

Flow induced on a salt waterbody due to the impingement of a freshwater drop or a water source

The particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) techniques are used to study the flow induced on the surface of a body of saltwater when a drop impinges on its surface or when a source is present on the surface. The measurements show that the impingement of a fresh water drop causes a strong axisymmetric solutocapillary flow about the vertical line passing through the center of impact. The fluid directly below the center of impact rises upward, and near the surface it moves away from the center of impact. The flow, which develops within a fraction of second after the impact, persists for several seconds. In comparison, when a freshwater drop falls on a body of freshwater, the flow induced on the surface is much weaker and persists for a relatively shorter duration of time and the volume of water circulated is two orders of magnitude smaller. Similarly, when a fresh water source is present on a body of saltwater there is a solutocapillary flow which on the surface is away from the source and below the surface is towards the source.     

Diffusional interaction of drops in a liquid

The method of combining asymptotic expansions (with respect to a large Peclet number) is used to investigate the three-dimensional problem of steady-state convective diffusion to the surface of drops, around which flows a laminar stream of a viscous incompressible liquid whose velocity field is assumed to be known from the solution of the corresponding hydrodynamic problem. It is shown that for large Peclet numbers the heat and mass transfer between drops is completely determined by the mutual arrangement of special (starting or ending at the surface of a drop) lines of flow; under these circumstances, in the flow there are chains of drops which have no mutual diffusional effect on one another, and the total diffusional flow to a drop is determined by diffusion to particles located upstream in the same chain. For the case where the distance between the drops in the chain is much leas than P^1/2 (P is the Peclet number), formulas for the distribution of the concentration and the total diffusional flow to the surface of each drop are obtained. It is shown that the total diffusional flow to the surface of a drop approaches zero in inverse proportion to its order number in a chain, which generalizes [1], in which the axisymmetric case is considered. A solution of the diffusional case is obtained for the case where there are critical lines at the surface of the drop. The problem is solved to the end if the singular flow lines are not closed and depart to infinity. With the presence of a region of closed circulation behind the drops, the problem is reduced to an integral equation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika, Zhidkosti i Gaza, No. 2, pp. 44–56, March–April, 1978.The author thanks Yu. P. Gupalo and Yu. S. Ryazantsev for their interest in the work.     

Dam-Break Flows Over a Bottom Drop

The single-layer shallow-water model is used to study flows generated by dam break over a bed level discontinuity in the form of a drop from which water flows. Emphasis is given to submerged regimes in which downstream wave processes affect the upstream flow. The paper considers solutions in which the total flow energy is conserved on the drop and solutions in which the energy is lost on the drop.     

Experimental investigation of the flow pattern,pressure drop and void fraction of two-phase flow in the corrugated gap of a plate heat exchanger

The two-phase flow in the corrugated gap created by two adjacent plates of a plate heat exchanger was investigated experimentally. One setup consisting of a transparent corrugated gap was used to visualize the two-phase flow pattern and study the local phenomena of phase distribution, pressure drop and void fraction. Saturated two-phase R365mfc and an air-water mixture were used as working fluids.In a second experimental setup, the heat transfer coefficients and the pressure drop inside an industrial plate heat exchanger during the condensation process of R134a are determined. Both experimental setups use the same type of plates, so the experimental results can be connected and a flow pattern model for the condensation in plate heat exchangers can be derived. In this work the results of the flow pattern visualization, the two-phase pressure drop in the corrugated gap and the void fraction analysis by measurement of the electrical capacity are presented. A new pressure drop correlation is derived, which takes into account different flow patterns, that appear during condensation. The mean deviation of the presented pressure drop model compared to the experimental data and data from other experimental works is 18.9%. 81.7% of the calculated pressure drop lies within ±30% compared to the experimental data.     

Parametric study of a model for determining the liquid flow-rates from the pressure drop and water hold-up in oil–water flows

A flow-pattern-dependent model, traditionally used for calculation of pressure drop and water hold-up, is accustomed for calculation of the liquid production rates in oil–water horizontal flow, based on the known pressure drop and water hold-up. The area-averaged steady-state one-dimensional two-fluid model is used for stratified flow, while the homogeneous model is employed for dispersed flow. The prediction errors appear to be larger when the production rates are calculated instead of pressure drop and water hold-up. The difference in the calculation accuracies between the direct and inverse calculation is most probably caused by the different uncertainties in the measured values of the input variables and a high sensitivity of the calculated phase flow-rates on even small change of the water hold-up for certain flow regimes. In order to locate the source of error in the standard two-fluid model formulation, several parametric studies are performed. In the first parametric study, we investigate under which conditions the momentum equations are satisfied when the measured pressure drop and water hold-up are imposed. The second and third parametric studies address the influence of the interfacial waves and drop entrainment on the model accuracy, respectively. These studies show that both interfacial waves and drop entrainment can be responsible for the augmentation of the wall-shear stress in oil–water flow. In addition, consideration of the interfacial waves offers an explanation for some important phenomena of the oil–water flow, such as the wall-shear stress reduction.     

Models for the deformation of a single ellipsoidal drop: a review

Dilute polymer blends and immiscible liquid emulsions are characterized by a globular morphology. The dynamics of a single drop subjected to an imposed flow field has been considered to be a valuable model system to get information on dilute blends. This problem has been studied either theoretically by developing exact theories for small drop deformations or by developing simplified models often based on phenomenological assumptions. In this paper, a critical overview of the available models for the dynamics of a single drop is presented, discussing four different systems, namely the Newtonian system, where a single Newtonian drop is immersed in an infinite Newtonian matrix; the non-Newtonian system, where at least one of the components, the drop fluid or the matrix one, is non-Newtonian; the confined Newtonian system, where the matrix is confined and wall effects alter the drop dynamics; and the confined non-Newtonian system.     

Liquid/liquid dispersion in a chaotic advection flow

Mixing by chaotic advection in a twisted-pipe flow is used here to investigate the efficiency of this flow in the liquid/liquid dispersion process. This study focuses on water/oil dispersions produced by continuous water injection into a main oil flow, for small Dean numbers. The drop sizes obtained with the chaotic-advection twisted-pipe flow are compared with those in a straight pipe and a helically coiled flow for the same conditions. It is found that the resulting dispersions are finer and more mono-dispersed in the chaotic advection flow. These results are compared with the theoretical maximum diameter _dmax$d_{\text{max}}$ determined by the Grace theory in which the viscous stress controls the breakup phenomena. For this purpose, the kinematic field is computed from the theoretical formulae for Dean flow. The strain rate fields in the pipe cross-section are then analytically computed and used to predict the maximum drop diameter. The theoretical values are identical for the three configurations (straight, helically coiled, and twisted pipe) up to a critical Dean number, where the secondary flow becomes significant. Beyond this value, the shear stress is enhanced in the twisted-pipe flow compared with the straight-pipe flow, and the predicted drop diameters are smaller. An interpretation of the higher dispersive performance of the chaotic flow is provided by the Lagrangian trajectories of the particles.     

Viscous flow of a suspension of liquid drops in a cylindrical tube

Viscous flow in a circular cylindrical tube containing an infinite line of viscous liquid drops equally spaced along the tube axis is considered under the assumption that a surface tension, sufficiently large, holds the drops in a nearly spherical shape. Three cases are considered: (1) axial translation of the drops, (2) flow of the external fluid past a line of stationary drops, and (3) flow of external fluid and liquid drops under an imposed pressure gradient. Both fluids are taken to be Newtonian and incompressible, and the linearized equations of creeping flow are used.The results show that both drag and pressure drop per sphere increase as the spacing increases at fixed radius and also increase as the radius of the drop increases. The presence of the internal motion reduces the drag and pressure gradients in all cases compared to rigid spheres, particularly for drops approaching the size of the tube.     

Interaction between two consecutive axisymmetric Taylor drops flowing in a heavier liquid in a vertical tube

A study regarding the interaction between two consecutive Taylor drops flowing in a heavier liquid in a vertical tube is reported. Under certain conditions, due to the wake of the leading drop, the trailing drop accelerates, leading to coalescence of the two drops. This study was developed using a numerical model based in the Volume of Fluid method in an axisymmetric geometry. The simulations reported in the present work had to fulfill two conditions: axisymmetry (due to the numerical model) and a high enough drop Reynolds number (which is related to the disturbances in the wake of an isolated drop, and thus to the tendency to drop interaction). Relevant dimensionless numbers are used to assess the effect of the acting forces. Detailed flow patterns and drop shapes are provided. Furthermore, the approaching velocity acquired by the trailing drop is analyzed and velocity profiles between the leading and the trailing drop are also reported. In general, the trailing drop shows an accelerating region, followed by a deceleration near the leading drop. The increase of Eotvos number promotes higher accelerations, while the increase in Morton number and viscosity ratio has the opposite effect. By comparison to literature gas-liquid studies, it was also found that interfacial forces promote the shape stability of the drops.     

Stokes flow in a cylindrical tube containing a line of spheroidal particles

Viscous flow in a circular cylindrical tube containing an infinite line of rigid spheroidal particles equally spaced along the axis of the tube is considered for (a) uniform axial translation of the spheroids (b) flow past a line of stationary spheriods and (c) flow of the suspending fluid and spheroids under an imposed pressure gradient. The fluid is assumed to be incompressible and Newtonian. The Reynolds number is assumed to be small and the equations of creeping flow are used. Two types of solutions are developed: (i) an exact solution in the form of an infinite series which is valid for ratios of the spheroid diameter to the tube diameter up to 0.80, (ii) an approximate solution using lubrication theory which is valid for spheroids which nearly fill the tube. The drag on each spheroid and the pressure drop are computed for all cases. Both prolate and oblate spheroids are considered. The results show that the drag and pressure drop depend on the spheroidal diameter perpendicular to the axis of tube primarily and the effects of the spheroidal thickness and spacing are secondary. The results are of interest in connection with mechanics of capillary blood flow, sedimentation, fluidized beds, and fluid-solid transport.     

Two-phase pressure drop and flooding characteristics in a horizontal-vertical pulsed sieve-plate column

In this paper, an experimental investigation on the two-phase pressure drop has been carried out in a novel class of extractors entitled "horizontal-vertical pulsed sieve-plate column". The liquid-liquid systems used in this work are toluene–water, n-butyl acetate–water and butanol-water. The effects of operating parameters including the dispersed and continuous phases flow rates and pulsation intensity on total pressure drop under and at the flooding points have been studied. It is achieved that the pressure drop is strongly affected by the continuous and dispersed flow rates as well as pulsation intensity. In fact, the column experiences higher pressure drop with an increase in the values of Af, Q _c and Q _d. The interfacial tension is a physical property which has significant impact on pressure drop. Two theoretical-experimental correlations for prediction of pressure drop under and at the flooding in the column, and one correlation for maximum throughput are proposed by using dimensional analysis method with Average Absolute Relative Error (AARE) values of 2.15%, 3.56 and 6.85% respectively. Moreover, a particular approach for preventing flooding in pulsed extraction columns is developed based on evaluation of pressure drop through the column length.     

Deformation and breakup of a non-Newtonian slender drop in an extensional flow

The deformation and breakup of a non-Newtonian slender drop in a Newtonian liquid in a simple extensional and creeping flow has been theoretically studied. The power-law was chosen for the fluid inside the drop, and the deformation of the drop is described by a single ordinary differential equation, which was numerically solved. Asymptotic analytical expressions for the local radius were derived near the center and close to the end of the drop. The results for the shape of the drop and the breakup criterion are presented as a function of the capillary number, the viscosity ratio and type of non-Newtonian fluid inside the drop. An approximate analytical solution is also suggested which is in good agreement with the numerical results.