A nonlinear analysis of the effect of heat transfer on capillary jet instability
TL;DR: In this paper, the authors investigated the breakup of a viscous jet emanating from an orifice in the presence of convective heat transfer and found that the heat loss from the jet to the ambient fluid can shorten the breakup length of the jet.
Abstract: Breakup of slender liquid jets under isothermal conditions has been studied extensively. In this work, we investigate the breakup of a viscous jet emanating from an orifice in the presence of convective heat transfer. We study the case where heat is transferred from the jet to the ambient fluid. The temperature varies axially and both viscosity and surface tension are taken to be temperature dependent. Marangoni stresses caused by a thermally induced surface tension gradient are included here. A numerical model based on a one-dimensional slender jet approximation of the equations of motion and heat transfer is used. This results in three coupled nonlinear partial differential equations, which are solved using the method of lines. The advantages of using this approximation lie in (i) its computational elegance and (ii) the physical insight that it provides. We compare the model predictions of both spatial and temporal stability analysis with experiments of a jet of molten Woods metal in water. Molten Woods metal emanating from various orifice diameters (1-10 mm) into water under the action of gravity is analysed for drop sizes and these are compared with the numerical predictions. The presence of heat transfer is found to shorten the breakup length of the jet. This is attributed to the increase in surface tension induced by the heat loss from jet to the ambient. It is found that including the effect of temperature dependence of viscosity and surface tension, however, does not affect the drop size. A critical dimensionless number (Π1 ∼ 10) is found to exist beyond which the breakup is dominated by Marangoni stresses. Below this critical number, the jet breaks up due to the combined effects of the capillary force and the Marangoni stresses. It is shown that including the effect of gravity is necessary to predict the drop size accurately. The results of this work have implications in evaluating safety strategies in the event of a core disruptive accident in a nuclear reactor. A wider application of this analysis is in improving the efficiency of thermally modulated inkjet printing.
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TL;DR: In this article, a facile, scalable technique to produce biodegradable porous microspheres by combining continuous ink-jetting through a piezoelectric nozzle with thermally induced phase separation was described.
Abstract: Porous microspheres capable of delivering high payloads of biomolecules with suitable biodegradability and biocompatibility would be valuable in delivery systems to aid tissue regeneration. This study describes a facile, scalable technique to produce biodegradable porous microspheres by combining continuous ink-jetting through a piezoelectric nozzle with thermally induced phase separation (TIPS). A selection of biomaterials is investigated to suit delivery in tissue engineering, the synthetic polyesters poly(lactic-co-glycolic acid) (PLGA), and poly caprolactone (PCL) and a natural polymer, gelatin. The parameters governing the microsphere production are determined experimentally and compared to theoretical predictions derived from the fluid mechanics and heat transfer during the ink-jetting process. The microspheres produced have open interconnected pores with mean particle diameters of 80-200 μm and no significant skin region. The physical properties, such as the mean particle diameter, pore size, and surface area could be controlled by varying production parameters including the ink-jetting pressure, nozzle height, and the size and oscillation frequency of the nozzle. The technique is demonstrated to successfully encapsulate a model hydrophobic molecule during microsphere production with uniform distribution. Porous PLGA microspheres are also used to achieve much higher adsorption capacities of a short peptide than non-porous microspheres of the same material. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
20 citations
TL;DR: In this paper, the mass median diameter of the fragmented debris is predicted from nonlinear stability analysis of slender jets for lead jet and using Rayleigh's classical theory of jet breakup for aluminium jet.
7 citations
26 Oct 2021
TL;DR: In this paper, different regimes of temperature modulated breakup were studied using a slender jet model, where instability is induced through capillary and Marangoni stresses and can be used to control droplet formation in terms of intact length and resultant drop size distribution, which is otherwise irregular due to the inevitable presence of background noise.
Abstract: Different regimes of temperature modulated breakup were studied using a slender jet model. The instability is induced through capillary and Marangoni stresses and can be used to control droplet formation in terms of intact length and resultant drop size distribution, which is otherwise irregular due to the inevitable presence of background noise. When thermal modulation is weak, the surface tension gradient forces act only as a trigger and curvature-gradient forces soon take over and grow exponentially downstream of the jet due to inertio-capillary growth. When thermal modulation is strong, the surface tension gradient forces not only act as a trigger, but remain significant till breakup.
3 citations
TL;DR: In this article , the authors study the dynamics of a liquid jet issued from a rotating orifice, whose breakup is regulated by a vibrating piezo element, and exploit the slenderness of the jet to separate the calculation of the base flow and the growth of perturbations.
Abstract: Abstract We experimentally and numerically study the dynamics of a liquid jet issued from a rotating orifice, whose breakup is regulated by a vibrating piezo element. The helical trajectory of the spiralling jet yields fictitious forces varying along the jet whose longitudinal projections stretch and thin the jet, affecting the growth of perturbations. We show that by quantifying these fictitious forces, one can estimate the jet intact length and size distribution of drops formed at jet breakup. The presence of the locally varying fictitious forces may render high-frequency perturbations, that would otherwise be stable in the abscence of stretching, unstable, as observed similarly in the case of straight jets stretching under gravity. The perturbation amplitude then dictates how strong the perturbation is coupled to the jet compared with random noise that is inherently present in any experimental set-up. In the present study we exploit the slenderness of the jet to separate the calculation of the base flow and the growth of perturbations. The fictitious forces calculated from the base flow trajectory are then used in a nonlinear slender-jet model, which treats the spiralling jet as a quasi-straight jet with locally varying body forces. We show both experimentally and numerically that jet breakup characteristics (e.g. intact length and drop size distribution) can be controlled by finite-amplitude perturbations created by mechanically induced pressure modulations. Finally, we revisit the integrated net gain approach developed for straight jets under gravity and we provide simple analogous relations for spiralling jets.
2 citations
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2,819 citations
TL;DR: In this paper, it was shown that for a very viscous liquid column the maximum instability occurs when the wave-length of the varicosity is very large in comparison with the radius of the cylinder, i.e., when λ = ∞ theoretically.
Abstract: 1—The dynamical theory of the instability of a long cylindrical column of an incompressible perfect liquid under the action of capillary force has been given by Rayleigh, neglecting the effect of the surrounding fluid. According to his results, if the column becomes varicose with wave-length λ , the equilibrium of the column is unstable, provided λ exceed the circumference 2π a of the cylinder, in accordance with the result of Plateau’s statical theory; and the degree of instability, as indicated by the value of q in the exponential eqt to which the motion is assumed to be proportional, depends upon the value of λ reaching a maximum when λ = 4.51 × 2 a . The case of a long cylindrical column of an incompressible viscous liquid has also been discussed by Rayleigh, again leaving out of consideration the effect of the surrounding fluid. Assuming the viscosity to be very great compared with the inertia and neglecting the effect of the latter, he has shown that for a very viscous liquid column the maximum instability occurs when the wave-length of the varicosity is very large in comparison with the radius of the cylinder, i. e ., when λ = ∞ theoretically. Quite recently G. I. Taylor has made interesting experimental researches, together with some theoretical investigations, upon the mode of formation of the cylindrical thread by the disruptive effect of the viscous drag of one fluid on the other, by putting a small drop of a viscous liquid in definable shearing fields of flow of another viscous liquid. He has thus thrown much light upon the mechanism of the formation of emulsions. In the course of his experiments he observed an interesting phenomenon, in one case when the ratio of the viscosity of the liquid forming the thread to that of the surrounding liquid is 0.91, that after the apparatus which was used to produce the field of flow was stopped the final thread gradually broke up into a number of small drops spaced at nearly regular intervals, although it had seemed quite stable while the apparatus was in motion. In connection with this interesting phenomenon, Professor G. I. Taylor kindly suggested to the writer a problem of investigating the character of the equilibrium of a long cylindrical thread of a viscous liquid surrounded by another viscous fluid under the action of interfacial surface tension as well as under the effect of viscous forces acting on the liquid inside the column by the surrounding viscous fluid. The effect of the latter is expected to play some important role in the phenomenon under consideration, although, as mentioned already, its effect had been neglected by Rayleigh in his investigation.
1,006 citations
901 citations
TL;DR: This work considers the viscous motion of an axisymmetric column of fluid with a free surface and the Navier-Stokes equation forms a singularity as the height of the fluid neck goes to zero.
Abstract: We consider the viscous motion of an axisymmetric column of fluid with a free surface. The Navier-Stokes equation forms a singularity as the height of the fluid neck goes to zero. Close to pinchoff, the solutions have a scaling form characterized by a set of universal exponents. The shape of the neck and its velocity field is described by scaling functions, which we predict without adjustable parameters.
587 citations
TL;DR: In this paper, the velocity and radius of a column of axisymmetric fluid with a free surface were derived from the Navier-Strokes equation, where the equations form singularities as the fluid neck is pinching off.
Abstract: We consider the viscous motion of a thin axisymmetric column of fluid with a free surface. A one-dimensional equation of motion for the velocity and the radius is derived from the Navier–Strokes equation. We compare our results with recent experiments on the breakup of a liquid jet and on the bifurcation of a drop suspended from an orifice. The equations form singularities as the fluid neck is pinching off. The nature of the singularities is investigated in detail.
550 citations