System and method of obtaining entrained cylindrical fluid flow
A method and system for entraining fluids is provided. The method and system may be used to create filaments. As one example, a filament may be produced by entraining a first fluid within a second fluid by flowing a third fluid, the flowing third fluid at least partly constraining the second fluid in at least one dimension. As another example, a filament may be produced by entraining a first fluid within a second fluid based on a model of a dynamic response of the first and second fluids as functions of densities of the first and second fluids, viscosities of the first and second fluids, Reynolds numbers of the first and second fluids, and Weber numbers of the first and second fluids.
This application claims the benefit of U.S. Provisional Application No. 60/648,102, filed Jan. 27, 2005. U.S. Provisional Application No. 60/648,102, filed Jan. 27, 2005 is hereby incorporated by reference herein in its entirety.
FIELDThe present application relates to a method and apparatus for obtaining entrained fluid flow and more specifically, a method and apparatus for obtaining a stable entrained cylindrical fluid flow.
BACKGROUNDFormation of bubbles or filaments in a fluid, such as a liquid or gas, may be of interest. For example, bubbles may be used in a variety of scientific fields, such as in the fields of biomedicine (e.g., in diagnosis, as potential gene therapy vectors, to convey tiny amounts of therapeutic gases in the bloodstream without the risk of embolism, etc.), advanced physics studies (bubble sonoluminiscence, damping agents in neutron spallation sources, etc.), chemical engineering, and as a strong allied in environmental protection (e.g., microbubble drag reduction in marine transport, dissolved air flotation water depuration techniques, etc.). As another example, filaments may be used to create fibers or the like.
Forming the bubbles or filaments in the fluid may be difficult. The interface between the bubbles or filaments and the surrounding fluid may be complicated, thereby making it difficult to control a system to make stable and acceptable bubbles or filaments. Therefore, there is need for a system that enables the creation of stable and acceptable bubbles or filaments.
BRIEF SUMMARYIn one aspect of the invention, a filament is produced by entraining a first fluid within a second fluid by flowing a third fluid, the flowing third fluid at least partly constraining the second fluid in at least one dimension. The third fluid may flow through a variety of methods, such as by applying pressure to the fluid flow. The third fluid flow may constrain the second fluid axisymmetrically. Further, the third fluid may apply a force on the second fluid to at least partly drag or withdraw the second fluid from its nozzle and/or reservoir. In turn, the second fluid may apply a force on the first fluid to at least partly drag or withdraw the first fluid from its nozzle and/or reservoir. In this manner, the force used to entrain the first fluid may be more due to dragging or withdrawing rather than on a direct force on the first fluid (such as increasing pressure applied to the reservoir housing the first fluid). Specifically, if the force used to entrain the first fluid may be due in part, or entirely, on the fluid properties of the first and second liquid. For example, the first fluid may be entrained within the second fluid based on the viscosities of the first and second fluids. When a filament is produced, a part of the second fluid and a part of the first fluid (such as if the first fluid is a liquid) may be solidified in order to form a fiber. When the first fluid is withdrawn, in order to maintain a constant pressure, the first fluid's reservoir may need to be filled with additional first fluid. Alternatively, instead of applying no pressure on one or more of the fluids (such as moving the fluid only by dragging or withdrawal), one or more of the fluids may be “sucked upward,” so that an additional amount of a dragging force is required to move the fluid in the direction opposite to the force sucking upward.
In another aspect of the invention, a filament being produced by entraining a first fluid within a second fluid based on a model of a dynamic response of the first and second fluids as functions of densities of the first and second fluids, viscosities of the first and second fluids, Reynolds numbers of the first and second fluids, and Weber numbers of the first and second fluids. The model of the dynamic response may define a phase space of a stable entraining of the first fluid within the second fluid. Further, the system may be controlled such that values of the Reynolds numbers of the first and second fluid and Weber numbers of the first and second fluid may be selected to be in the phase space of the stable entraining of the first fluid within the second fluid. The model may be derived numerically and/or analytically. When a filament is produced, a part of the second fluid and a part of the first fluid (such as if the first fluid is a liquid) may be solidified in order to form a fiber.
The foregoing summary has been provided only by way of introduction. Nothing in this section should be taken as a limitation on the following claims, which define the scope of the invention.
BRIEF DESCRIPTION OF THE DRAWINGS
As discussed in the background, there are many applications for bubbles or filaments. For example, in the context of filaments, hollow cylinders or tubes and compound fibers with an inner diameter of micron and sub-micron sizes have a variety of applications. One of the most promising is in fiber optics. If glass is used as the exterior fluid and the interior is either left hollow or filled with a material with a different index of refraction, one can create optical waveguides whose properties can be varied in a flexible way by changing the composition of the two fluids and by changing the dimensions of the fiber. In other contexts, if a polymer solution or melt is used as the exterior fluid and then solidified, the resultant tubes may be used in membrane filters, capillaries for chromatography as well as bioreactors and as cylindrical microfluidic channels. Compound fibers comprised of an inner metal core and an outer insulator sheath may be used as cables in microelectronic applications. The outer sheath may also be a metal. Possible applications for a metal structure comprised of one or more tubes include: (i) heat exchangers for biology, biomedicine, and cardiovascular applications; (ii) surgical devices; (iii) scientific & laboratory optical or microfluidic instruments; and (iv) reactors for chemical reactions. Other possible materials that may be used include polymers such as polysaccharides and polypeptides.
A method and system are provided in order to create stable and/or acceptable bubbles or filaments. One way to create filaments is to produce an extensional flow, such as by entraining a fluid within another fluid. For example, fluid that is more viscous than the fluid being entrained may flow from a nozzle. The combination of the entrained fluid and the outer fluid may be used to create hollow cylinders (for example, by entraining a gas within a fluid) or compound fibers on micron and sub-micron scales. As discussed herein, fluid may comprise a liquid, a gas, or a combination of a liquid and a gas.
As discussed in the background, the ability to create stable and/or acceptable bubbles or filaments depends, at least in part, on the forces at the interface between the multiple fluids. As discussed below, a model is created to analyze the interface between fluids. The model may be used in order to adjust the system (including dynamically adjusting the system) in order to create bubbles or filaments. For example, creating a filament by entraining a fluid within another fluid may be achieved by applying a force to the fluids (including the inner fluid or the outer fluid). The model, discussed below, may be used to determine the forces to entrain the fluid.
The force may be applied directly or indirectly to the fluids in order to produce an extensional flow. There are several examples of a direct force that may be applied to a fluid. Where the fluid is in a tank or a reservoir, pressure may be applied so that the fluid is forced from a nozzle connected to the tank or reservoir. Where the fluid is conductive, a voltage may be applied so that the electric field generated from the voltage applies a force to the conductive fluid. Co-electrospinning is an example of using a voltage to apply a force to the fluid. Further, a combination of direct forces, such as applying pressure and co-electrospinning, may be used to apply a direct force to a fluid.
One or more of the fluids may also be subject to an indirect force. As one example, the inner fluid may be entrained, not by any force applied directly to it (such as applying pressure to the inner fluid or co-electrospinning of the inner fluid), but by proximity of the inner fluid to movement of another fluid (such as movement of an outer fluid). The movement of the outer fluid may be caused by a direct force (such as by applying pressure to the outer fluid or co-electrospinning), or may be caused by an indirect force applied to it as well. In effect, the inner fluid is dragged along or withdrawn by the outer fluid, rather than pushed along.
Further, a fluid may be subject to multiple direct or indirect forces. For example, a fluid may be subject to the multiple direct forces of pressure and co-electrospinning. As another example, the fluid may be subject to an indirect dragging force (such as caused by an outer fluid dragging an inner fluid) and may be subject to a direct force (such as pressure applied to tank supplying the inner fluid). In the case of multiple direct and indirect forces, one may compare the amount of each of the forces. A fluid that has a greater indirect force may be considered to have a greater dragging force than pushing force. Similarly, a fluid that has a greater direct force may be considered to have a greater pushing force than dragging force.
Referring to
A model may be derived for the interaction of the flowing fluids. Referring to
The liquid filament 1 and co-flowing liquid 2 may have liquid viscosities μ1,2 and densities ρ1,2 cylindrical coordinates r, z. In analyzing the spatio-temporal stability depicted in
With these assumptions, the system response may be analyzed for small perturbations proportional to ei(kz−Ωt). In analyzing the dispersion relation for a viscous liquid cylinder in an immiscible viscous ambient liquid, as depicted in
Re=ρ1VRjμ1−1, We=ρ1V2Rjσ−1, α=ρ2/ρ1, β=μ2/μ1 (1)
The conservation equations of mass and momentum of the liquid flow, together with the boundary conditions at the jet surface (including normal and tangential stress balance) and at infinity, lead to the dispersion relation between the perturbation wave frequency Ω and its wavenumber k. Thus, a dimensionless dispersion relation S({circumflex over (ω)}, x; Re, We, α,β)=0 (with {circumflex over (ω)}=RjΩV−1 and x=Rjk) may be simplified with the aid of a mathematical tool, such as Mathematica V5.01, by introducing a speed V of the two fluids into:
where “viscous” wave numbers are defined for both liquids as:
y12=x2−iRe{circumflex over (ω)}, y22=x2−iαβ−1Re{circumflex over (ω)}, (3)
and functions N and M are expressed as:
N≡2xβy1y2[K0(y2)I1(y1)y1+I0(y1)K1(y2)y2]+x[x2(β−1)−y12+βy22]2I0(x)I1(y1)K0(x)K1(y2)+4x3y1y2(β−1)2I0(y1)I1(x)K0(y2)K1(x)−−y2I1(y1)K0(y2){[x4+y12y22+x2(y12−y22)]βI1](x)+[y14+x4(1−2β)2−2x2y12(β−1)]I0(x)K1(x)}+y1I0(y1)K1(y2){[x4(β−2)2+2x2y22β(β−1)+β2y24]I1(x)K0(x)+[x2(x2−y12)+y22(x2+y12)]βI0(x)K1(x)} (4)
M≡x{[y2K0(y2)K1(x)−xK0(x)K1(y2)](y12−x2)I1(x)I1(y1)+β[y1I0(y1)I1(x)−xI0(x)I1(y1)](y22−x2)K1(x)K1(y2)} (5)
Here, I0, I1, K0, and K1 stand for the modified Bessel functions of order 0 and 1. Further, the limit α→0, β→0 yields:
This leads to the liquid-vacuum dispersion relation of:
One may also use a spectral numerical code developed for the stability analysis of swirling flows in pipes. Here, the linearized equations may be discretized in the r-direction using Chebyshev spectral collocation points (ni points for the inner fluid and ne points for the outer one). For a given wave frequency Ω, one may linearize the non-linear (quadratic) eigenvalue problem for the wave number x using a linear companion matrix method. The resulting linear eigenvalue problem may be solved numerically with the help of an eigenvalue solver subroutine (DGVCCG from the IMSL library) which provides the entire spectrum of eigenvalues and eigenfunctions. Spurious eigenvalues may be excluded by comparing the computed spectra obtained for different values of the number of collocation points. The use of the numerical procedures allows: (i) to check that both techniques render the same results, and (ii) to use the numerical spectral technique in further studies to investigate the influence of other parameters, such as the existence of other basic velocity profiles or the case of a bounded liquid flow, which are not considered in this work.
Based on the preceding, one may determine several things. First, to change the reference system from a traveling observer to a fixed observer anchored at the nozzle, one simply needs to replace the wave frequency Ω=VRj−1{circumflex over (ω)} by Ω′=VRj−1(ω−x) in the dispersion relation. The new ω is the dimensionless wave frequency for the static observer. This may be proved by retaining the linearized convective terms Vuz and VRz in the momentum equation and the kinematic condition at the interface, respectively. In a fixed coordinate system, y1 and y2 are:
y1=±[x2−iRe(ω−x)]1/2, y2=±[x2−iαβ−1Re(ω−x)]1/2 (8)
Second, both roots of the viscous wave numbers y1 and y2 may be explored to encompass all potential sources of spatio-temporal instability. The theoretical frame supporting the results does not require such a precaution. The dispersion model may be symmetric with respect to y1, so that identical {(ω, x} pairs may result, regardless of which root ±y is chosen. This may not be the case with y2, whose positive and negative roots may yield completely different results, implying different wave solution pairs {ω, x}.
Third, consistent with the spatial-temporal stability analysis, both ω and x may be considered to be complex variables. Therefore, ω=ωr+iωi and x=xr+i xi, {ωr, ωi,xr,xi} being real numbers (“oscillation frequency”, “local growth rate”, “wave number” and “spatial growth rate”, respectively). Following the well established spatial-temporal formalism to describe the absolute/convective character of axisymmetric instabilities in the {Re, We, α, β} parametrical space of our problem, solutions of dω/dx=0 in the dispersion relation (2) with non-zero imaginary parts of ω and x. The system may be defined to be absolutely unstable if dω/dx=0 for Im(x)<0, and Im(ω)>0. One may specially care to choose all solutions whose spatial branches departing from the saddle point dω/dx=0 originate from distinct halves of the x-plane, i.e., the only ones providing the absolute instability growth rate.
A specific application of the above formulation may be applied in the low Reynolds regime (discussed with regard to
To create a stable entrained inner cylinder, the innermost fluid may be less viscous than the entraining fluid, the two fluids may be immiscible, and both may have finite surface tension. Given any two such fluids, if the flow rates and reservoir pressures are controlled to satisfy the continuous portion of the phase diagram of
Either the spout or the entraining fluid or both may be an emulsion or a dispersion, if the concentration of the droplets or particles is kept sufficiently dilute to maintain Newtonian rheological properties. For example, carbon black may be incorporated into the sheath to provide antistatic properties. In contrast to existing techniques, e.g. chemical synthesis or co-electrospinning, in one aspect of the invention, the process may rely only on the fluid mechanics for the entrainment; therefore, it may be robust and may function for a wide variety of materials. For co-electrospinning, which also partially relies on a mechanical process, to be successful the fluid pair used may satisfy certain conditions on their viscosities, densities and electric conductivities. In one aspect, the process may have the interior fluid be less viscous than the exterior fluid. Alternatively, in another aspect, the process may rely exclusively on chemical synthesis or co-electrospinning, or may rely on a combination of chemical synthesis, co-electrospinning and/or fluid mechanics.
With the same configuration but working in a different range of flow rates, one can allow the compound liquid cylinder to breakup into micron and submicron-sized compound liquid droplets or bubbles. Again, because such droplets may be prepared of a size comparable to the wavelength of light, they may have unique optical properties and may have potential applications, such as in the creation of an optical Bragg switch. Such compound drops may also have applications in controlled drug delivery, catalysis, and in various cosmetic and food applications which involve emulsions.
Referring to
Referring to
Referring to
Analyzing the dispersion model, one may investigate the stability, and the type (absolute vs. convective) of the instabilities that lead to break-up of hollow capillary jets in a co-flowing unbounded liquid medium. This analysis may be over a wide range (such as six orders of magnitude) of both Reynolds and Weber (We) numbers. In contrast to what occurs with liquid jets, hollow jets in unbounded co-flowing liquids may be absolutely unstable, leading to local bubbling for all values of the Reynolds and Weber numbers of the co-flowing liquid. The presence of a gas (or any other fluid with finite viscosity) inside the jet may elicit a transition from the absolute to convective character of the instability for a finite {Re, We} pair. This transition may correspond to the bubbling-jetting crisis similar to the dripping-jetting transition for capillary liquid jets. Experiments analyzing previously collected data and discussed below support these conclusions, which delimit the parametrical realm of micro-bubbling in unbounded co-flowing liquids.
The dispersion model may be analyzed in several ways. The dispersion model may be easily reduced to a limit by setting β=0. At this limit, there may be a single wave solution, absolutely unstable, for both positive and negative roots of y12 Traveling away from this limit solution, under fixed Re and α (e.g. Re=11.2; α=1), β may be changed to evaluate the jetting-dripping transition loci. Referring to
Steady micro-jetting may give rise to greater productivity (larger liquid flow rates), with a well controlled and small drop size. On the contrary, dripping may give rise to much larger, isolated droplets under similar Re and We. Dripping usually yields highly monodisperse spray, but it may also exhibit bi-disperse or polydisperse droplet distributions. Here, such non-linear complex dynamics may arise whenever a given parametrical instance {Re,We,α,β} leads to more than one absolutely unstable wave solutions and these solutions exhibit similar local growth rate ωi but different local oscillation frequency ωr.
Another analysis of the dispersion model comprises the solution for each combination of {Re,We,α,β} with the largest temporal growth rate Im(ω)>0, i.e. the one that dominates the break-up dynamics.
Circles in
One result of the analysis is that in the limit of vanishing viscosity and density of the inner fluid (α,β→∞), the jet may be absolutely unstable for any combination of values of the Reynolds and Weber numbers. When the viscosity and density of the inner fluid are small but finite, for any value of the Reynolds number (either low or high) there may be a finite value of the Weber number at which the transition from an absolute to a convective character of the instability takes place.
The dispersion model may be generated analytically, such as by using the formulas shown above. Or, it may be generated numerically, such as by analyzing experimental data. The dispersion model developed analytically was compared with experimental results. A stainless steel fluid focusing device with dimensions D=D1=150 μm, L=160 μm, and H=125 μm is used. The inner edge of the orifice has been rounded to minimize vena contracta effects. The ambient focusing fluid is distilled water at T=23° C. (ρ2=995 kg·m−1, μ2=0.001 Pa·s). Three silicone oils with nominal Newtonian viscosities μ1 equal to 0.005, 0.02 and 0.1 Pa·s and measured oil-water surface tensions ρ=33.2, 30.4, and 28 mN/m at T=23° C. are used as the jet-forming liquid. The oil densities are ρ1=965±0.2% kg·m−1. Surfactants need not be used. Thus, the study explores three values β=0.2, 0.05, and 0.01, with α=1.033.
To compare the experiments with the theory, the diameter of the unperturbed jet radius at the orifice exit is estimated by assuming both liquids to issue at an approximately uniform velocity V=4(Q1+Q2)/(πD2), Q1 and Q2 being the oil and water flow rates (Re2 ranges from 262 to 1362): Rj˜(D/2)(Q1/Q1+Q2))1/2. Knowing Rj and Re, We can be calculated. There are dispersed five oil flow rates Q1=2, 5, 10, 25, 50, and 100 ml/h, using a syringe pump Harvard Apparatus mod. 4455 with B-D 1 cc plastic syringes (Q1=1 and 2 ml/h), 5 cc (Q1=10 ml/h) and 20 cc (Q1=25 and 50 ml/h). Two water flow rates Q2=1.82 and 5.16 ml/min (±0.5%) were supplied, using a pressurized 300 cc water reservoir.
Therefore, the experiments depicted in
In spite of experimental difficulties, the model provides an acceptable fit of the jetting-dripping transition data as illustrated by the pictures in
Additional comparison of results is shown in
One conclusion from this analysis is that a cylindrical gas spout in a high viscosity liquid moving with speed Vmay be absolutely unstable, and may prevent the formation of long gas spouts, below a finite value of the Weber number or, alternatively, below a finite value of the Capillary number Ca=We/Re. Thus, the solution for gas spouts entrained in extensional viscous flows discussed in regard to
In those experiments, to provide a flow as close as possible to the true extensional one, the liquid stream is surrounded by another gas stream in order to avoid the liquid contact with the exit orifice wall. This is not a true unbounded liquid flow, but the diameter of the spout is small in comparison to the outer diameter of the liquid-jet, and the results illustrate well our findings. The influence on the ratio dl/dg of the outer diameter of the liquid-jet to the diameter of the gaseous jet is verified using an alternative spectral collocation code. For dl/dg=100, the differences in the critical Weber numbers with those of unbounded liquid were less than 3% for large Reynolds numbers, while the differences were less than 1% for small Reynolds numbers.
The model may be applied in a variety of instances. For example, a hollow optical fiber with a cylindrical hole may only be drawn if the Weber number is above the critical one, or if there is an alternative mechanism providing local stability. This mechanism may be a longitudinal positive gradient of viscosity (e.g., the one due to “fiber quenching”, when the glass solidifies) or an external negative pressure gradient (a potential alternative in ultra-high speed fiber drawing).
The model may also be applied in other configurations, such as that shown in
This methodology enables creating compound fibers wherein the inner diameter can be made far smaller than the outer diameter of the fiber. The disparity in the interior and exterior diameters has at least two useful consequences. First, by placing a group of nozzles in close proximity, the entrainment process can be used to create a single fiber containing multiple interior cylinders which are either hollow or made of a second material (
It is therefore intended that the foregoing detailed description be regarded as illustrative rather than limiting, and that it be understood that it is the following claims, including all equivalents, that are intended to define the spirit and scope of this invention. Other variations may be readily substituted and combined to achieve particular design goals or accommodate particular materials or manufacturing processes.
Claims
1. A filament being produced by:
- entraining a first fluid within a second fluid by flowing a third fluid, the flowing third fluid at least partly constraining the second fluid in at least one dimension.
2. The filament of claim 1, further comprising solidifying at least a part of the second fluid to form a fiber.
3. The filament of claim 2, further comprising solidifying at least a part of the first fluid to form the fiber.
4. The filament of claim 1, wherein entraining a first fluid within a second fluid is based only on fluid properties of the first fluid and the second fluid
5. The filament of claim 4, wherein the fluid properties are viscosity of the first fluid and the second fluid; and
- wherein the second fluid is more viscous than the first fluid.
6. The filament of claim 1, wherein the first fluid comprises a liquid or a gas that is immiscible with the second fluid.
7. The filament of claim 1, wherein a plurality of fluids are entrained within the second fluid.
8. The filament of claim 7, wherein the third fluid flows at least partly by co-electrospinning.
9. The filament of claim 7, wherein the third fluid flows at least partly by pressure applied to the third fluid.
10. The filament of claim 7, wherein the second fluid is axisymmetrically constrained by the flowing of the third fluid to surround the second fluid.
11. The filament of claim 7, wherein the first fluid flows from a first nozzle and the second fluid flows from a second nozzle; and
- wherein the first nozzle is concentric with the second nozzle.
12. The filament of claim 7, wherein the second fluid flows to entrain the first fluid; and
- wherein the flow of the second fluid is due more to drawing of the second fluid by the flowing of the third fluid than to pressure applied to the second fluid.
13. The filament of claim 12, wherein the entraining of the first fluid within the second fluid is due more to drawing of the first fluid by the flowing of the second fluid than to pressure applied to the first fluid.
14. A filament being produced by:
- entraining a first fluid within a second fluid based on a model of a dynamic response of the first and second fluids as functions of densities of the first and second fluids, viscosities of the first and second fluids, Reynolds numbers of the first and second fluids, and Weber numbers of the first and second fluids.
15. The filament of claim 14, wherein the model of the dynamic response defines a phase space of a stable entraining of the first fluid within the second fluid; and
- wherein values of the Reynolds numbers of the first and second fluid and Weber numbers of the first and second fluid are selected to be in the phase space of the stable entraining of the first fluid within the second fluid.
16. The filament of claim 15, wherein the entraining of the first fluid within the second fluid is performed by a system that controls velocity of the first fluid and second fluid; and
- wherein the velocity of the first fluid and the second fluid are selected such that the model is in the phase space of the stable entraining of the first fluid within the second fluid.
17. The filament of claim 15, wherein the model is derived numerically.
18. The filament of claim 15, wherein the model is derived analytically.
19. The filament of claim 18, wherein the model is a function of:
- the ratio of the densities of the first and second fluid,
- the ratio of the viscosities of the first and second fluid,
- the Reynolds number of the first fluid
- Re1=ρ1VR1/μ1
- with ρ1 being the density of the first fluid, μ1 being the viscosity of the first fluid, R1 being the radius of a cylindrical jet through which the first fluid flows, and Vbeing the uniform velocity of the first and second fluids relative to an observer,
- the Reynolds number of the second fluid
- Re2=ρ2VR2/μ2
- with ρ2 being the density of the first fluid, μ2 being the viscosity of the first fluid, and R2 being the radius of a cylindrical jet through which the second fluid flows,
- the Weber number of the first fluid
- We1=ρ1V2R1/σ
- where σ being the surface tension, and
- the Weber number of the second fluid
- We2=ρ2V2R2/σ.
20 The filament of claim 14, further comprising solidifying at least a part of the second fluid to form a fiber.
21. The filament of claim 14, wherein operating conditions are selected in order to be in a specific phase space within the model so that the flow of the first fluid is continuous for a predetermined time.
22. The filament of claim 21, wherein the operating condition comprises pressure; and
- wherein the pressure to at least one of the first and second fluids is dynamically adjusted to maintain a shape of an interface between the first fluid and the second fluid for the predetermined time.
Type: Application
Filed: Jan 27, 2006
Publication Date: Oct 19, 2006
Inventors: Wendy Zhang (Chicago, IL), Eric Ginsburg (Chicago, IL), Alfonso Calvo (Seville), Jose Lopez-Herrera (Seville), Pascual Riesco-Chueca (Seville), Miguel-Angel Herrada-Gutierrez (Seville), Piotr Garstecki (Warsaw)
Application Number: 11/341,096
International Classification: D02G 3/00 (20060101);