Transition from laminar to turbulent flow in liquid filled microtubes

The transition to turbulent flow is studied for liquids of different polarities in glass microtubes having diameters between 50 and 247 µm. The onset of transition occurs at Reynolds numbers of ~1,800–2,000, as indicated by greater-than-laminar pressure drop and micro-PIV measurements of mean velocity and rms velocity fluctuations at the centerline. Transition at anomalously low values of Reynolds number was never observed. Additionally, the results of more than 1,500 measurements of pressure drop versus flow rate confirm the macroscopic Poiseuille flow result for laminar flow resistance to within –1% systematic and ±2.5% rms random error for Reynolds numbers less than 1,800.An erratum to this article can be found at     

Investigation of droplet deposition from a turbulent gas stream

Turbulent deposition of particles from two-phase flow onto the smooth wall of a tube has been studied theoretically and experimentally. A model is proposed for the deposition motion of large particles based on turbulent diffusion in the core followed by a free flight towards the wall. The theory shows that within the Stokes regime, the dimensionless deposition velocity $\text{k-}{}_{\mathrm{<mtext>d</mtext>}}\text{/}\text{u}$* depends on Re and $\text{τ}{}^{\mathrm{+}}$ only, where u* is the friction velocity, Re is the tube Reynolds number and $\text{τ}{}^{\mathrm{+}}$ is the dimensionless particle relaxation time. Deposition data are obtained for air-water droplet flow through a 12.7-mm i.d. acrylic tubing at $\text{Re}\text{= 52,500}$ and 94,600. The proposed theory satisfactorily describes the existing deposition data as well as present measurements, covering a wide range of Re and $\text{τ}{}^{\mathrm{+}}$.     

Transition mechanism from bubble flow to slug flow in a riser

An experiment was performed to examine the mechanism of flow pattern transition from bubble flow to slug flow in a riser. The flow was measured by a double resistivity probe system, and photographs of the flow were taken using strobe lights. The negative diffusion distance of bubbles was estimated using a voidage wave equation and compared with the interbubble distance. The flow pattern transition from bubble flow to slug flow occurred when the diffusion distance was larger than the interbubble distance. Conversely, when the diffusion distance was smaller than the interbubble distance, the bubble flow was sustained. Therefore, it is found that the negative diffusion caused by the instability of the voidage wave brings about the flow pattern transition.     

Cavitation flow around a plate in a channel by a stream of heavy liquid

The nonlinear problem of cavitation flow around a plate by a stream of heavy liquid is investigated in precise formulation; the plate is located on the horizontal floor of a channel when the gravity vector is directed perpendicular to the wall of the channel. Two flow systems are considered-Ryabushinskii's and Kuznetsov's system [1]. This problem was investigated in linear formulation in [2], Similar problems were considered earlier in [3–7] for unrestricted flow. Below, on the basis of a method proposed by Birkhoff [8, 9], all the principal hydrodynamic and geometric characteristics are calculated for the problem being considered.Translated from Ivestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 3, pp. 3–9, May–June, 1973.     

Explosive boiling of a liquid droplet

A mathematical model describing growth of an internal vapor bubble produced by homogeneous nucleation within a liquid droplet during explosive boiling is presented. Existing experimental results for explosive boiling of superheated droplets confirm the predictions of the model. The difference between the present model and the classical theories of bubble growth is discussed.     

The secondary flow induced around a sphere in an oscillating stream of elastico-viscous liquid

The present paper is devoted to the theoretical study of the secondary flow induced around a sphere in an oscillating stream of an elastico-viscous liquid. The boundary layer equations are derived following Wang's method and solved by the method of successive approximations. The effect of elasticity of the liquid is to produce a reverse flow in the region close to the surface of the sphere and to shift the entire flow pattern towards the main flow. The resistance on the surface of the sphere and the steady secondary inflow increase with the elasticity of the liquid.Nomenclature a radius of the sphere - b ^ik contravariant components of a tensor - e contravariant components of the rate of strain tensor - F() see (47) - G total nondimensional resistance on the surface of the sphere - g _ik covariant components of the metric tensor - f, g, h secondary flow components introduced in (34) - k ₀ measure of relaxation time minus retardation time (elastico-viscous parameter) - K =k ₀ ²/V ₀ ² , nondimensional parameter characterizing the elasticity of the liquid - n measure of the ratio of the boundary layer thickness and the oscillation amplitude - N, T defined in (44) - p arbitrary isotropic pressure - p _ik covariant components of the stress tensor - p ^ik contravariant components of the stress tensor associated with the change of shape of the material - R =V ₀ a/v, the Reynolds number - S =a/V ₀, the Strouhall number - r, , spherical polar coordinates - u, v, w r, , component of velocity - t time - V(, t) potential velocity distribution around the sphere - V ₀ characteristic velocity - u, v, t, y, P nondimensional quantities defined in (15) - reciprocal of s - density - defined in (32) - defined in (42) - ₀ limiting viscosity for very small changes in deformation velocity - complex conjugate of - oscillation frequency - = ₀/, the kinematic coefficient of viscosity - , defined in (52) - (, y) stream function defined in (45) - =(NT/2n)^1/2 y - /t convective time derivative (1) _ik      

Transition from stratified to slug regime in countercurrent flow

In many two-phase flow situations the prediction on the conditions likely to instigate the change of flow pattern from the stratified regime to the slug flow condition is important. Since published material on such predictions for countercurrent flow is scarce this paper considers the influencing parameters for these conditions and then uses the data recorded from an experimental test rig to quantify the developed instability criterion equation.     

Visual measurements of droplet size in gas–liquid annular flow

Drop size distributions have been measured for nitrogen–water annular flow in a 9.67 mm hydraulic diameter duct, at system pressures of 3.4 and 17 bar and a temperature of 38 °C. These new data extend the range of conditions represented by existing data in the literature, primarily through an increase in system pressure. Since most existing correlations were developed from data obtained at lower pressures, it should be expected that the higher-pressure data presented in this paper would not necessarily follow those correlations. For two volume median correlations tested, one does not predict the new data very well, while the other only predicts those data taken at the lower pressure of 3.4 atm. An existing maximum drop size correlation predicts the current data to a reasonable approximation. Similarly, a related correlation for the Sauter mean diameter can predict the new data, provided the coefficient in the equation is adjusted.     

Motion of a liquid droplet in a vibrating fluid

The motion of a liquid droplet in a liquid with density different from that of the liquid composing the droplet and subjected to harmonic excitations is investigated. Nonlinear equations are obtained that describe the translational motion of the droplet and its oscillations. It is shown by numerical means that, under the essential resonance conditions, the droplet ascends by a cascade method if the value of the load coefficient is small.S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 31, No. 7, pp. 78–83, July, 1995.     

Abnormal rotation of a deformed liquid crystal droplet immersed in an isotropic fluid after transient flow

The morphology evolution of liquid crystal droplets immersed in an isotropic fluid in flow field is found to be different from flexible polymer droplets. In this paper, we investigated the retraction of a liquid crystal droplet after transient flow. It is found that the liquid crystal droplet will rotate during the shape recovery, which has never been observed for an isotropic droplet. The factors that influence the rotational angle of a single liquid crystal droplet during retraction progress were studied, including the temperature, the dimension of the droplets, the time of shear flow, the shear rate, the flow type, and the properties of liquid crystal molecules. The rotation of liquid crystal droplet during shape recovery is ascribed to both the bulk elasticity of liquid crystal droplets and the anisotropic properties of the interface between liquid crystal and isotropic fluid.     

Calculation of the breakaway flow of a flat stream of a nonviscous liquid around bodies

The article gives relationships which, within the framework of the theory of an ideal liquid, permit calculating breakaway flow around bodies of arbitrary form. It gives examples of the calculation, by numerical methods using a digital computer, of the flow of a flat stream around a round cylinder and a flat plate. The results obtained are in agreement with the experimental data in the self-similar region.Moscow. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 72–82, March–April, 1972.     

Hydrodynamics of a drying multicomponent liquid droplet

Using microscopy methods on light and dark fields, the flow patterns developing in drying droplets of pure transparent liquids, solutions, and suspensions of micro- and nanoparticles are investigated. The flow patterns inside drying droplets of real, colloid, and mixed solutions containing nanoand microparticles-markers are studied by means of video and photo registration of microscopic images. The analysis of particle displacements indicates the existence of a global convective flow which forms a toroidal circulation with an ascending jet at the droplet center. The typical types of the structures depending on the droplet composition are distinguished. It is shown that the intensity of the flow inside the droplet affects the surface convection. The effect of the hydrodynamic flow on the transport of a substance, forming the dry-deposit texture, is studied.     

Flow behavior near an infinite droplet stream

This paper presents an experimental study examining the behavior of a single droplet displaced radially from an infinite droplet stream. The displaced droplet behaves as a tracking particle that responds to the velocity profile generated by the droplet stream. This profile changes with droplet spacing. The measurements show that the velocity field of the infinite stream extends more than 15 droplet diameters from the stream axis, with the largest gradients residing within 5 diameters. The effects of drag and electrostatic forces are quantified to demonstrate that lift forces contribute to the displaced droplets's motion.The monetary support for this work was provided through a NSF Presidential Young and Investigator grant. The authors also recognize the laboratory efforts of Dameon Wood in setting up the charge deflection apparatus.     

Primary instabilities of liquid film flow sheared by turbulent gas stream

Evolution of excited waves on a viscous liquid film has been investigated experimentally for the annular gas–liquid flow in a vertical tube. For the first time the dispersion relations are obtained experimentally for linear waves on liquid film surface in the presence of turbulent gas flow. Both cocurrent and countercurrent flow regimes are investigated. As an example of comparison with theory, the experimental data are compared to the results of calculations based on the Benjamin quasi-laminar model for turbulent gas flow. The calculation results are found to be in good agreement with experiments for moderate values of film Reynolds number.     

Unsteady mass transfer to a droplet (bubble) in a three-dimensional shear flow

An exact analytic solution of the problem of unsteady convective mass transfer to a spherical droplet (bubble) from an arbitrary three-dimensional linear deformational shear flow, whose undisturbed velocity field is given by a symmetric shear tensor, is obtained in the diffusion boundary layer approximation. The dependence of the mean Sherwood number on time and the Péclet number is determined. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 111–119, November–December, 1986. The authors are grateful to Yu. S. Ryazantsev and L. A. Chudov for their interest and useful comments.