Showing papers on "Ohnesorge number published in 2007"
TL;DR: In this article, the authors investigated the effect of inertial effects on droplet spreading at relatively large rates of spreading and found that the initial inertia-dominated regime is characterized by a rapidly extending region affected by the spreading, giving the appearance of a capillary wave travelling from the contact line.
Abstract: Axisymmetric droplet spreading is investigated numerically at relatively large rates of spreading, such that inertial effects become important. Results from two numerical methods that use different means to alleviate the stress singularity at moving contact lines (a diffuse interface, and a slip-length-based level-set method) are shown to agree well. An initial inertial regime is observed to yield to a regime associated with Tanner's law at later times. The spreading rate oscillates during the changeover between these regimes. This becomes more significant for a fixed (effective) slip length when decreasing the value of an Ohnesorge number. The initial, inertia-dominated regime is characterized by a rapidly extending region affected by the spreading, giving the appearance of a capillary wave travelling from the contact line. The oscillatory behaviour is associated with the rapid collapse that follows the point at which this region extends to the entire droplet. Results are presented for the apparent contact angle as a function of dimensionless spreading rate for various values of Ohnesorge number, slip length and initial conditions. The results indicate that there is no such universal relation when inertial effects are important.
155 citations
TL;DR: In this article, the formation of liquid drops of incompressible Newtonian fluids from a simple capillary tube by imposing a transient flow rate upstream of the nozzle exit is studied.
Abstract: Motivated by the desire to improve the theoretical understanding of drop-on-demand (DOD) ink-jet printing, a computational analysis is carried out to simulate the formation of liquid drops of incompressible Newtonian fluids from a simple capillary tube by imposing a transient flow rate upstream of the nozzle exit. Since the flow in a typical ink-jet nozzle is toward the nozzle outlet during part of the time and away from the nozzle outlet at other times, an inflow rate is adopted here that captures the essential physics and is given in dimensionless form by Q=(πWe∕2)sinΩt, where We is the Weber number (inertial/surface tension force), Ω is the frequency, and t is time. The dynamics are studied as functions of We, Ω, and the Ohnesorge number Oh (viscous/surface tension force). For a common ink forming from a nozzle of 10μm radius, Oh=0.1. For this typical case, a phase or operability diagram in (We,Ω)-space is developed that shows that three regimes of operation are possible. In the first regime, where We ...
119 citations
TL;DR: The transition between deposition and rebound is shown to be influenced by the impact The authors, Oh, and advancing and receding static contact angles, and the influence of They and Oh on the dynamic contact angle is investigated.
74 citations
TL;DR: In this paper, the deformation and drag coefficients of decelerating drops in axisymmetric flows are numerically computed and compared with those of solid spheres in the case of drops, and the behavior of the drag coefficient is dependent on the internal circulation of the drops in addition to the factors which are important for solid spheres.
Abstract: Transient deformation and drag coefficients of decelerating drops in axisymmetric flows are numerically computed. The drag coefficients are compared with those of solid spheres. In the case of drops, the behavior of the drag coefficient is dependent on the deformation and internal circulation of the drops in addition to the factors which are important for solid spheres. These, in turn, are dependent on the gas-based Weber number (Weg) and the Ohnesorge number (Ohl). At the relatively low Weg of 1, when the deformation is small, the drag coefficients are about the same for the solid sphere and drop. When Weg is increased, the deformation increases and the difference increases. At the highest Weg of 100, the drop reaches a point of secondary breakup. In general, oblate shapes result in greater drag and prolate shapes in lower drag relative to the solid sphere. Increasing Ohl, which implies increasing viscous forces in the liquid relative to surface tension forces, leads to less deformation and hence lesser ...
49 citations
TL;DR: In this paper, the Navier-Stokes equations were solved using a finite-volume formulation with a two-step projection method on a fixed grid, and the free surface of the liquid ligament was tracked by a coupled level set and volume-of-fluid method with the surface tension force determined by the continuum surface force model.
Abstract: The time-dependent relaxation dynamics of a moderately elongated liquid ligament in air have been numerically studied. The Navier-Stokes equations are solved using a finite-volume formulation with a two-step projection method on a fixed grid. The free surface of the liquid ligament is tracked by a coupled level set and volume-of-fluid method with the surface tension force determined by the continuum surface force model. The relaxation process of the elongated liquid ligament has been simulated and the end-pinching mechanism of the breakup process has been thoroughly examined. It has been found that the formation of a neck is not necessarily a precursor for breakup as inaccurately theorized in the end-pinching mechanism in the literature. The neck may reopen after undergoing an initial development towards pinch-off. In such an instance, droplet pinch-off will not occur. The determining factor for the reopening of a pinching neck has been identified. The experimentally observed restabilization phenomenon, in which further increase of the elongation ratio beyond the critical value would lead to cessation of pinch-off breakup, has also been investigated. Finally, the effects of several parameters on the relaxation mechanism have been examined. The initial end shape and length of the ligament and the Ohnesorge number have been found to play a vital role in the overall relaxation process.
25 citations
TL;DR: In this article, a basic study on the characteristics of capillary wave propagation on a water ligament surface is presented, and the analysis is based on 2D numerical simulation and linear wave analysis, revealing the basic characteristics such as contraction speed, wave speed and associated flow field structures.
Abstract: This paper presents a basic study on the characteristics of capillary wave propagation on a water ligament surface. The capillary wave plays an important role in de-stabilizing ligaments created by the turbulent motion of liquid jet. The ligament end contracts due to capillary force and emanates surface waves. The analysis is based on 2D numerical simulation and linear wave analysis, and reveals the basic characteristics such as contraction speed, wave speed and the associated flow field structures. The phenomenon can be parameterized by the Ohnesorge number, and the numerical results are in good agreement with the linear analysis. The higher pressure cases, where the Ohnesorge number is high, will be investigated in the next step.
6 citations
01 Jan 2007
TL;DR: The hydrodynamic stability limit is described by the ratio of the forces acting to destroy the particles, the shear forces t, where t is the tangential force per unit surface, and the force acting to retain the particle form, for example, surface tension forces σ d πD d as discussed by the authors.
Abstract: Consider pool flow, that is, flow without any wall influence. Fluid particles in multiphase mixtures experience forces acting to destroy them and forces acting to retain their initial form. The hydrodynamic stability limit is usually described by the ratio of the forces acting to destroy the particles, the shear forces t \(\pi D^2_d\), where t is the tangential force per unit surface, and the forces acting to retain the particle form, for example, surface tension forces σ d πD d (see Figs. 8.1 and 8.2),
5 citations
Dissertation•
01 Jan 2007
TL;DR: In this paper, a volume of fluid (VOF) based code is used to solve the governing equations and capture the interface between a viscous liquid sheet and the surrounding gas.
Abstract: The primary breakup of liquid sheets into ligaments has a great effect on the size, velocity, and penetration of the droplets produced further by the disintegration of ligaments. The generated ligaments can be categorized in two general types based on their orientation with respect to the flow field; span-wise and stream-wise ligaments. This work contains a two- and three-dimensional computational study of the primary breakup of a viscous liquid sheet. A Volume of Fluid (VOF) based code is used to solve the governing equations and capture the interface between the liquid sheet and the surrounding gas. Since the interaction between the liquid and gas is the major source of the breakup, the liquid-gas interface boundary is modified in this work and it is implemented using linear stability analysis. The variation in the breakup time and breakup length of liquid sheets with fluid properties is investigated by a two-dimensional study. Fluid properties are stated in three non-dimensional numbers: Weber number, Ohnesorge number and the gas to liquid density ratio. The liquid surface tension shows a stabilizing effect by increasing both the breakup time and breakup length of liquid sheets. The liquid viscosity has more complicated effects; it increases the breakup length while at a certain range of Weber numbers, increasing the viscosity decreases the breakup time. Increasing the surrounding gas density decreases both breakup length and time. The study is extended to three-dimension to capture the stream-wise ligaments as well as span-wise ligaments captured in two-dimension. The effect of fluid parameters on the formation of stream-wise ligaments is presented. A mesh refinement study is conducted which demonstrates that providing at least 7 computational cells per sheet thickness would lead to results which are not dependent on the mesh size.
1 citations