Spatial B-jump at sudden channel enlargements with abrupt drop

An analytical and experimental study of the hydraulic jump in stilling basins with abrupt drop and sudden enlargement, called the spatial B-jump here, is carried out for finding the sequent depth ratio and resulting energy dissipation. The spatial B-jump studied has its toe downstream of the expansion section, and the stream lines at the toe are characterized by downward curvature. An expression is obtained for the sequent depth ratio based on the momentum equation with suitable assumptions for the extra pressure force term because of the abrupt drop in the bed and sudden enlargement in the basin width. Predictions compare favorably with experiments. It is shown that the spatial B-jump needs less tailwater depth, thereby enhancing the stability of the jump when compared either with spatial jump, which forms in sudden expanding channels, or with B-jump, which forms in a channel with an abrupt drop in bed. It is also shown that there is a significant increase in relative energy loss for the spatial B-jump compared to either the spatial jump or B-jump alone.

Experimental Studies on Drop Formation at the Tip of Melting Rods

Drop formation at the conical tips of melting rods has been experimentally studied using the transparent wax-alcohol/acetonitrile system. The effects of cone angle, rod diameter, immersion depth, and bath temperature on the detached drop mass have been studied over a wide range, besides recording useful qualitative information based on visual observation. The experimental results suggest that the phenomenon of drop formation at the tip of melting rods has a close parallel with the drop formation at conical tips, at least on a qualitative basis. However, the results could not be quantified owing to difficulties in characterizing the physical properties of the system, despite efforts to minimize them.

An absolute method for the determination of surface tension of liquids using pendent drop profiles

Drop formation at conical tips which is of relevance to metallurgists is investigated based on the principle of minimization of free energy using the variational approach. The dimensionless governing equations for drop profiles are computer solved using the fourth order Runge-Kutta method. For different cone angles, the theoretical plots of XT and ZT vs their ratio, are statistically analyzed, where XT and ZT are the dimensionless x and z coordinates of the drop profile at a plane at the conical tip, perpendicular to the axis of symmetry. Based on the mathematical description of these curves, an absolute method has been proposed for the determination of surface tension of liquids, which is shown to be preferable in comparison with the earlier pendent-drop profile methods.

Analysis of drop formation at conical tips : 1. Theory

The phenomenon of drop formation at conical tips under near zero flow conditions has been investigated using a theoretical approach. The analysis permits the prediction of drop profile and drop volume, until the onset of instability. A semiempirical approach based on the similarity of drop shapes has been adopted to predict the detaching drop volumes at conical tips. The effects of base diameter of the cone, cone angle, interfacial tension, and the densities of the drop and the surrounding fluid on the maximum and detached drop volumes are predicted.

Drop impact on a solid surface comprising micro groove structure

Spreading and receding processes of water drops impacting on a stainless steel surface comprising rectangular shaped parallel grooves are studied experimentally. The study was confined to the impact of drops in inertia dominated flow regime with Weber number in the range 15 - 257. Measurements of spreading drop diameter and drop height were obtained during the impact process as function of time. Experimental measurements of spreading drop diameter and drop height obtained for the grooved surface were compared with those obtained for a smooth surface to elucidate the influence of surface grooves on the impact process. The grooves definitely influence both spreading and receding processes of impacting liquid drops. A more striking observation from this study is that the receding process of impacting liquid drops is dramatically changed by the groove structure for all droplet Weber number.

Drop formation studies in liquid—liquid systems

Benzene drops were formed in continuous media of water and glycerine of varying physical properties. The effect on drop volumes of variables like volumetric flow-rate, interfacial tension, continuous phase viscosity and capillary diameter was studied. An equation has been developed, based on a two stage drop formation mechanism, which predicts drop volumes within an average error of 7 per cent for the range of physical properties employed in this investigation.

A unified approach to bubble and drop formation

An approach, starting with the bubble formation model of Khurana and Khumar, has been presented, which is found to be reasonably applicable to the formation of both bubbles and drops from single submerged nozzles. The model treats both the phenomena jointly as the formation of a dispersed phase entity resulting from injection, whose size depends upon operating parameters and physical properties.

Drop formation in non-newtonian liquids under pulsed conditions

Drop formation from single nozzles under pulsed flow conditions in non-Newtonian fluids following the power law model has been studied. An existing model has been modified to explain the experimental data. The flow conditions employed correspond to the mixer—settler type of operation in pulsed sieve-plate extraction columns. The modified model predicts the drop sizes satisfactorily. It has been found that consideration of non-Newtonian behaviour is important at low pulse intensities and its significance decreases with increasing intensity of pulsation. Further, the proposed model for single orifices has been tested to predict the sizes of drops formed from a sieve-plate distributor having four holes, and has been found to predict the sizes fairly well in the absence of coalescence.

Effect of surfactants on drop breakage in turbulent liquid dispersions

The existingm odels of drop breakage in stirred dispersions grossly overpredict the maximum drop size when surface active agents are present inspite of using the lowered value of interfacial tension. It is shown that the difference in the values of dynamic and static interfacial tension, aids the turbulent stresses in drop breakage. When the difference is zero, e.g. for pure liquids and for high concentration of surfactants, the influence of the addition of surfactant is merely to reduce the interfacial tension and can be accounted for by existingm odels. A modified model has been developed, where the drop breakage is assumed to be represented by a Voigt element. The deforming stresses are due to turbulence and the difference between dynamic and static interfacial tensions. The resisting stresses arise due to interfacial tension and the viscous flow inside the drop. The model yields the existing expressions for dmax as special cases. The model has been found to be satisfactory when tested against experimental results using the styrene-water-teepol system.

A multi-stage model for drop breakage in stirred vessels

Existing models for dmax predict that, in the limit of μd → ∞, dmax increases with 3/4 power of μd. Further, at low values of interfacial tension, dmax becomes independent of σ even at moderate values of μd. However, experiments contradict both the predictions show that dmax dependence on μd is much weaker, and that, even at very low values of σ,dmax does not become independent of it. A model is proposed to explain these results. The model assumes that a drop circulates in a stirred vessel along with the bulk fluid and repeatedly passes through a deformation zone followed by a relaxation zone. In the deformation zone, the turbulent inertial stress tends to deform the drop, while the viscous stress generated in the drop and the interfacial stress resist deformation. The relaxation zone is characterized by absence of turbulent stress and hence the drop tends to relax back to undeformed state. It is shown that a circulating drop, starting with some initial deformation, either reaches a steady state or breaks in one or several cycles. dmax is defined as the maximum size of a drop which, starting with an undeformed initial state for the first cycle, passes through deformation zone infinite number of times without breaking. The model predictions reduce to that of Lagisetty. (1986) for moderate values of μd and σ. The model successfully predicts the reduced dependence of dmax on μd at high values of μd as well as the dependence of dmax on σ at low values of σ. The data available in literature on dmax could be predicted to a greater accuracy by the model in comparison with existing models and correlations.

A multi-stage model for drop breakage in stirred vessels

Existing models for dmax predict that, in the limit of μd → ∞, dmax increases with 3/4 power of μd. Further, at low values of interfacial tension, dmax becomes independent of σ even at moderate values of μd. However, experiments contradict both the predictions show that dmax dependence on μd is much weaker, and that, even at very low values of σ,dmax does not become independent of it. A model is proposed to explain these results. The model assumes that a drop circulates in a stirred vessel along with the bulk fluid and repeatedly passes through a deformation zone followed by a relaxation zone. In the deformation zone, the turbulent inertial stress tends to deform the drop, while the viscous stress generated in the drop and the interfacial stress resist deformation. The relaxation zone is characterized by absence of turbulent stress and hence the drop tends to relax back to undeformed state. It is shown that a circulating drop, starting with some initial deformation, either reaches a steady state or breaks in one or several cycles. dmax is defined as the maximum size of a drop which, starting with an undeformed initial state for the first cycle, passes through deformation zone infinite number of times without breaking. The model predictions reduce to that of Lagisetty. (1986) for moderate values of μd and σ. The model successfully predicts the reduced dependence of dmax on μd at high values of μd as well as the dependence of dmax on σ at low values of σ. The data available in literature on dmax could be predicted to a greater accuracy by the model in comparison with existing models and correlations.

Fuel drop size measurement in a carburetted induction system with 2 throttling methods

A new throttling system far SI engines is examined. The SMD of the fuel droplets in the induction system is measured to evaluate the performance of the new device with respect to the conventional throttle plate arrangement. The measurements are conducted at steady now conditions. A forward angular scattering technique with a He-Ne laser beam is used for droplet size measurement. The experiments are carried out with different mixture strength, stream velocity and throttle positions. It is observed that A/F ratio has no effect on SMD. However, stream velocity and throttle position have a significant influence on SMD. The new throttling method is found to be more effective in reducing the SMD, particularly at low throttle opening and high stream velocity compared to the conventional throttle plate.

Breakage of a drop of inviscid fluid due to a pressure fluctuation at its surface

In this work, an attempt is made to gain a better understanding of the breakage of low-viscosity drops in turbulent flows by determining the dynamics of deformation of an inviscid drop in response to a pressure variation acting on the drop surface. Known scaling relationships between wavenumbers and frequencies, and between pressure fluctuations and velocity fluctuations in the inertial subrange are used in characterizing the pressure fluctuation. The existence of a maximum stable drop diameter d(max) follows once scaling laws of turbulent flow are used to correlate the magnitude of the disruptive forces with the duration for which they act. Two undetermined dimensionless quantities, both of order unity, appear in the equations of continuity, motion, and the boundary conditions in terms of pressure fluctuations applied on the surface. One is a constant of proportionality relating root-mean-square values of pressure and velocity differences between two points separated by a distance l. The other is a Weber number based on turbulent stresses acting on the drop and the resisting stresses in the drop due to interfacial tension. The former is set equal to 1, and the latter is determined by studying the interaction of a drop of diameter equal to d(max) with a pressure fluctuation of length scale equal to the drop diameter. The model is then used to study the breakage of drops of diameter greater than d(max) and those with densities different from that of the suspending fluid. It is found that, at least during breakage of a drop of diameter greater than d(max) by interaction with a fluctuation of equal length scale, a satellite drop is always formed between two larger drops. When very large drops are broken by smaller-length-scale fluctuations, highly deformed shapes are produced suggesting the possibility of further fragmentation due to instabilities. The model predicts that as the dispersed-phase density increases, d(max) decreases.