WO2017103314A1

WO2017103314A1 - Production of viscoelastic capillary jets by means of gas focussing

Info

Publication number: WO2017103314A1
Application number: PCT/ES2016/070896
Authority: WO
Inventors: Alberto TORRES PONCE; Emilio José VEGA RODRÍGUEZ; José María MONTANERO FERNÁNDEZ; Alfonso M. GAÑÁN CALVO
Original assignee: Universidad De Extremadura; Universidad De Sevilla
Priority date: 2015-12-18
Filing date: 2016-12-15
Publication date: 2017-06-22
Also published as: ES2625035A1; ES2625035B1

Abstract

The invention relates to a method for forming viscoelastic capillary jets or long filaments. The method includes forcing an elastic liquid of a constant viscosity, such as a Boger liquid consisting of a polymer solution, through the channel of a supply source to the centre of the interior of a pressurised chamber; and forcing a gas into the interior of the pressurised chamber such that it leaves the chamber through the outlet of the chamber arranged directly downstream from the trajectory of the liquid that flows out of the supply source. The gas focusses the liquid, substantially reducing the diameter thereof and the polymers present in the liquid allow the liquid to form a long and stabilised jet by means of an axial tension, with a Weber number close to zero.

Description

PRODUCTION OF VISCOELASTIC CAPILLARY JETS THROUGH

GASEOUS FOCUS

DESCRIPTION

FIELD OF THE INVENTION

The invention makes general reference to the field of fluid dynamics, and, in particular, to a method for forming a capillary stream of a viscoelastic liquid, said stream flowing concentrically with an accelerated gas stream and much faster so that a stabilized filament is formed by a tension stretching mechanism.

BACKGROUND OF THE INVENTION

The production and control of jets on the micrometric scale is of great interest in technological fields as varied as the pharmaceutical industry [1], biotechnology [2, 3], industrial engineering [4], food industry and agriculture [5]. In the Newtonian regime, the produced jets break into droplets with diameters of the order of the jet due to Rayleigh's capillary instability [6]. In this way, collections of relatively monodispersed drops (same size and morphology) can be obtained from different experiments in jetting mode with applications in, for example, medicine and pharmacy [1]. On the other hand, a great variety of physical-chemical processes are used to solidify the micro-puppies produced before their rupture. In particular, viscous liquids are continuously stretched under a jetting regime (stable jet emission) and subsequently solidified to form sub-millimeter glass or silk fibers [7], with obvious applications in the telecommunications and textile industry, respectively.

Many of the applications mentioned above involve the treatment of polymeric viscoelastic liquids, where the interactions between the processing conditions and the rheology (non-Newtonian character) of the fluid play a fundamental role. These interactions fundamentally alter the dynamic response of the system and considerably complicate the analysis of the problem. However, rheology becomes more manageable when working with Boger fluids [8]. These types of fluids are polymer solutions diluted in solvents with a sufficiently high viscosity so that elastic stresses are measurable. Further, Boger fluids exhibit a constant viscosity (the "shear thinning" effect, a pseudoplastic behavior characterized by the decrease in viscosity under a shear stress, can be neglected), so that the elastic effects can be separated from the viscous ones. The constitutive equation Oldroyd-B [9] provides reasonably accurate predictions for these viscoelastic liquids under certain conditions.

Various methods have been proposed to form micro and nanometric fibers from viscoelastic jets. Among them, electrospinning (or electro-spinning) [10] is one of the most popular because it can be applied to mass production of fibers "one by one" using different polymers. However, this method makes use of intense electric fields, which imposes certain restrictions on the electrical properties of the liquid used. Micrometric viscoelastic jets are also produced that solidify into fibers by purely mechanical or hydrodynamic means. In the classical "melt spinning" technique (so called because it originally referred to fusion spinning and stretching under centrifugal forces) [11], the liquid is extruded through a small hole and collected at a speed greater than the average extrusion speed. The resulting filament undergoes self-sustained oscillations when the ratio between the collection speed and the extrusion speed exceeds a critical value close to 20. This is called draw resonance instability [11, 12], the which considerably limits both the production rate and the minimum diameter of the fiber that can be obtained. The "selective withdrawal" method (or selective extraction) [13] allows fibers to be produced from polymer solutions by sucking a liquid stream through a hole located in front of the viscoelastic bath. The drag and suction forces (viscosity and pressure) produced by the current collaborate to deform the bath interphase, form a meniscus and stretch it until it emits a small stream from its tip. There are other examples where hydrodynamic forces have been applied to obtain fibers with sizes ranging from the millimeter scale to the nanometric scale. Among them is the coaxial atomization of viscoelastic ligaments, used in turn to measure the rheological properties [14]. Benavides et al. [15] obtained nanofibers by exposing a polymeric drop drop to a high velocity gas stream (aerodynamic method). In the "melt blowing" method, a polymer stream molten is dragged by two convergent air jets symmetrically directed to both sides of a two groove die [16, 17].

Flow focusing, [18, 19], has become a very popular method for producing submillimeter Newtonian jets using only hydrodynamic forces. In this technique, a meniscus hangs from a feeding capillary through which liquid is injected at a constant flow rate. An external fluid current focuses and stretches the meniscus in front of a hole. The meniscus emits a fine stream that co-flows with the external current through the hole. In the original axis focusing configuration of flow focusing [18], the external medium was a high velocity gas stream driven by an applied pressure drop. This configuration was subsequently adapted to the flat or two-dimensional (2D) topology [19] to form jets that co-flow with an external liquid stream, which boosted its application in microfluidics [1]. In both cases, the capillary-hole distance and its diameters are of the same order and the entire jet emitted is influenced by the focusing effect [19,20].

Flat flow focusing has been used in liquid-liquid configuration to produce micrometric jets of Boger fluids [21, 22, 23, 24, 25, 26]. For weak elastic effects, the "pinch-off" (clamping or narrowing of the jet interface causing the rupture of the jet) is initiated by capillary inertia mechanisms followed by an elasto-capillary regime [22]. As the polymer relaxation time increases, the dynamics of the filament becomes mainly controlled by the elasto-capillary mechanism, and both the length of the jet and the clamping time increase [22]. The flow regimes [25,26], the resulting droplet size [21,23], the effects of surfactants [24], or the appearance of flow asymmetries [27] have been analyzed both numerically and experimentally.

The axisimetric flow focusing has been applied to the formation of viscoelastic jets, focused through an oil phase [28]. A transition from dripping to stable jet emission was observed for sufficiently high values of the injected flow rate. This transition has been explained in terms of equilibrium between the destabilizing capillary force and the stabilizing tension associated with polymer elongation [29]. An effective value of this tension was estimated taking into account the polymer elongation produced by both the Poiseuille type flow in the feeding capillary [30] and the subsequent stretching of the filament in the region of in focus. In all experiments, the stretched meniscus remained anchored to the end of the feeding capillary.

SUMMARY OF THE INVENTION

The present invention describes both a method for creating elongated capillary jets (filaments) and the jet itself obtainable according to the method. The method comprises forcing a viscoelastic liquid, such as a liquid or Boger fluid, through the channel of a capillary tube, preferably cylindrical, as a power source. The viscoelastic liquid imposes a speed of passage through the channel that causes the liquid to exit the outlet opening of the channel maintaining its filament or jet shape. The end or exit opening of the channel is inside a pressurized chamber. Through the pressurized chamber the passage of a gas, such as air, is forced so that the gas leaves said pressurized chamber through the exit orifice of the chamber that is directly opposite and downstream of the liquid path viscoelastic Also, the gas focuses the flow of the viscoelastic liquid, so that liquid and gas flow concentrically, and transforms the jet of the liquid into an elongated jet that has a diameter substantially smaller than the diameter of the initial jet leaving the opening of the channel. Finally, the narrow elongated stream of viscoelastic liquid and the surrounding gas leave the pressurized chamber through the exit orifice. Said elongated capillary jet or filament can be collected as it exits through the outlet port of the pressurized chamber. According to particular embodiments, the method is performed such that the resulting Weber number is less than one, less than 1x10 ^"1 , less than 1x10 ^{" 2} , less than 1x10 ^"3 , less than 1x10 ^{" 4} , or less than 1x10 ^"6

According to other particular embodiments of the invention, the viscoelastic liquid, such as a Boger liquid, is introduced through the channel at a rate in the range of 0.001 to 100 microliters per second, or between 0.01 and 10 microliters per second. , or between 50 microliters and 2,000 microliters per second, or 100 to 500 microliters per second.

According to other particular embodiments of the invention, the gas is forced through the orifice of the pressurized chamber at a speed in the range of 50 μΙ / sec to 20,000 μΙ / sec, or between 100 to 500 μΙ / sec. As indicated previously, the gas velocity must be greater than the velocity of the viscoelastic liquid that comes out of the channel opening.

The channel of the power supply is a feeding tube or capillary, which may be in the form of a cylindrical or substantially cylindrical tube. According to certain variants of the invention, the feed capillary has an outlet diameter of less than 0.5 mm, less than 0.4 mm, less than 0.2 mm, or less than 0.1 mm.

The outlet of the capillary channel or tube is preferably located at a distance less than 0.5 mm from the outlet opening of the pressurized chamber. In a particular embodiment, the outlet opening of the power supply is located at a point at a distance in the range of 0.2 to 0.5 mm from the outlet opening of the pressurized chamber. In order to obtain a particularly appropriate result, once an initial jet is formed, it is convenient to gradually increase the capillary-hole distance, until reaching a final or maximum capillary-hole distance of, for example, approximately 12 mm or less, such as approximately 11 mm , 10 mm, 9 mm or less.

The outlet opening of the pressurized chamber, which is located directly in front of the outlet opening of the power supply, is generally circular. Preferred diameters for said exit port of the pressurized chamber are below 0.25 mm, for example in the range of 0.1 mm to 0.25 mm. According to certain variants of the invention, the feeding tube or capillary has an outlet diameter of less than 0.5 mm, less than 0.4 mm, less than 0.2 mm, or less than 0.1 mm, and the outlet of the capillary channel or tube is located at a distance less than 0.5 mm from the outlet opening of the pressurized chamber. According to certain variants of the invention, the outlet opening of the power supply channel has a diameter less than 0.5 mm, the outlet opening of the pressurized chamber has a diameter less than 0.25 mm, and the opening of The output channel of the power supply is located at a point less than 0.5 mm from the outlet hole of the pressurized chamber. According to certain variants of the invention, the outlet opening of the power supply channel has a diameter in the range of 0.1 mm to 0.5 mm, the outlet opening of the pressurized chamber has a diameter in the range of 0.1 mm to 0.25 mm, and the outlet opening of the power supply channel is located at a point at a distance in the range of 0.2 to 0.5 mm from the outlet hole of the pressurized chamber .

As indicated above, the initial or minimum distance between the outlet opening of the power supply channel and the outlet opening of the pressurized chamber, which is generally less than 0.5 mm, preferably increases progressively during the method until reaching a final or maximum capillary-hole distance of for example about 12 mm or less, such as about 11 mm, 10 mm, 9 mm or less. In general, gas (for example, air) can be forced into the pressurized chamber at a pressure in the range of 50 to 2,000 mbar above atmospheric pressure and viscoelastic liquid (for example, a Boger liquid) can have a velocity in the range of 1x10 ^"4 kg / m / sec to 1 kg / m / sec. An important aspect of the invention is a method of focusing viscoelastic jets of a liquid, such as a Boger liquid, using a stream of air. The flow Axisymmetric air focuses the Boger liquid so that said Boger liquid is micrometric jets According to the present invention, the viscoelastic liquid is a low concentration polymer solution, for example less than 1500 ppm, such as 1000 ppm, 500 ppm or 250 ppm In principle, the nature of the polymer is not important, since as one skilled in the art knows a wide variety of polymers leading to viscoelastic solutions. Polymers contemplated in the present invention They include, but are not limited to, polymers based on carbon chemistry, polymers based on silicon chemistry, fluoropolymers, proteins, DNAs, RNAs, etc. In a particular embodiment, the viscoelastic liquid is a solution of poly (acrylic) acid (PAA). In another aspect, the present invention is directed to the elongated liquid capillary jet (filament) obtainable according to the method of the invention. In addition, from said elongated capillary jet a solid filament or solid fiber can be obtained by a process of solidification or phase change between those considered, but not restricted to: solvent evaporation, cooling, chemical curing, chemical interaction with the forcing gas, chemical interaction with the environment gas in which the capillary jet is discharged, or heat hardening.

The filament or fiber obtained from the elongated capillary jet is useful in different industries, for example, such as: textile material, material for biomedical, surgical or prosthetic use, material for structural use in mechanical applications, material for the elaboration of wires or cables of very high resistance to breakage, such as mechanical reinforcement fiber in materials with low tensile strength, substrate for biotechnological use, or material associated with telecommunication.

Viscoelastic capillary jets can be produced by flow focusing. In this technique, the liquid is injected at preferably constant flow through a feed capillary located in front of a discharge orifice. A gaseous stream co-flows with the jet through the orifice driven by a constant pressure drop. The gas stream sucks and drags the liquid, reducing the diameter of the jet to values far below the diameter of the hole. Due to the rheological nature of the liquid, this focusing phenomenon differs from that observed in the Newtonian regime in several aspects. The conditions under which especially satisfactory results are obtained are those that lead to the "jetting" mode. Outside this interval, the jet could suffer from instability called "pull-out" or rupture before reaching the hole. Thanks to the stabilizing effect of the polymeric contribution to axial stress, micrometer jets of up to 1 cm in length can be produced, and Weber numbers of the order of 10 ^"4 can be achieved.

These and other objectives, advantages and characteristics of the present invention can be made apparent to those skilled in the art after reading the details of the method described more fully below. BRIEF DESCRIPTION OF THE FIGURES

The invention is better understood on the basis of the detailed description that follows when read in combination with the accompanying figures. It should be emphasized that, according to usual practice, the different details of the figures are not to scale. On the contrary, the dimensions of some details are augmented or arbitrarily reduced for clarity. Included in the drawings are the following figures:

Figure 1 is a schematic view of the basic components used in connection with an example according to the present invention. Q: flow rate at which the viscoelastic liquid is injected through the feed capillary, Δρ: pressure drop that drives the gaseous current through the discharge orifice, H: distance between the feed capillary (feed channel outlet opening ) and the discharge hole of the pressurized chamber.

Figure 2 consists of two graphs that we refer to as the graph on the left and the graph on the right. The graph on the left is a schematic view of an experimental assembly of the components that are used in relation to the method of the invention and that allow the observation and measurement of various system parameters. (A) capillary, (B) discharge hole, (C) orientation system, (D) translation platform, (E) ultra-high speed camera, (F) triaxial translation platform, (G) fiber optic, and (H) anti-vibration isolation system. The graph on the right shows an example of a jet, in relation to the present invention, of a solution of poly (acrylic) acid (PAA) with c = 1000 ppm, Δρ = 250 mbar produced at a flow rate Q = 4.5 ml / h. H = 6.7 mm.

Figure 3 consists of two graphs that we refer to as the graph on the left and the graph on the right. The graph on the left shows the dependence of the shear viscosity of the solution μ versus the shear rate γ ^' and the graph on the right shows the first viscometric function "+ Ί versus the shear rate γ ^' , for the PAA solutions In this experiment, c = 250 ppm (hollow symbols) and 1000 ppm (solid symbols) The starting points of the curves are determined by the rheometer sensitivity. Figure 4 consists of six connected images that are shown to illustrate the phenomenon of meniscal de-anchoring ("pull-out"). The meniscus of the fluid leaving the end of the capillary oscillates around an equilibrium position inside the feeding capillary. The jet emitted from the capillary was produced with c = 1000 ppm, Q = 40 ml_ / h, and H = 2 mm.

Figure 5 shows a graph of the temporal dependence of the radius of the free surface at 1 14 μηι (solid symbols) and 539 μηι (hollow symbols) of the capillary end. The jet was produced with c = 1000ppm, Q = 40ml / h, and H = 0.93mm.

Figure 6 shows six different connected images that are a sequence of images that illustrate the rupture of the hair jet due to the bulging effect. The jet was produced using c = 1000ppm, Q = 5ml / h, and H = 6.25mm. Figure 7 is a graph showing the minimum and maximum values, H _min and H _max, of the distance from the capillary to the hole in which the triple contact line anchors the end of the capillary. The hollow and solid symbols correspond to the PAA solutions with c = 250 and 1000ppm respectively. Figure 8 is a graph showing the experimental results of the Reynolds number and the aspect ratio values Λ of the experiments with c = 250ppm (hollow symbols) and 1000 ppm (solid symbols).

Figure 9 is a graph showing the results of both the velocity distribution v (dotted line) and the gauge pressure p _g (solid line) along the axis of the hole as a function of the distance Z to the center of the hole. The velocity is divided by its value in the internal section of hole vi. The simulation was carried out with air at a pressure of Δρ = 250 mbar and a hole with a passage diameter □ = 200μηι. The inserted box shows the pressure field near the hole.

Figure 10 consists of two separate graphs that we refer to as the left graph and the right graph. The left graph shows the experimental values of the Weber and Reynolds numbers. The right graph shows the experimental values for the Deborah number and the dimensionless polymeric stress. The Hollow and solid symbols correspond to PAA solutions with c = 250 and 1000 ppm respectively.

Figure 11 consists of two separate graphs which we refer to as the left graph and the right graph. The left graph shows the radius of the jet just in front of the hole depending on the aspect ratio Λ. The right graph shows the number of Deborah (De) versus the aspect ratio Λ. The hollow and solid symbols correspond to the PAA solutions of c = 250 and 1000ppm, respectively. Figure 12 shows a graph of the shear rate versus shear stress. The graph is provided to show the properties of a Newtonian fluid relative to the increase in shear rate versus shear stress in Newtonian and Non-Newtonian fluids. DEFINITIONS

In this document, the term "non-Newtonian fluid" refers to any fluid with properties that differ in some way from those that Newtonian fluids have. In a non-Newtonian fluid, the relationship between shear stress and shear rate is different and may even vary over time. The difference is shown in Figure 12, the difference with respect to a direct linear relationship can be 5% or greater, 10% or greater, 20% or greater, 40% or greater, etc. Therefore, a constant viscosity coefficient cannot be defined with a non-Newtonian fluid. Mostly, the viscosity (the measure of the ability of a fluid to withstand the gradual deformation produced by the tensile or shear force) of non-Newtonian fluids depends on the shear rate at the time or time. Some non-Newtonian fluids even having a viscosity independent of the shear force, have other behaviors other than normal versus force or other non-Newtonian behaviors. Many salt solutions or molten polymers are non-Newtonian fluids, as are many common substances such as ketchup, custard, toothpaste, yeast suspensions, paint, blood and shampoo. In a Newtonian fluid, the relationship between the shear force and the shear rate is linear, passing through the origin, the viscosity coefficient being the constant of proportionality as shown in Figure 12. The Weber number (We) is a dimensionless number in fluid mechanics and is useful in the analysis of fluid flows in which there is an interface between two fluids, especially in multiphase fluids with very curved surfaces. Its name comes from Moritz Weber (1871-1951). It can be considered as a measure of the relative importance of fluid inertia compared to surface tension. The value is useful for the analysis of thin layer flows and the formation of drops and bubbles.

Weber's number can be defined as:

ü v ^¿ i.

We _^

σ

where

P is the density of the fluid (kg / m ³ );

v is its speed (m / s);

I is its characteristic length, usually the drop diameter (m); Y

is the surface tension (N / m).

As mentioned, liquids called "Boger" type are elastic fluids with constant viscosity. This creates an effect on the fluid that makes it flow like a liquid, although it behaves like an elastic solid when stretched. Most elastic fluids show a pseudoplastic behavior (viscosity decreases when shear stress is applied), because the solutions contain polymers. But Boger fluids are exceptions since they are highly diluted solutions, so that the pseudoplastic behavior caused by polymers can be ignored. Boger fluids are made by adding a small amount of polymer to a Newtonian fluid of high viscosity, the most original solution is polyacrylamide mixed with corn syrup. It is a very simple compound to synthesize but important for the study of rheology because the elastic effects and shear effects can be distinguished in experiments performed with Boger fluids. In Boger fluids it is difficult to determine whether non-Newtonian effects are caused by elasticity, pseudoplasticity or both; the non-Newtonian flow caused by elasticity is rarely identified. Since Boger fluids can have constant viscosity, experiments can be performed where the result of the flow rates of a Boger liquid and a Newtonian liquid with the same viscosity can be compared, and the difference in flow rates could show the change caused. by the elasticity of the liquid Boger. A fluid Boger is an elastic liquid with a constant viscosity. Because the viscosity is independent of the shear rate or almost, the elastic effects can be separated from the viscoelastic flow viscous effects because the latter can be determined with Newtonian fluids.

DETAILED DESCRIPTION OF THE INVENTION

Before describing the method and product resulting from this invention, it should be understood that this invention is not limited to the particular steps and components described, since these, of course, may vary. It should also be understood that the terminology used herein is only intended to describe particular embodiments of the invention, and is not intended to be limiting since the scope of the present invention is limited only by the claims that are included. When a range of values is provided, it is understood that each value, up to one tenth of the lower limit unit as long as the text does not clearly indicate otherwise, between the lower limit and the indicated upper limit is specifically included. Each range below that existing between a indicated value or a value included within a indicated range and any other value indicated or included in said range, is covered by the invention. The upper or lower limits of these smaller ranges may be included or excluded from the range independently, and each of the ranges in which neither or both limits are included in the small ranges are included in the invention, subject to the specific exclusion of the limits of the ranges indicated. In cases where the ranges indicated include one or both limits, the ranges that exclude one or both of those limits included are also included in the invention.

Unless defined differently, all the technical and scientific terms used here have the same meaning as the one commonly understood by a person skilled in the art as to which the invention belongs. Although methods and materials similar or equivalent to those described herein can be used for the practice or testing of the present invention, some preferred methods and potential materials are described below. All the mentioned publications are incorporated as a reference to show and describe the methods and / or material related to the cited publications. It is understood that this The invention replaces any other description of any incorporated publication when there is a contradiction.

It should be noted that, as used herein and in the claims included, the singular forms "a / -a" and "the" include the reference to plurals unless the context clearly indicates otherwise. Thus, for example, the reference to "a stream" indicates a plurality of said stream and the reference to "the stream" includes the reference to one or more streams and thus different equivalents known to those skilled in the art.

The publications shown here are provided with the intention of displaying them prior to the application date of the present invention. Nothing should be construed as an acknowledgment that the present invention has no right to precede these publications by virtue of a priority invention. Moreover, the publication dates shown may be different from the current publication dates that must be confirmed individually.

Figure 1 provides a schematic view of an example of fluid configuration of the method of the invention. A cylindrical feed capillary, which has a length of several times its diameter, is located in front of the discharge orifice, whose diameter is of the order of the capillary diameter. The viscoelastic liquid is injected through the constant flow feed capillary Q, while a gaseous stream passes through the discharge orifice driven by a constant pressure drop Δρ. Especially satisfactory results are obtained if the distance H between the feed capillary and the discharge orifice is within a certain range, then a liquid jet of a Boger fluid is formed that begins at the edge of the capillary end and extends downstream in a flow direction far from the end of the capillary. The gas stream sucks and drags the Boger liquid, which reduces the diameter of the jet to values far below that of the discharge orifice. For example, the diameter of the jet downstream of the end of the capillary is focused by the surrounding gas so that it can be 50% or less, 25% or less, 10% or less, or 1% or less than the diameter of the jet when This leaves the end of the capillary. Both the liquid jet and the stream of cofluing gas flow across the orifice of exit. Due to the rheological nature of the liquid, this focusing phenomenon differs substantially from that produced in the Newtonian regime. In particular, the appropriate values of the capillary-hole distance H are normally much greater than their counterparts in the classical flow focusing configuration. The aerodynamic focusing effect can be confined within a very small region compared to the total length of the jet. Therefore, the liquid flows freely, without significant interaction with the surrounding environment. The instability mechanisms that prevent steady jetting from being achieved are also different from those of the Newtonian mode. Polymeric forces stabilize the liquid filament, allowing jets to be formed with Weber numbers close to zero.

The present invention is directed to the long (of the order of millimeters) jets formed between the end of the feed capillary and the discharge orifice. The invention specifies appropriate conditions for obtaining the "jetting" regime as well as the instability mechanisms that limit this regime. Some of the candidates for such mechanisms are reviewed, including capillary instability [28] and the fact that surface tension causes waves to grow on the surface of the jet until they finally pinch the interphase. Absolute instability [31] as well as convective instability could prevent the system from reaching the "jetting" mode. If the downstream convection disturbances pinch the interphase before reaching the hole, the suction effect is interrupted. This causes the ejection of the filament to cease, and prevents the jetting regime from recovering. This phenomenon does not occur when the process is carried out using a Newtonian fluid, where capillary waves grow beyond the hole [20].

Capillary instability is not desirable and can be modulated by elastic axial stress. The tension associated with polymeric stretching results in a strong increase in extensional viscosity. This partially inhibits capillary instability [32, 33]. The flow of Poiseuille in the feeding capillary causes a first stretching of the polymers. If a jet evolves at a constant speed (diameter), then the polymers relax at their winding state at distances from the capillary end that are equivalent to the diameter of the jet [34, 35, 36]. However, the acceleration of the jet caused by the co-flowing gas stream maintains the polymeric tension and can increase the polymeric tension near the hole.

Lateral oscillations ("whipping") may appear in jets that co-flow with a current that has a much higher velocity [37, 38]. In this case, the surface tension has a stabilizing effect, and the destabilization mechanism is aerodynamic: a disturbance in the interphase causes the co-flowing fluid to accelerate as it passes through a ridge, reducing the pressure at that point and causing the growth in size of said crest. A question that arises naturally is whether "whipping" can play an important role in fluidic settings. Experiments have shown that this is the case when Newtonian liquids are focused within a convergent nozzle [39], where the gas stream has a significant axial impulse in the focusing region. However, the "whipping" is confined upstream of the discharge hole in the classical configuration of flow focusing [20, 40]. This is because the flow of radial gas in front of the hole constitutes a hydrodynamic barrier to lateral disturbances.

The instability of the jet may also be due to the so-called "pull-out" of the filament which occurs due to fiber spinning [41, 42, 43] under axial stresses above the stability limit. If the filament is stretched by a sufficiently high spinning force, its retraction can occur with respect to the end of the feeding capillary. The balance between the spinning force and the normal tension in the capillary determines the new position of the meniscus inside the capillary. The meniscus can remain motionless in the capillary or oscillate around the equilibrium position [43]. There are other instability mechanisms such as stretching resonance ("draw resonance") mentioned previously [11] or known as "melt fracture" [44]. The stretching resonance is linked to the prescription of the jet velocity at some point downstream [45]. This condition does not apply to flow focusing, and therefore this phenomenon does not occur in relation to the present invention.

Information on both the stability and the forces that characterize the "jetting" regime in flow focusing of viscoelastic jets is provided here. The experimental procedure and the rheological properties of working liquids are described in the later section of Materials and Methods. Experimental data is presented and analyzed in the subsequent Results section.

EXAMPLES

The following examples are presented to provide those skilled in the art with a complete explanation and description of how to make and use the present invention, and it is not intended to limit the scope of what the inventors recognize as their invention nor is it intended to indicate that the experiments described below are the only experiments performed. An effort has been made to ensure the accuracy of the numbers used (eg quantities, temperature, etc.) but it must be taken into account that there may be errors or experimental deviations. Unless otherwise indicated, the parts are parts by weight, the molecular weight is the average molecular weight, the temperature is in degrees Centigrade and the pressure is or is very close to atmospheric.

MATERIALS AND METHODS

Figure 2 shows a non-Newtonian fluid injected at a constant flow rate Q by a stepper motor (not shown) through a steel capillary (A), for example, 3.5 cm in length and 200 μηι in diameter, with a sharp capillary end. Said end of the capillary is placed in front of a hole (B) perforated in the upper face of a stainless steel cell. The hole (B) is, for example, 200 μηι in diameter and 500 μηι in thickness. A negative gauge pressure Δρ is applied inside the cell by using a suction pump (not shown). A high precision orientation system (C) and a translation system (D) are used to ensure the correct alignment of the flow focusing elements, and to establish the capillary-hole distance H.

The viscoelastic jet is formed outdoors due to the action of the air stream sucked through the hole in the cell. Digital images can be acquired using two or more cameras (E) with optical axes perpendicular to each other, and equipped with very different magnification lenses. The camera with the highest magnification moves both horizontally and vertically using a triaxial translation platform (F) to focus part of the liquid jet, while the other camera acquires images of the entire ligament. In this way, the radius of the jet R (of the order of tens of microns) and the capillary-hole distance H (of the order of millimeters) can be measured simultaneously. The fluid configuration lights up to backlight on the two axes (in front of the two cameras) by cold white light provided by two optical fibers (G) connected to light sources. All these elements are mounted on an optical table with a pneumatic anti-vibration isolation system (H) to dampen vibrations from the surrounding environment.

Experiments are carried out at 24 ± 2 ° C. The feed capillary is placed at a distance from the cell hole that is substantially the same as the hole diameter. The pressure drop is set at Δρ = 250 mbar in the air stream. An equal, non-Newtonian liquid is injected a flow rate Q through the capillary.

After a brief transitory regime, the capillary emits a liquid filament that crosses the orifice driven by the air current. The capillary-hole distance H is progressively increased, keeping Δρ and Q constant. In order to achieve the "jetting" regime, it is convenient to strictly follow the above sequence. For example, if the process is started using a H value that is much larger than the diameter of the hole, then the air flow cannot easily establish a necessary degree of elastic tension in the liquid filament, thus hindering the formation of the jet. The procedure described above can be repeated for different flow rates Q and two polymer solutions. You can acquire images during the course of the process. The position of the free surface can be determined by processing the images with a super-resolution technique at the sub-pixel level [46].

The behavior of two poly (acrylic) acid (PAA) solutions (Mw = 18 x 10 ⁶ g / mol) in pure distilled water with concentrations of c = 250 and 1000 ppm can be examined. Non-Newtonian fluid solutions can be prepared by dissolving polymer in a solvent by stirring at very low speeds, in order to avoid breakage of the polymer chains. The shear viscosity dependence μ of the solution and first viscometric function "+ Ί versus the shear rate γ ^' can be measured with a Physica MCR 301 rheometer. The results are shown in Figure 3.

The polymeric relaxation time λ can be measured with the HAAKE CABER 1 extensional rheometer by applying the slow retraction method [47]. The values were λ = 20 and 140 ms for 250 and 1000 ppm, respectively. The surface tension γ can be measured with the TIFA method [48]. It can be verified that γ ~ 72 mN / myp ^ 997 kg / m ³ in all cases, that is, these two properties do not depend significantly on the polymer concentration. Figure 2 shows a jet with c = 1000 ppm produced at a flow rate Q = 4.5 ml / h.

The gaseous flow focusing of the two viscoelastic liquids described above behaves as follows. When the feeding capillary is located near the discharge orifice, the liquid meniscus separates from the edge of the capillary end and climbs up the inner wall of the capillary. The meniscus either reaches an equilibrium position inside the capillary or oscillates around it. This is the phenomenon called "pull-out" that has been observed in fiber spinning [41, 42, 43]. The final position of the triple contact line is essentially determined by the balance between the tensile force caused by the flow of Poiseuille in the capillary, and that exerted by the emitted jet. A small lateral disturbance causes the jet to touch the inner surface of the capillary. Due to the strong tendency of the liquid to wet the steel, the jet remains in contact with the wall while sliding on it. The result is the steady emission of a jet ("steady jetting") that passes through the discharge orifice driven by the air flow.

A sequence of images is shown in Figure 4 to illustrate the phenomenon of "pull-out". The steel capillary is replaced by one made of silica (transparent).

By carefully moving the feed capillary and the discharge orifice, the film flowing inside the capillary goes outside and becomes part of the outdoor jet. This process continues until the end of the capillary reaches the meniscus position. That is when the triple contact line anchors to the edge of the capillary.

Contrary to what happens with Newtonian liquids, both the triple contact line and the free surface of the jet oscillate. This oscillatory behavior is caused by a transient bulge ("swell-die effect"), which appears continuously just outside the capillary, probably stimulated by the local relaxation of the elastic tension at that point. The bulge of the filament is conveyed downstream, causing the entire jet to oscillate. Figure 5 shows the temporal dependence of the radius of the free surface for two sections of the jet. The magnitude of the oscillation increases with H. There is a maximum capillary-orifice distance in which the emission is interrupted (Figure 6). This occurs because the strain rate in that case is not high enough to convene the bulging of the interphase. Then, the jet continues to bulge at the outlet of the feed capillary, so that a drop is formed anchored to its edge. The drop sucks the liquid from the quasi-cylindrical thread that hangs from it. The radius of the thread is reduced by an elastocapillary regimen similar to that shown in a capillary rupture rheometer [47, 49], which ultimately leads to the "beads-on-a-string" structure and the free surface clamping.

The symbols H _min and H _max are used to represent the capillary-orifice distances at which the triple contact line first anchor to the capillary edge and the jet emission is interrupted, respectively. "Steady jetting" with "pull-out" is obtained for H <H _min , while an oscillating jet is observed for H _min <H <H _max .

Figure 7 shows the values of H _min and H _max corresponding to PAA solutions with c = 250 and 1000 ppm. The lines delimit the parametric regions where the jets anchor the feeding capillary. No jets could be produced for Q <1 ml / h. In what follows, we will focus on the jet configurations that have their contact lines anchored to the end of the feed capillary.

Figure 8 shows the experimental values of the Reynolds number Re = pv _Q R ^ _Q defined in terms of the radius R _Q and the velocity v ₀ of the jet at the outlet of the feed capillary, the density of the liquid p and the shear viscosity a shear rates for small velocity gradients ("zero-shear viscosity") μ ₀ . This last value was obtained by extrapolating the curves of Figure 3 for γ = 0. As can be seen, Re <10 ^"2 and, consequently, the shear stresses are dominant over the inertia of the liquid. , it can be assumed that the viscous radial diffusion of the moment flattens the velocity profile just at the exit of the capillary, forcing the Poiseuille type velocity field to evolve towards a flat distribution very close to the capillary.

Figure 8 also shows the aspect ratio values Λ = R _Q / H. Slender liquid filaments (Λ ~ 10 ^"2 ) are formed between the feeding capillary and the orifice of discharge. Under these conditions, the equation 1 D (or slenderness) of the amount of axial movement provides an accurate description of the dynamics of the liquid.

In the present flow focusing configuration, the air flow is accelerated in the region located in the vicinity of the discharge orifice, said region having a size much smaller than that of the liquid filament. In order to illustrate this, numerical simulations with FLUENT 6.3 of the laminar and incompressible flow of air crossing the circular orifice used in the experiments were carried out. Figure 9 shows both the velocity distribution and the manometric pressure distribution along the axis of the hole as a function of the distance Z to the center of the hole. As can be seen, the focusing effect is confined within a region of size Z / D-1, where D is the diameter of the hole. In this region, the force per unit volume exerted by the stream of air in the jet scales as Δρ / D [50]. The size of the focusing region is much smaller than the length of the jet and, therefore, most of the liquid filament flows freely, without significant interaction with the surrounding air.

The equation of quantity of movement 1 D can be expressed as a function of the following dimensional quantities: the density p of the liquid and its surface tension Y, the viscosity of the solvent (water) μ ₃ (JJ _S = 10 ^"3 kg / ms) , the radius of the jet R (z) and the axial velocity v (z) along the axis of the jet z, as well as the spatial distributions of the polymeric contributions axial σ _ζ (ζ) and radial or _r (z) to the stress total, if you ignore it in [37]

where C is the local curvature of the free surface. In order to establish the ranking of the terms that appear in the equation, the radial and axial lengths are scaled with R _Q and H, respectively; the velocity of the jet with v ₀ and the polymeric stresses with the axial polymeric stress at the outlet of the feed capillary or _z0 . This last magnitude can be estimated as or _z0 = γ ^'2 , where Ψι (γ) is the first viscometric function (Figure 3) and γ ^' is the "effective" shear rate that characterizes the flow of Poiseuille in the capillary, that is, γ ^' = 4Q / (n Rc) (R _c is the radius of the capillary) [28]. The resulting dimensionless equation is:

Where R = R / R _Q and v = v / v ₀ are the radius and jet velocity scaled, respectively; \ Ne = pvoR ₀ / y is the Weber number, C = CR ₀ is the dimensionless local curvature of the free surface, Te = O _z0 (Y / R ₀ ) is the axial polymeric stress at the outlet of the feed capillary at As a function of capillary pressure, Re _s = pv ₀ R ₀ / μ _s ^{is the} Reynolds number based on the viscosity of the solvent μ ₃ and _ζ = σ _ζ / σ _ζ0 is the field of scaled polymeric stresses. In addition, the premium denotes the derivative d / dz with respect to the scaled axial coordinate z = z / H.

The variations along the jet of its radius and velocity are of the order of R ₀ and v ₀ , respectively. Due to the slenderness of the jet, C ~ 1 / Therefore, R ~ v ~ v '~ C' ~ l, and {R ² v ')': ¾ 1. Consider now the Deborah number defined as De = 21dv / dz. According to, for example, the Oldroyd-B model [9], if (De)> 1 the polymeric contribution to axial stress σ _ζ grows exponentially, while the radial component σ _Γ is negligible [37]. In the experiments the average Deborah number (De) = Zk (v _x ^■■■■ V _Q ) / H was measured, where \ is the velocity of the jet just in front of the discharge orifice. If (De)> 1, then it can be assumed that [β ² (σ _ζ —σ _Γ )] 'grows exponentially throughout the entire stream.

Figure 10 shows the experimental values of the numbers of Weber, Reynolds, and Deborah, as well as the dimensionless polymeric tension Te. As can be seen, We, ARe ^ ¹ «1 in all cases and, consequently, II» I »IV in the dimensionless equation of paragraph [0070]. In addition, (De)> 1 in all experiments and hence the term III of the aforementioned equation is expected to grow exponentially downstream. It is concluded that the movement of the jet away from the hole is driven by the gradient of the polymeric axial stress, while the surface tension generates a significant resistance force. In other words, the balance of forces is reduced approximately to:

R ² C '= Te (R ² d _z y Importantly, very small Weber number values were obtained in the experiments. In fact, capillary jets with We ~ 6 x 10 ^"4 were produced for the highest polymer concentration and the lowest flow rate. If one compares their kinetic and interfacial energies, it can be said that these jets hang virtually at rest from the feeding capillary For these very small Weber numbers, the jet must be expected to be absolutely unstable [31] This implies that the waves grow and travel both upstream and downstream on the free surface, avoiding a steady jetting emission Stationary jet, perfect As mentioned above, self-sustained oscillations of small amplitude over the entire liquid domain were observed in the experiments Absolute instability may contribute in part to the occurrence of such oscillations.

It should be noted that, contrary to what could happen to Newtonian liquids, these oscillations fail to clamp the free surface due to the stabilizing role played by the polymeric axial stress not only in the linear deformation, but also in the non-linear strangulation process.

Finally, attention is paid to the radius of the viscoelastic jet just in front of the hole. The radius of the jet decreases with Λ (Figure 1 - left). This result can be interpreted in terms of the effective Deborah number (De) measured in the experiments. This parameter also decreases with Λ (Figure 1-right), which implies that both the average strain rate and the extensional (apparent) viscosity associated with the stretching of the polymer also decrease with Λ. Therefore, the dissipation of energy in the entire liquid filament should decrease with Λ. Because Δρ remained constant in all experiments, the jet energy injection was essentially the same in all cases. Then, it can be concluded that the kinetic energy of the jet (radius) in front of the hole should increase (decrease) when the aspect ratio decreases.

CONCLUSIONS

The invention described herein shows the production of viscoelastic capillary jets of non-Newtonian fluids using the gaseous flow focusing configuration. The rheological nature of the liquid alters the phenomenon of focusing on several important aspects. This technique allows to form jets with lengths of more than one hundred times its radii, and with Weber numbers of the order of 10 ^"4. Although the focusing region is confined in a small region near the discharge hole, the polymer chains transmit the upstream suction effect throughout the liquid yarn In this way, the resistance offered by the surface tension is overcome despite the fact that the kinetic energy is much smaller than the interfacial. The jetting regime (stable jet emission) can be achieved within of an interval of the capillary-hole distance that depends largely on both the polymer concentration and the flow rate (see figure 7). For distances below that interval, a pull-out of the liquid meniscus was found, while if the distance exceeds the maximum value of the interval the jet breaks in. The achievement of a perfect steady jetting was a relatively rare event. Jet urations, significant oscillations of the free surface were observed. The rupture of the jet that takes place behind the discharge orifice was not examined, since it does not differ substantially from the process widely analyzed in the literature (see, for example, [21, 37, 49, 51, 52]). The macromolecules in solution suppress the formation of satellite drops, and produce large extensional efforts, which lead to the formation of blisters ("blistering") and "beads-on-string" structures (pearl chain).

The competition between surface tension and polymeric stresses is the result of a complex interaction between liquid rheology, flow rate, and applied pressure drop, as well as geometric constraints.

The above simply illustrates the principles of the invention. It is aware that those skilled in the art will be able to imagine embodiments that, although not explicitly described or shown here, are based on the foundation and principles of the invention and therefore are included in its spirit and scope. Additionally, all the examples and conditional language used here have the main intention of helping the reader understand the principles of the invention and the concepts that the inventors contribute to promote the subject, and their intention is not to limit the invention to the examples and conditions shown. Moreover, all statements describing principles, aspects and embodiments of the invention, as well as the specific examples shown, are intended to cover both the structural equivalents such as functional equivalents. Additionally, the intention is that those equivalents include both those currently known and those that will be developed in the future, eg any element developed to perform the same function regardless of its structure. The scope of the present intention, therefore, is not intended to be limited to the embodiments included in the examples and described herein. Moreover, the scope and spirit of the present invention is what is framed by the following claims.

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Claims

1. A method for creating an elongated capillary jet or filament of a viscoelastic liquid, characterized by:

force a viscoelastic liquid through a channel of a power supply at a speed that causes the liquid to exit the outlet opening of the channel, said opening being inside a pressurized chamber; force a gas in the pressurized chamber to exit through an orifice positioned in front of the path of the viscoelastic liquid that exits the outlet opening of the channel, so that the gas flows concentrically with the viscoelastic liquid that exits the exit opening of the channel, the gas velocity being greater than the liquid velocity; where the dynamic forces that the gas exerts on the surface of the viscoelastic liquid that emerges from the outlet opening of the channel cause an elongated capillary jet or filament of the liquid to form, as a consequence of which said dynamic forces generate as a global result on the liquid viscoelastic, an axial tension maintained along the axis of the jet, which stabilizes it; and allow the elongated capillary stream or filament to exit, surrounded by the gas, from the chamber pressurized by the hole in the chamber.

2. Method according to Claim 1, characterized in that the viscoelastic liquid is a Boger liquid.

3. Method according to any one of the preceding claims, characterized in that the Weber number of the jet is less than 1.

Method according to any one of the preceding claims, characterized in that the Weber number of the jet is less than 1x10 ^"1 .

5. Method according to any one of the preceding claims, characterized in that the Weber number of the jet is less than 1x10 ^"2 .

Method according to any one of the preceding claims, characterized in that the viscoelastic liquid is forced through the channel at a speed in the range of 0.001 μΙ / sec to 100 μΙ / sec.

Method according to any one of the preceding claims, characterized in that the gas is forced through the orifice of the pressurized chamber at a speed within the range of 50 μΙ / sec to 20,000 μΙ / sec.

Method according to any one of the preceding claims, characterized in that the gas is forced through the orifice of the pressurized chamber at a speed within the range of 100 μΙ / sec to 500 μΙ / sec.

Method according to any one of the preceding claims, characterized in that the channel of the power supply is a capillary or cylindrical tube.

Method according to any one of the preceding claims, characterized in that the channel of the power supply has an outlet diameter of less than 0.5 mm.

1 Method according to any one of the preceding claims, characterized in that the outlet opening of the power supply channel and the outlet opening of the pressurized chamber are located at a distance of less than 0.5 mm.

12. Method according to any one of the preceding claims, characterized in that the outlet opening of the power supply channel has a diameter of less than 0.5 mm, the outlet opening of the pressurized chamber has a diameter of less than 0.25 mm , and the outlet opening of the power supply channel is located at a point less than 0.5 mm from the outlet opening of the pressurized chamber.

13. Method according to any one of the preceding claims, characterized in that the outlet opening of the power supply channel has a diameter in the range of 0.1 mm to 0.5 mm, the outlet opening of the pressurized chamber has a diameter in the range of 0.1 mm to 0.25 mm, and the outlet opening of the power supply channel is located at a point at a distance in the range of 0.2 to 0.5 mm from the hole output of the pressurized chamber.

14. Method according to any one of the preceding claims, characterized in that the distance between the outlet opening of the power supply channel and the outlet opening of the pressurized chamber increases progressively to a maximum final distance of 12 mm or less.

15. Elongated capillary jet or viscoelastic liquid filament obtainable according to the method defined in any one of the preceding claims.

16. Solid filament or solid fiber obtainable according to the method defined in any one of claims 1 to 14 followed by a solidification or phase change process.

17. Solid filament or solid fiber according to claim 16, characterized in that the solidification or phase change process is carried out by solvent evaporation, cooling, chemical curing, chemical interaction with the forcing gas, chemical interaction with the ambient gas in which the hair jet is discharged, or heat hardening.

18. Use of the filament or fiber according to claim 17 as textile material, material for biomedical, surgical or prosthetic use, material for structural use in mechanical applications, material for the elaboration of wires or cables of very high resistance to breakage, as fiber of mechanical reinforcement in materials with low tensile strength, substrate for biotechnological use, or material associated with telecommunication.