Patent Publication Number: US-2023137355-A1

Title: Methods and apparatus for manufacturing a glass ribbon

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit of priority under 35 U.S.C. § 119 of U.S. Provisional Application Ser. No. 63/019,540 filed on May 4, 2020, the content of which is relied upon and incorporated herein by reference in its entirety. 
    
    
     FIELD 
     The present disclosure relates generally to methods for manufacturing a glass ribbon and, more particularly, to methods for manufacturing a glass ribbon with a glass manufacturing apparatus comprising a cooling tube. 
     BACKGROUND 
     Glass ribbons are commonly used, for example, in display applications, such as, liquid crystal displays (LCDs), electrophoretic displays (EPDs), organic light emitting diode displays (OLEDs), plasma display panels (PDPs), touch sensors, photovoltaics, or the like. Such displays can be incorporated, for example, into mobile phones, tablets, laptops, watches, wearables and/or touch capable monitors or displays. Glass ribbons are commonly fabricated by flowing molten glass to a forming body whereby a glass web may be formed by a variety of ribbon forming processes, for example, slot draw, float, down-draw, fusion down-draw, rolling, tube drawing, or up-draw. The glass ribbon may be periodically separated into individual glass ribbons. The thickness of a ribbon of glass-forming material can be controlled before the ribbon of glass-forming material cools into a glass ribbon. However, there is a need for methods of manufacturing a glass ribbon that can more effectively and quickly cool a ribbon of glass-forming material. 
     SUMMARY 
     The following presents a simplified summary of the disclosure to provide a basic understanding of some embodiments described in the detailed description. 
     In some embodiments, a glass manufacturing apparatus can comprise a cooling tube comprising a first tube positioned within a second tube. A first cooling fluid can flow through the first tube and may exit the first tube toward a ribbon of glass-forming material. In some embodiments, a portion of the first cooling fluid may undergo a phase change from a solid or liquid to a gas within the first tube. In addition, or in the alternative, in some embodiments, upon exiting the first tube, another portion of the first cooling fluid may undergo a phase change from a solid or liquid to a gas. The phase change can cause a reduction in temperature of the ribbon of glass-forming material. Due to the elevated temperature (e.g., within a range from about 400° Celsius (“C”) to about 1000° C.) that the cooling tube is exposed to, and to limit the phase change from occurring within the first tube and prior to the first cooling fluid&#39;s exit from the first tube as a result of the elevated temperature, a second cooling fluid can flow through the second tube. The second cooling fluid can impinge upon the first tube. The second cooling fluid can be maintained at a temperature that is lower than a temperature of a surrounding environment. As such, the second cooling fluid can thermally shield the first tube from the surrounding environment and, thus, control a location at which the first cooling fluid undergoes the phase change. 
     In accordance with some embodiments, a glass manufacturing apparatus can comprise a forming apparatus defining a travel path extending in a travel direction. The forming apparatus can convey a ribbon of glass-forming material along the travel path in the travel direction. The glass manufacturing apparatus can comprise a cooling tube comprising a first end and a second end opposite the first end. The second end can be positioned adjacent to the travel path. The cooling tube can comprise a first tube comprising a closed first sidewall surrounding a first channel. The first tube can receive a first cooling fluid within the first channel. The cooling tube can comprise a second tube comprising a closed second sidewall surrounding a second channel. The first tube can be positioned within the second tube such that the second channel may be between the closed first sidewall and the closed second sidewall. The second tube can receive a second cooling fluid within the second channel. The cooling tube can comprise a nozzle attached to the first tube. The nozzle can comprise a nozzle cavity that may be in fluid communication with the first channel. The nozzle can receive the first cooling fluid and direct the first cooling fluid toward the travel path. 
     In some embodiments, the first tube can comprise a first cross-sectional size at a first location between the first end and the second end, and a second cross-sectional size at a second location adjacent to the second end. The first cross-sectional size can be different than the second cross-sectional size. 
     In some embodiments, the first cross-sectional size can be greater than the second cross-sectional size. 
     In some embodiments, the first tube and the second tube may be coaxial and extend along a longitudinal axis. 
     In some embodiments, an axis that may be orthogonal to the longitudinal axis can intersect the closed first sidewall and the closed second sidewall. 
     In some embodiments, the closed first sidewall can isolate the first channel from the second channel. 
     In accordance with some embodiments, methods of manufacturing a glass ribbon can comprise forming a ribbon of glass-forming material. Methods can comprise moving the ribbon of glass-forming material along a travel path in a travel direction. Methods can comprise delivering a first cooling fluid through a first tube toward a nozzle. Methods can comprise cooling the first tube by delivering a second cooling fluid through a second tube that surrounds the first tube such that the second cooling fluid is in convective contact with the first tube. Methods can comprise cooling an area of the ribbon of glass-forming material by directing the first cooling fluid from an end of the first tube and through the nozzle toward the area of the ribbon of glass-forming material. 
     In some embodiments, methods can comprise isolating the first cooling fluid from the second cooling fluid when the second cooling fluid is delivered through the second tube and when the first cooling fluid is directed from the end of the first tube. 
     In some embodiments, the cooling the first tube can comprise thermally shielding the first tube from a surrounding environment by absorbing heat from the surrounding environment with the second cooling fluid. 
     In some embodiments, methods can comprise controlling a phase change of the first cooling fluid within the first tube by accelerating a flow of the first cooling fluid within a first portion of the first tube prior to reaching the end of the first tube. 
     In some embodiments, the accelerating can comprise reducing a cross-sectional size of the first portion of the first tube relative to a flow direction of the first cooling fluid. 
     In some embodiments, the accelerating can comprise enabling a phase change of a portion of the first cooling fluid within the first portion from one or more of a liquid phase or a solid phase to a gas phase. 
     In some embodiments, the cooling the area can comprise changing a phase of the first cooling fluid while the first cooling fluid is flowing toward the area of the ribbon of glass-forming material. 
     In some embodiments, the first cooling fluid comprises carbon dioxide. 
     In accordance with some embodiments, methods of manufacturing a glass ribbon can comprise forming a ribbon of glass-forming material. Methods can comprise moving the ribbon of glass-forming material along a travel path in a travel direction. Methods can comprise delivering a first cooling fluid through a first tube toward a nozzle. Methods can comprise controlling a phase change of the first cooling fluid within the first tube by accelerating a flow of the first cooling fluid within a first portion of the first tube prior to reaching the nozzle. Methods can comprise cooling an area of the ribbon of glass-forming material by directing the first cooling fluid from an end of the first tube and through the nozzle toward the area of the ribbon of glass-forming material. 
     In some embodiments, the accelerating can comprise reducing a cross-sectional size of the first portion of the first tube relative to a flow direction of the first cooling fluid. 
     In some embodiments, the accelerating can comprise enabling a phase change of a portion of the first cooling fluid within the first portion from one or more of a liquid phase or a solid phase to a gas phase. 
     In some embodiments, the cooling the area can comprise changing a phase of the first cooling fluid while the first cooling fluid is flowing toward the area. 
     In some embodiments, the first cooling fluid can comprise carbon dioxide. 
     In some embodiments, methods can comprise extracting the first cooling fluid by suction after the first cooling fluid has been directed from the end of the first tube and through the nozzle. 
     Additional features and advantages of the embodiments disclosed herein will be set forth in the detailed description that follows, and in part will be clear to those skilled in the art from that description or recognized by practicing the embodiments described herein, including the detailed description which follows, the claims, as well as the appended drawings. It is to be understood that both the foregoing general description and the following detailed description present embodiments intended to provide an overview or framework for understanding the nature and character of the embodiments disclosed herein. The accompanying drawings are included to provide further understanding and are incorporated into and constitute a part of this specification. The drawings illustrate various embodiments of the disclosure, and together with the description explain the principles and operations thereof. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       These and other features, embodiments and advantages are better understood when the following detailed description is read with reference to the accompanying drawings, in which: 
         FIG.  1    schematically illustrates example embodiments of a glass manufacturing apparatus in accordance with embodiments of the disclosure; 
         FIG.  2    illustrates a perspective cross-sectional view of the glass manufacturing apparatus along line  2 - 2  of  FIG.  1    in accordance with embodiments of the disclosure; 
         FIG.  3    illustrates a cross-sectional view similar to  FIG.  2    of the glass manufacturing apparatus comprising one or more cooling apparatuses for cooling a ribbon of glass-forming material in accordance with embodiments of the disclosure; 
         FIG.  4    illustrates a cross-sectional view along line  4 - 4  of  FIG.  3    of a first cooling apparatus in accordance with embodiments of the disclosure; 
         FIG.  5    illustrates a cross-sectional view along line  5 - 5  of  FIG.  4    of the first cooling apparatus comprising a first tube and a second tube in accordance with embodiments of the disclosure; 
         FIG.  6    illustrates a cross-sectional view of the first cooling apparatus similar to  FIG.  5    with one or more coolant particles being emitted from the first tube toward the ribbon of glass-forming material in accordance with embodiments of the disclosure; 
         FIG.  7    illustrates a cross-sectional view along line  5 - 5  of  FIG.  4    of additional embodiments of a first cooling apparatus comprising a first tube with a non-constant cross-sectional size in accordance with embodiments of the disclosure; 
         FIG.  8    illustrates a cross-sectional view of the first cooling apparatus similar to  FIG.  7    with one or more coolant particles being emitted from the first tube toward the ribbon of glass-forming material in accordance with embodiments of the disclosure; and 
         FIG.  9    illustrates a cross-sectional view along line  5 - 5  of  FIG.  4    of additional embodiments of a first cooling apparatus comprising a first cooling fluid that cools a first tube in accordance with embodiments of the disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     Embodiments will now be described more fully hereinafter with reference to the accompanying drawings in which example embodiments are shown. Whenever possible, the same reference numerals are used throughout the drawings to refer to the same or like parts. However, this disclosure may be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. 
     The present disclosure relates to a glass manufacturing apparatus and methods for producing a glass ribbon. Methods and apparatus for producing a glass ribbon from a ribbon of glass-forming material will now be described by way of example embodiments. As schematically illustrated in  FIG.  1   , in some embodiments, an exemplary glass manufacturing apparatus  100  can comprise a glass melting and delivery apparatus  102  and a forming apparatus  101  comprising a forming vessel  140  designed to produce a ribbon of glass-forming material  103  from a quantity of molten material  121 . In some embodiments, the ribbon of glass-forming material  103  can comprise a central portion  152  positioned between opposite edge portions (e.g., edge beads) formed along a first outer edge  153  and a second outer edge  155  of the ribbon of glass-forming material  103 , wherein a thickness of the edge portions can be greater than a thickness of the central portion. Additionally, in some embodiments, a separated glass ribbon  104  can be separated from the ribbon of glass-forming material  103  along a separation path  151  by a glass separator  149  (e.g., scribe, score wheel, diamond tip, laser, etc.). 
     In some embodiments, the glass melting and delivery apparatus  102  can comprise a melting vessel  105  oriented to receive batch material  107  from a storage bin  109 . The batch material  107  can be introduced by a batch delivery device  111  powered by a motor  113 . In some embodiments, an optional controller  115  can be operated to activate the motor  113  to introduce a desired amount of batch material  107  into the melting vessel  105 , as indicated by arrow  117 . The melting vessel  105  can heat the batch material  107  to provide molten material  121 . In some embodiments, a melt probe  119  can be employed to measure a level of molten material  121  within a standpipe  123  and communicate the measured information to the controller  115  by way of a communication line  125 . 
     Additionally, in some embodiments, the glass melting and delivery apparatus  102  can comprise a first conditioning station comprising a fining vessel  127  located downstream from the melting vessel  105  and coupled to the melting vessel  105  by way of a first connecting conduit  129 . In some embodiments, molten material  121  can be gravity fed from the melting vessel  105  to the fining vessel  127  by way of the first connecting conduit  129 . For example, in some embodiments, gravity can drive the molten material  121  through an interior pathway of the first connecting conduit  129  from the melting vessel  105  to the fining vessel  127 . Additionally, in some embodiments, bubbles can be removed from the molten material  121  within the fining vessel  127  by various techniques. 
     In some embodiments, the glass melting and delivery apparatus  102  can further comprise a second conditioning station comprising a mixing chamber  131  that can be located downstream from the fining vessel  127 . The mixing chamber  131  can be employed to provide a homogenous composition of molten material  121 , thereby reducing or eliminating inhomogeneity that may otherwise exist within the molten material  121  exiting the fining vessel  127 . As shown, the fining vessel  127  can be coupled to the mixing chamber  131  by way of a second connecting conduit  135 . In some embodiments, molten material  121  can be gravity fed from the fining vessel  127  to the mixing chamber  131  by way of the second connecting conduit  135 . For example, in some embodiments, gravity can drive the molten material  121  through an interior pathway of the second connecting conduit  135  from the fining vessel  127  to the mixing chamber  131 . 
     Additionally, in some embodiments, the glass melting and delivery apparatus  102  can comprise a third conditioning station comprising a delivery chamber  133  that can be located downstream from the mixing chamber  131 . In some embodiments, the delivery chamber  133  can condition the molten material  121  to be fed into an inlet conduit  141 . For example, the delivery chamber  133  can function as an accumulator and/or flow controller to adjust and provide a consistent flow of molten material  121  to the inlet conduit  141 . As shown, the mixing chamber  131  can be coupled to the delivery chamber  133  by way of a third connecting conduit  137 . In some embodiments, molten material  121  can be gravity fed from the mixing chamber  131  to the delivery chamber  133  by way of the third connecting conduit  137 . For example, in some embodiments, gravity can drive the molten material  121  through an interior pathway of the third connecting conduit  137  from the mixing chamber  131  to the delivery chamber  133 . As further illustrated, in some embodiments, a delivery pipe  139  can be positioned to deliver molten material  121  to forming apparatus  101 , for example the inlet conduit  141  of the forming vessel  140 . 
     Forming apparatus  101  can comprise various embodiments of forming vessels in accordance with features of the disclosure, for example, a forming vessel with a wedge for fusion drawing the glass ribbon, a forming vessel with a slot to slot draw the glass ribbon, or a forming vessel provided with press rolls to press roll the glass ribbon from the forming vessel. In some embodiments, the forming apparatus  101  can comprise a sheet redraw, for example, with the forming apparatus  101  as part of a redraw process. For example, the glass ribbon  104 , which can comprise a first thickness, may be heated up and redrawn to achieve a thinner glass ribbon  104  comprising a smaller second thickness. By way of illustration, the forming vessel  140  shown and disclosed below can be provided to fusion draw molten material  121  off a bottom edge, defined as a root  145 , of a forming wedge  209  to produce the ribbon of glass-forming material  103 . For example, in some embodiments, the molten material  121  can be delivered from the inlet conduit  141  to the forming vessel  140 . The molten material  121  can then be formed into the ribbon of glass-forming material  103  based, in part, on the structure of the forming vessel  140 . For example, as shown, the molten material  121  can be drawn off the bottom edge (e.g., root  145 ) of the forming vessel  140  along a draw path extending in a travel direction  154  of the glass manufacturing apparatus  100 . In some embodiments, edge directors  163 ,  164  can direct the molten material  121  off the forming vessel  140  and define, in part, a width “W” of the ribbon of glass-forming material  103 . In some embodiments, the width “W” of the ribbon of glass-forming material  103  extends between the first outer edge  153  of the ribbon of glass-forming material  103  and the second outer edge  155  of the ribbon of glass-forming material  103 . 
     In some embodiments, the width “W” of the ribbon of glass-forming material  103 , which extends between the first outer edge  153  of the ribbon of glass-forming material  103  and the second outer edge  155  of the ribbon of glass-forming material  103 , can be greater than or equal to about 20 millimeters (mm), for example, greater than or equal to about 50 mm, for example, greater than or equal to about 100 mm, for example, greater than or equal to about 500 mm, for example, greater than or equal to about 1000 mm, for example, greater than or equal to about 2000 mm, for example, greater than or equal to about 3000 mm, for example, greater than or equal to about 4000 mm, although other widths less than or greater than the widths mentioned above can be provided in further embodiments. For example, in some embodiments, the width “W” of the ribbon of glass-forming material  103  can be within a range from about 20 mm to about 4000 mm, for example, within a range from about 50 mm to about 4000 mm, for example, within a range from about 100 mm to about 4000 mm, for example, within a range from about 500 mm to about 4000 mm, for example, within a range from about 1000 mm to about 4000 mm, for example, within a range from about 2000 mm to about 4000 mm, for example, within a range from about 3000 mm to about 4000 mm, for example, within a range from about 20 mm to about 3000 mm, for example, within a range from about 50 mm to about 3000 mm, for example, within a range from about 100 mm to about 3000 mm, for example, within a range from about 500 mm to about 3000 mm, for example, within a range from about 1000 mm to about 3000 mm, for example, within a range from about 2000 mm to about 3000 mm, for example, within a range from about 2000 mm to about 2500 mm, and all ranges and subranges therebetween. 
       FIG.  2    shows a cross-sectional perspective view of the forming apparatus  101  (e.g., forming vessel  140 ) along line  2 - 2  of  FIG.  1   . In some embodiments, the forming vessel  140  can comprise a trough  201  oriented to receive the molten material  121  from the inlet conduit  141 . For illustrative purposes, cross-hatching of the molten material  121  is removed from  FIG.  2    for clarity. The forming vessel  140  can further comprise the forming wedge  209  comprising a pair of downwardly inclined converging surface portions  207 ,  208  extending between opposed ends  210 ,  211  (See  FIG.  1   ) of the forming wedge  209 . The pair of downwardly inclined converging surface portions  207 ,  208  of the forming wedge  209  can converge along the travel direction  154  to intersect along the root  145  of the forming vessel  140 . A draw plane  213  of the glass manufacturing apparatus  100  can extend through the root  145  along the travel direction  154 . In some embodiments, the ribbon of glass-forming material  103  can be drawn in the travel direction  154  along the draw plane  213 . As shown, the draw plane  213  can bisect the forming wedge  209  through the root  145  although, in some embodiments, the draw plane  213  can extend at other orientations relative to the root  145 . In some embodiments, the ribbon of glass-forming material  103  can move along a travel path  221  that may be co-planar with the draw plane  213  in the travel direction  154 . 
     Additionally, in some embodiments, the molten material  121  can flow in a direction  156  into and along the trough  201  of the forming vessel  140 . The molten material  121  can then overflow from the trough  201  by flowing over corresponding weirs  203 ,  204  and downward over the outer surfaces  205 ,  206  of the corresponding weirs  203 ,  204 . Respective streams of molten material  121  can then flow along the downwardly inclined converging surface portions  207 ,  208  of the forming wedge  209  and be drawn off the root  145  of the forming vessel  140 , where the flows converge and fuse into the ribbon of glass-forming material  103 . The ribbon of glass-forming material  103  can then be drawn along the travel direction  154 . In some embodiments, the ribbon of glass-forming material  103  comprises one or more states of material based on a vertical location of the ribbon of glass-forming material  103 . For example, at a first location, the ribbon of glass-forming material  103  can comprise the viscous molten material  121 , and at a second location, the ribbon of glass-forming material  103  can comprise an amorphous solid in a glassy state (e.g., a glass ribbon). 
     The ribbon of glass-forming material  103  comprises a first major surface  215  and a second major surface  216  facing opposite directions and defining a thickness “T” (e.g, average thickness) of the ribbon of glass-forming material  103  therebetween. In some embodiments, the thickness “T’ of the ribbon of glass-forming material  103  can be less than or equal to about 2 millimeters (mm), less than or equal to about 1 millimeter, less than or equal to about 0.5 millimeters, for example, less than or equal to about 300 micrometers (μm), less than or equal to about 200 micrometers, or less than or equal to about 100 micrometers, although other thicknesses may be provided in further embodiments. For example, in some embodiments, the thickness “T’ of the ribbon of glass-forming material  103  can be within a range from about 20 micrometers to about 200 micrometers, within a range from about 50 micrometers to about 750 micrometers, within a range from about 100 micrometers to about 700 micrometers, within a range from about 200 micrometers to about 600 micrometers, within a range from about 300 micrometers to about 500 micrometers, within a range from about 50 micrometers to about 500 micrometers, within a range from about 50 micrometers to about 700 micrometers, within a range from about 50 micrometers to about 600 micrometers, within a range from about 50 micrometers to about 500 micrometers, within a range from about 50 micrometers to about 400 micrometers, within a range from about 50 micrometers to about 300 micrometers, within a range from about 50 micrometers to about 200 micrometers, within a range from about 50 micrometers to about 100 micrometers, within a range from about 25 micrometers to about 125 micrometers, comprising all ranges and subranges of thicknesses therebetween. In addition, the ribbon of glass-forming material  103  can comprise a variety of compositions, for example, borosilicate glass, alumino-borosilicate glass, alkali-containing glass, or alkali-free glass, alkali aluminosilicate glass, alkaline earth aluminosilicate glass, soda-lime glass, etc. 
     In some embodiments, the glass separator  149  (see  FIG.  1   ) can separate the glass ribbon  104  from the ribbon of glass-forming material  103  along the separation path  151  to provide a plurality of separated glass ribbons  104  (i.e., a plurality of sheets of glass). According to other embodiments, a longer portion of the glass ribbon  104  may be coiled onto a storage roll. The separated glass ribbon can then be processed into a desired application, e.g, a display application. For example, the separated glass ribbon can be used in a wide range of display applications, comprising liquid crystal displays (LCDs), electrophoretic displays (EPD), organic light emitting diode displays (OLEDs), plasma display panels (PDPs), touch sensors, photovoltaics, and other electronic displays. 
       FIG.  3    illustrates a cross-sectional perspective view of the glass manufacturing apparatus  100  similar to  FIG.  2   . In some embodiments, the glass manufacturing apparatus  100  is not limited to comprising the forming wedge  209 . Rather, in some embodiments, although not shown, the forming vessel  140  can comprise a pipe oriented to receive the molten material  121  from the inlet conduit  141  (e.g., the inlet conduit  141  illustrated in  FIG.  1   ). In some embodiments, the pipe can comprise a slot through which the molten material  121  can flow. For example, the slot can comprise an elongated slot that extends along an axis of the pipe at the top of the pipe. In some embodiments, a first wall can be attached to the pipe at a first peripheral location and a second wall can be attached to the pipe at a second peripheral location. The first wall and the second wall can comprise a pair of downwardly inclined converging surface portions. The first wall and the second wall can also at least partially define a hollow region within the forming vessel. In some embodiments, a pipe wall comprising the pipe, the first wall, and/or the second wall can comprise a thickness in a range from about 0.5 mm to about 10 mm, from about 0.5 mm to about 7 mm, from about 0.5 mm to about 3 mm, from about 1 mm to about 10 mm, from about 1 mm to about 7 mm, from about 3 mm to about 10 mm, from about 3 mm to about 7 mm, or any range or subrange therebetween. A thickness in the above range can result in overall reduced material costs compared to embodiments comprising thicker walls. 
     As illustrated in  FIG.  3   , the glass manufacturing apparatus  100  can comprise one or more cooling apparatuses  301  for cooling an area of the ribbon of glass-forming material  103 . For example, in some embodiments, the one or more cooling apparatuses  301  can comprise a first cooling apparatus  303 , a second cooling apparatus  305 , etc. The first cooling apparatus  303  can be positioned on a first side of the draw plane  213 , and the second cooling apparatus  305  can be positioned on a second side of the draw plane  213 . The draw plane  213  (e.g., and, thus, the ribbon of glass-forming material  103 ) can therefore extend between the first cooling apparatus  303  and the second cooling apparatus  305 . Although two cooling apparatuses are shown, the one or more cooling apparatuses  301  can comprise additional cooling apparatuses, for example, with cooling apparatuses located upstream or downstream from the first cooling apparatus  303  and/or the second cooling apparatus  305  relative to the travel direction  154 . In some embodiments, the first cooling apparatus  303  and the second cooling apparatus  305  may be substantially identical. As such, the description herein of the structure and function of the first cooling apparatus  303  is applicable to the second cooling apparatus  305  and other cooling apparatuses. 
     With reference to the first cooling apparatus  303 , the first cooling apparatus  303  can comprise a cooling tube  307  that can comprise a first end  319  and a second end  321 , wherein the second end  321  may be opposite the first end  319 . In some embodiments, the second end  321  may be positioned adjacent to the travel path  221 . For example, by being positioned adjacent to the travel path  221 , the second end  321  may be closer in proximity to the travel path  221  than the first end  319  is in proximity to the travel path  221 , such that the first cooling apparatus  303  can emit a cooling fluid (e.g., coolant particles  315  that undergo a phase change into a gas  322 ) toward the ribbon of glass-forming material  103  to cause cooling of an area  325  of the ribbon of glass-forming material  103 . For example, with the second end  321  adjacent to the travel path  221 , the coolant particles  315  can be emitted from the second end  321 , whereupon the coolant particles  315  may undergo a phase change (e.g., from a solid or a liquid) into the gas  322  as a result of the elevated temperature near the travel path  221 . The phase change can cause the area  325  to cool. In some embodiments, the cooling tube  307  can be in fluid communication with a coolant source  309 , such that the cooling tube  307  can receive a cooling fluid from the coolant source  309 . For example, the coolant source  309  can comprise a pump, a canister, a cartridge, a boiler, a compressor, and/or a pressure vessel. In some embodiments, the coolant source  309  may store the cooling fluid in one or more of a gas phase, a liquid phase, or a solid phase. 
     In some embodiments, the cooling tube  307  can comprise a nozzle  311 . The nozzle  311  can be attached to and/or in fluid communication with the second end  321 . The nozzle  311  can receive the cooling fluid from the second end  321 , whereupon the cooling fluid can exit an outlet  313  of the nozzle  311 . In some embodiments, the cooling fluid can exit the outlet  313  and can flow in a flow direction  323  along a central axis  317  toward the draw plane  213  (e.g., and, thus, the ribbon of glass-forming material  103 ). The central axis  317  can intersect the nozzle  311  and the travel path  221 . For example, in some embodiments, the central axis  317  may be substantially perpendicular to the travel path  221 . However, in some embodiments, the central axis  317  may not be perpendicular to the travel path  221 , and may form an angle relative to the travel path  221  that is greater than or less than 90 degrees. In some embodiments, the cooling fluid may comprise one or more coolant particles  315  as the cooling fluid exits the outlet  313 . In some embodiments, the one or more coolant particles  315  can comprise liquid and/or solid particles. The one or more coolant particles  315  can undergo a phase change, such as to the gas  322 , after the cooling fluid has exited the outlet  313  and as the one or more coolant particles  315  travel in the flow direction  323  along the central axis  317 . In some embodiments, the first cooling apparatus  303  can reduce a temperature of the ribbon of glass-forming material  103  at the area  325 , and the second cooling apparatus  305  can reduce a temperature of the ribbon of glass-forming material  103  at an area  327 . 
     In some embodiments, methods of manufacturing a glass ribbon can comprise forming the ribbon of glass-forming material  103  and moving the ribbon of glass-forming material  103  along the travel path  221  in the travel direction  154 . For example, the ribbon of glass-forming material  103  can be formed by overflowing the molten material  121  (e.g., illustrated in  FIG.  1   ) from the trough  201  by flowing over the weirs  203 ,  204  and downward over the outer surfaces  205 ,  206 . In some embodiments, the ribbon of glass-forming material  103  can move downwardly in the travel direction  154  along the travel path  221 . As the ribbon of glass-forming material  103  moves along the travel path  221 , the ribbon of glass-forming material  103  can move past the first cooling apparatus  303  and the second cooling apparatus  305 . The first cooling apparatus  303  and the second cooling apparatus  305  may be adjacent to the ribbon of glass-forming material  103 , such that as the ribbon of glass-forming material  103  moves in the travel direction  154 , one or more portions of the ribbon of glass-forming material  103  may be cooled by the first cooling apparatus  303  and/or the second cooling apparatus  305 . 
       FIG.  4    illustrates a sectional view of the cooling tube  307  of the first cooling apparatus  303  along line  4 - 4  of  FIG.  3   .  FIG.  5    illustrates a sectional view of the cooling tube  307  of the first cooling apparatus  303  along line  5 - 5  of  FIG.  4   . Referring to  FIGS.  4 - 5   , the cooling tube  307  can comprise a first tube  401 . The first tube  401  can comprise a closed first sidewall  403  that surrounds a first channel  405 . In some embodiments, the first tube  401  can receive a first cooling fluid  407  (e.g., from the coolant source  309  illustrated in  FIG.  3   ) within the first channel  405 . By being closed, the closed first sidewall  403  may be free of openings, orifices, voids, vents, or the like, such that the first cooling fluid  407  may be prevented from exiting the first channel  405  by passing through the closed first sidewall  403 . In some embodiments, the closed first sidewall  403  may define a hollow interior that can form the first channel  405 . 
     The first tube  401  can extend between a first end  411  and a second end  413 . The first end  411  may be in attachment with and/or in fluid communication with the coolant source  309  of  FIG.  3   . The second end  413 , which may be located at an opposite end of the first tube  401  from the first end  411 , may be positioned adjacent to and facing the ribbon of glass-forming material  103 . The first tube  401  may therefore comprise an inlet  417  located at the first end  411  and an outlet  419  located at the second end  413 . The first tube  401  may receive the first cooling fluid  407  within the first channel  405  through the inlet  417  at the first end  411 . The first cooling fluid  407  can exit the first tube  401  from the first channel  405  through the outlet  419  at the second end  413 . In some embodiments, the first tube  401  can comprise a thermally conductive material, such as one or more of stainless steel, nickel alloys, titanium alloys, molybdenum alloys, tungsten alloys or cobalt alloys. For example, the thermal conductivity of stainless steel may be about 
     
       
         
           
             
               16.3 
               
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     the thermal conductivity of a nickel alloy may be about 
     
       
         
           
             
               91 
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                   kelvin 
                 
               
             
             , 
           
         
       
     
     the thermal conductivity of a titanium alloy may be within a range from about 
     
       
         
           
             6 
             ⁢ 
             
               watts 
               
                 meter 
                 × 
                 kelvin 
               
             
           
         
       
     
     to about 
     
       
         
           
             
               22 
               ⁢ 
               
                 watts 
                 
                   meter 
                   × 
                   kelvin 
                 
               
             
             , 
           
         
       
     
     the thermal conductivity of a molybdenum alloy may be about 
     
       
         
           
             
               138 
               ⁢ 
               
                 watts 
                 
                   meter 
                   × 
                   kelvin 
                 
               
             
             , 
           
         
       
     
     the thermal conductivity of a tungsten alloy may be about 
     
       
         
           
             
               174 
               ⁢ 
               
                 watts 
                 
                   meter 
                   × 
                   kelvin 
                 
               
             
             , 
           
         
       
     
     and the thermal conductivity of a cobalt alloy may be about 
     
       
         
           
             100 
             ⁢ 
             
               
                 watts 
                 
                   meter 
                   × 
                   kelvin 
                 
               
               . 
             
           
         
       
     
     Due to the first tube  401  comprising a metal material in some embodiments, the first tube  401  may be thermally conductive, and, thus, may efficiently conduct heat. In some embodiments, the first tube  401  can comprise a substantially constant cross-sectional size between the first end  411  and the second end  413 . The cross-sectional size of the first tube  401  may be measured between an inner surface of the closed first sidewall  403  along an axis that is perpendicular to a longitudinal axis  415  along which the first tube  401  extends. For example, the first tube  401  may comprise a circular cross-sectional shape such that the first tube  401  can comprise a substantially constant diameter between the first end  411  and the second end  413 . In some embodiments, the cross-sectional size (e.g., diameter) across the inner surface of the first tube  401  can be within a range from about 0.05 mm to about 2 mm, or within a range from about 0.25 mm to about 0.75 mm. The cross-sectional size of the first tube  401  can be selected such that a pressure drop between the first end  411  and the second end  413  can be achieved, wherein the pressure drop can assist in maintaining a phase (e.g., liquid phase or solid phase) of the first cooling fluid  407  within the first tube  401 . However, the first tube  401  is not limited to a constant cross-sectional size, and as illustrated and described relative to  FIGS.  7 - 8   , in some embodiments, the first tube  401  may comprise a non-constant cross-sectional size. 
     In some embodiments, the cooling tube  307  can comprise a second tube  431 . The second tube  431  can comprise a closed second sidewall  433  surrounding a second channel  435 . The first tube  401  can be positioned within the second tube  431  such that the second channel  435  may be between the closed first sidewall  403  and the closed second sidewall  433 . For example, by being positioned within, the first tube  401  may be received within an interior of the second tube  431 , such that the second tube  431  may comprise a cross-sectional size (e.g, diameter) that is larger than a cross-sectional size (e.g., diameter) of the first tube  401 ). In some embodiments, the first tube  401  and the second tube  431  may be coaxial and can extend along the longitudinal axis  415 . In some embodiments, an axis  437  that is orthogonal to the longitudinal axis  415  can intersect the closed first sidewall  403  and the closed second sidewall  433 . For example, originating at the longitudinal axis  415 , the axis  437  can first pass through the first channel  405 , followed by the closed first sidewall  403 , followed by the second channel  435  (e.g., which is located between the closed first sidewall  403  and the closed second sidewall  433 ), followed by the closed second sidewall  433 . 
     In some embodiments, the second tube  431  can receive a second cooling fluid  441  within the second channel  435 , whereupon the second cooling fluid  441  can flow within the second channel  435  between the closed first sidewall  403  and the closed second sidewall  433 . For example, the second channel  435  may be hollow and void of other structures such that a space (e.g., the second channel  435 ) may be located between the first tube  401  and the second tube  431 . By being closed, the closed second sidewall  433  may be free of openings, orifices, voids, vents, or the like, such that the second cooling fluid  441  may be prevented from exiting the second channel  435  by passing through the closed second sidewall  433 . With the closed first sidewall  403  also free of openings, the second cooling fluid  441  may remain within the second channel  435  and may not pass through the closed first sidewall  403 . The second tube  431  can extend between a first end  445  and a second end  447 . In some embodiments, the second end  447 , which may be located at an opposite end of the second tube  431  from the first end  445 , may be positioned adjacent to the ribbon of glass-forming material  103 . In some embodiments, the second tube  431  can comprise an inlet  451  and an outlet  455 . The inlet  451  can comprise an opening for an ingress  457  of the second cooling fluid  441  such that the second cooling fluid  441  can enter the second channel  435  by flowing through the inlet  451 . The outlet  455  can comprise an opening for an egress  459  of the second cooling fluid  441  such that the second cooling fluid  441  can exit the second channel  435  by flowing through the outlet  455 . In some embodiments, the inlet  451  can be positioned adjacent to the second end  447  of the second tube  431 , and the outlet  455  can be positioned adjacent to the first end  445  of the second tube  431 . For example, in some embodiments, the second tube  431  can be positioned within a refractory material  461 , such that the refractory material  461  can surround the second tube  431 . In some embodiments, the refractory material  461  may not surround the nozzle  311  (e.g., as illustrated in  FIG.  4   ), though, in some embodiments, the refractory material  461  can surround the nozzle  311 . When the refractory material  461  surrounds the nozzle  311 , the ingress  457  can allow for the second cooling fluid  441  to cool the walls of the nozzle  311 . In some embodiments, the inlet  451  can be in fluid communication with an opening in the refractory material  461 , such that the ingress  457  of the second cooling fluid  441  can flow through the opening in the refractory material  461  and through the inlet  451 . After flowing through the second channel  435 , the second cooling fluid  441  can exit the second channel  435  by exiting through the outlet  455 . In some embodiments, a second opening can be formed in the refractory material  461 , wherein the second opening may be in fluid communication with the outlet  455 . The egress  459  of the second cooling fluid  441  can therefore flow through the outlet  455  and through the second opening in the refractory material  461 . In some embodiments, the second cooling fluid  441  can flow in the same direction, or an opposing direction (e.g., as illustrated in  FIG.  5   ), from the first cooling fluid  407 . 
     In some embodiments, the second tube  431  can comprise a substantially constant cross-sectional size between the first end  445  and the second end  447 . The cross-sectional size of the second tube  431  may be measured between an inner surface of the closed second sidewall  433  along the axis  437  that is perpendicular to the longitudinal axis  415 . For example, the second tube  431  may comprise a circular cross-sectional shape such that the second tube  431  can comprise a substantially constant diameter between the first end  445  and the second end  447 . However, the second tube  431  is not so limited, and in some embodiments, the second tube  431  may comprise a non-constant cross-sectional size. The second tube  431  can comprise a larger cross-sectional size than the cross-sectional size of the first tube  401  such that the first tube  401  can be received within the second tube  431 . 
     In some embodiments, the cooling tube  307  can comprise the nozzle  311  attached to the first tube  401 . For example, in some embodiments, the nozzle  311  can be attached to the second end  413  of the closed first sidewall  403 . In some embodiments, by being attached to the first tube  401 , the nozzle  311  can be one-piece formed with the closed first sidewall  403 . In some embodiments, the nozzle  311  can be attached to the closed first sidewall  403  while not being one-piece formed. For example, one or more mechanical fasteners can attach the nozzle  311  and the closed first sidewall  403 . The mechanical fasteners may comprise, for example, adhesives, locking structures (e.g., male-female threading engagement), a welding attachment, etc., such that the nozzle  311  is limited from being inadvertently detached from the closed first sidewall  403  during operation. The refractory material  461  may surround none, some or all of the nozzle  311 . For example, in some embodiments, the refractory material  461  may surround some of or all of the nozzle  311 , while in other embodiments, the refractory material  461  may not surround the nozzle  311 . 
     The nozzle  311  can comprise a nozzle cavity  467  that may be in fluid communication with the first channel  405 . For example, by being in fluid communication, the nozzle  311  can receive the first cooling fluid  407  (e.g., within the nozzle cavity  467 ) and direct the first cooling fluid  407  toward the travel path  221 . In some embodiments, the nozzle cavity  467  may be substantially hollow and can form a chamber within which the first cooling fluid  407  enters after the first cooling fluid  407  exits the second end  413  of the closed first sidewall  403 . The nozzle  311  can comprise several different shapes, for example a conical shape, an elongated conical shape comprising a width (e.g., along the direction of the width W illustrated in  FIG.  1   ) that is greater than a height (e.g., along the travel direction  154  illustrated in  FIG.  1   ), etc. 
     In some embodiments, the nozzle  311  can comprise a diffuser. In some embodiments, a diffuser may comprise a wall defining an opening through which a fluid can pass. The wall opening can comprise an increasing cross-sectional size relative to a flow direction of the fluid, such that the velocity of the fluid can decrease within the diffuser. Without wishing to be bound by theory, a diffuser can decrease (e.g., reduce) the velocity of the first cooling fluid  407  in the nozzle  311 , which can inhibit (e.g., reduce, decrease, eliminate) the chance that the first cooling fluid  407  contacts a surface of the ribbon of glass-forming material  103 . Additionally, without wishing to be bound by theory, a diffuser can decrease the temperature of the first cooling fluid  407  flowing through the diffuser when the first cooling fluid  407  comprises a negative Joule-Thomson coefficient. In some embodiments, an atomizer may be positioned between the coolant source  309  and the nozzle  311  to generate particles (e.g., liquid droplets, solid particles). 
     In some embodiments, the nozzle  311  can comprise a boiling nozzle. In some embodiments, a boiling nozzle can comprise an inlet section that is converging (e.g., decreasing cross-sectional size) relative to a flow direction of the fluid, followed by an outlet section that is diverging (e.g., increasing cross-sectional size) relative to the flow direction of the fluid. Without wishing to be bound by theory, a boiling nozzle may generate particles (e.g., liquid droplets, solid particles) using the kinetic energy (e.g., acceleration) of the first cooling fluid  407  to separate the first cooling fluid  407  into particles. In some embodiments, portions of the first cooling fluid  407  may undergo a phase transformation to a gas (e.g., “boil”) when accelerated by a boiling nozzle. In some embodiments, portions of the first cooling fluid  407  may separate from one another based on the surface tension of the first cooling fluid  407  as the first cooling fluid  407  is thinned during acceleration in the nozzle  311 . 
     In some embodiments, the nozzle  311  can comprise a shear nozzle. In some embodiments, a shear nozzle can comprise a surface that forms a spiral upon which a fluid can impinge, such that the fluid can be separated into particles. Without wishing to be bound by theory, a shear nozzle may generate particles (e.g., liquid droplets, solid particles) from the first cooling fluid  407 . In some embodiments, the shear nozzle can induce a rotary fluid motion that can cause the first cooling fluid  407  to separate into particles based on the shear forces introduce therein. In further embodiments, a shear nozzle can form particles (e.g., liquid droplets, solid particles) by combining the first cooling fluid  407  and another fluid (e.g., gas). In even further embodiments, the first cooling fluid  407  may be circumscribed by another fluid within the shear nozzle. Without wishing to be bound by theory, shearing between the first cooling fluid  407  and the other fluid can produce particles of coolant. 
     Referring to  FIG.  6   , in some embodiments, methods of manufacturing a glass ribbon can comprise delivering the first cooling fluid  407  through the first tube  401  toward the nozzle  311 . For example, the first cooling fluid  407  can be supplied by the coolant source  309  (e.g., illustrated in  FIG.  3   ). The coolant source  309  can deliver the first cooling fluid  407  through the inlet  417  at the first end  411  and into the first channel  405 . The first cooling fluid  407  can flow in a flow direction  601  from the first end  411  toward the second end  413 . Upon reaching the second end  413 , the first cooling fluid  407  can exit the first channel  405  through the outlet  419  and may enter the nozzle  311  by being received within the nozzle cavity  467 . In some embodiments, the first cooling fluid  407  can undergo a phase change within the first tube  401 . For example, the first cooling fluid  407  may comprise a liquid that may be injected into the first tube  401  from the coolant source  309 . The first cooling fluid  407  may experience a pressure drop within the first tube  401 , causing the first cooling fluid  407  to undergo a phase change from liquid to gas, such that a region within the first tube  401  may comprise a mixture of liquid particles and gas. As the pressure continues to lower along the first tube  401 , the liquid may undergo a phase change to a solid. 
     In some embodiments, methods of manufacturing a glass ribbon can comprise cooling the first tube  401  by delivering the second cooling fluid  441  through the second tube  431  that surrounds the first tube  401  such that the second cooling fluid  441  is in convective contact with the first tube  401 . For example, the second cooling fluid  441  can be delivered to the second tube  431  through the inlet  451 . The second cooling fluid  441  can travel through the second channel  435  to an outlet  455 , whereupon the second cooling fluid  441  can exit the second channel  435 . In some embodiments, the second cooling fluid  441  can travel along the flow direction  601  in the same direction as the first cooling fluid  407  travels through the first tube  401 . In some embodiments, the second cooling fluid  441  can travel opposite the flow direction  601  in an opposite direction that the first cooling fluid  407  travels through the first tube  401 . In some embodiments, the second cooling fluid  441  can comprise a gas, for example, oxygen, nitrogen, etc. and/or a liquid, for example, liquid carbon dioxide, liquid nitrogen, etc. Due to the second channel  435  surrounding the first tube  401 , the second cooling fluid  441  can surround the closed first sidewall  403 . 
     In some embodiments, cooling the first tube  401  by delivering the second cooling fluid  441  through the second tube  431  can comprise thermally shielding the first tube  401  from a surrounding environment  603  by absorbing heat from the surrounding environment  603  with the second cooling fluid  441 . By thermally shielding the first tube  401  from the surrounding environment  603 , the second cooling fluid  441  can absorb heat from the surrounding environment  603 , which can cause a first temperature increase of the second cooling fluid  441  and a second temperature increase of the first cooling fluid  407 . However, due to the second cooling fluid  441  surrounding the first tube  401 , the first temperature increase can be greater than the second temperature increase, such that the effects of the elevated temperature of the surrounding environment  603  on the first cooling fluid  407  may be lessened. For example, the first tube  401  can be thermally shielded from the surrounding environment  603  due to a path between the surrounding environment  603  and the first tube  401  passing through the second channel  435 . In some embodiments, the surrounding environment  603  may be at an elevated temperature as compared to the first cooling fluid  407 . Exposing the first cooling fluid  407  to the elevated temperature may cause a phase change of the first cooling fluid  407  from a solid or liquid particle to a gas within the first channel  405 . As a result of this phase change, a reduced amount of the first cooling fluid  407  (e.g., in gas form) may reach the first end  411  of the first tube  401 , thus limiting the cooling capacity of the first cooling fluid  407 . The second cooling fluid  441  can therefore thermally shield the first tube  401  and, thus, the first cooling fluid  407 , from the elevated temperature of the surrounding environment  603 . For example, the second cooling fluid  441  may absorb a portion of the heat from the surrounding environment  603  as the second cooling fluid  441  flows through the second channel  435 . 
     In some embodiments, the closed first sidewall  403  can isolate the first channel  405  from the second channel  435 . For example, the closed first sidewall  403  may be free of openings, orifices, voids, vents, or the like, such that the first cooling fluid  407  may be prevented from passing through the closed first sidewall  403  from the first channel  405  to the second channel  435 . Likewise, the second cooling fluid  441  may be prevented from passing through the closed first sidewall  403  from the second channel  435  to the first channel  405 . As such, methods can comprise isolating the first cooling fluid  407  (e.g., by maintaining the first cooling fluid  407  within the first channel  405 ) from the second cooling fluid  441  (e.g., by maintaining the second cooling fluid  441  within the second channel  435 ) when the second cooling fluid  441  is delivered through the second tube  431  and when the first cooling fluid  407  is directed from the end (e.g., the second end  413 ) of the first tube  401 . 
     In some embodiments, methods can comprise cooling the area  325  (e.g., of the ribbon of glass-forming material  103 ) by directing the first cooling fluid  407  from the second end  413  of the first tube  401  and through the nozzle  311  toward the area  325  of the ribbon of glass-forming material  103 . For example, the first cooling fluid  407 , which may comprise the one or more coolant particles  315  in one or more of a liquid phase, a solid phase, or a gas phase, may exit the outlet  419  of the first tube  401  at the second end  413  and may pass through the nozzle cavity  467  of the nozzle  311 . In some embodiments, cooling the area  325  can comprise changing a phase of the first cooling fluid  407  while the first cooling fluid  407  is flowing toward the area  325  of the ribbon of glass-forming material  103 . For example, the one or more coolant particles  315  that exit the nozzle  311  can travel along the flow direction  601  toward the travel path  221 . In some embodiments, as the first cooling fluid  407  travels along the flow direction  601 , a portion of the first cooling fluid  407  can undergo a phase change and may evaporate. For example, an ambient temperature between the nozzle  311  and the area  325  the ribbon of glass-forming material  103  may be high enough (e.g., within a range from about 400° C. to about 1000° C.) and greater than a boiling point of the coolant particles  315  to cause at least some of the one or more coolant particles  315  to evaporate by undergoing a phase change from a liquid phase or a solid phase to a gas phase, such that the one or more coolant particles  315  can be converted to the gas  322 . In some embodiments, the phase change (e.g., to evaporate the one or more coolant particles  315  to form the gas  322 ) can occur after the first cooling fluid  407  has been discharged from the nozzle  311  but prior to the one or more coolant particles  315  reaching the ribbon of glass-forming material  103 . However, in some embodiments, the ambient temperature may be higher than a boiling point of the first cooling fluid  407 , such that the first cooling fluid  407  may be at risk of undergoing the phase change within the first tube  401  and prior to being discharged from the nozzle  311 . For example, in some embodiments, the first cooling fluid  407  can comprise carbon dioxide, water, liquid nitrogen, etc. 
     In some embodiments, the portion of the first cooling fluid  407  that undergoes a phase change and evaporates prior to reaching the ribbon of glass-forming material  103  can comprise all of the first cooling fluid  407  such that none of the one or more coolant particles  315  reach the travel path  221  to contact the ribbon of glass-forming material  103 . In some embodiments, the portion of the first cooling fluid  407  that undergoes a phase change and evaporates prior to reaching the ribbon of glass-forming material  103  can comprise some (e.g, less than all) of the first cooling fluid  407  such that some of the one or more coolant particles  315  reach the travel path  221  to contact the ribbon of glass-forming material  103 . However, the amount of the one or more coolant particles  315  that contact the ribbon of glass-forming material  103  (e.g., and are not converted to the gas  322 ) can be small enough so as not to affect the quality of the ribbon of glass-forming material  103 . Evaporation of the one or more coolant particles  315  into the gas  322  can yield several benefits. For example, when the one or more coolant particles  315  undergo a phase change and evaporate to form the gas  322 , a reduction in air temperature can be achieved. For example, the air temperature adjacent to the ribbon of glass-forming material  103  can be reduced, which can cause the ribbon of glass-forming material  103  adjacent to the nozzle  311  to cool. Further, by forming the gas  322 , some or none of the coolant particles  315  may contact the ribbon of glass-forming material  103 , thus reducing the likelihood of an accumulation of material on a surface of the ribbon of glass-forming material  103 . 
     In some embodiments, methods can comprise controlling a phase change of the first cooling fluid  407  within the first tube  401  by accelerating a flow of the first cooling fluid  407  within a first portion  619  of the first tube  401  prior to reaching the second end  413  (e.g, and prior to reaching the nozzle  311 ). For example, in some embodiments, by accelerating a flow of the first cooling fluid  407  within the first portion  619 , an amount of time that the first cooling fluid  407  spends within the first portion  619  can be reduced as compared to embodiments in which the flow of the first cooling fluid  407  within the first portion  619  is not accelerated. In some embodiments, the first tube  401  can comprise the first portion  619  and a second portion  621 . The second portion  621  can be located between the first end  411  of the first tube  401  and the first portion  619 . The first portion  619  can be located between the second end  413  and the second portion  621 . Therefore, a distance separating the second end  413  from the first portion  619  may be less than a distance separating the second end  413  from the second portion  621 . The first cooling fluid  407  can comprise one or more coolant particles  623  flowing within the first channel  405 . The one or more coolant particles  623  can comprise liquid particles, solid particles, and/or gas particles. In some embodiments, when the one or more coolant particles  623  undergo a phase change from a liquid particle to a gas particle, or from a solid particle to a gas particle, a change in density may occur, which can cause an acceleration of the one or more coolant particles  623 . 
     In some embodiments, accelerating the flow of the first cooling fluid  407  within the first portion  619  of the first tube  401  can comprise enabling a phase change of a portion of the first cooling fluid  407  within the first portion  619  from one or more of the liquid phase or the solid phase to the gas phase. For example, in some embodiments, a temperature of the first portion  619  of the first tube  401  may be greater than a temperature of the second portion  621 . This temperature variation may be due, in part, to a temperature near the ribbon of glass-forming material  103  being higher than a temperature near the first end  411  of the first tube  401 . Due to the higher temperature near the ribbon of glass-forming material  103  (e.g., and, thus, near the second end  413 ), a portion of the one or more coolant particles  623  within the first portion  619  and closer to the second end  413  than the first end  411  can undergo the phase change (e.g., from the solid phase or liquid phase to the gas phase), thus causing an acceleration within the first portion  619 . Enabling the phase change of the portion of the first cooling fluid  407  can be accomplished in several ways. For example, in some embodiments, a temperature of the second cooling fluid  441  entering the inlet  451  can be chosen such that a portion of the first cooling fluid  407  within the first portion  619  can undergo the phase change and, thus, the flow of the first cooling fluid  407  within the first portion  619  can be accelerated. In some embodiments, to enable the phase change, a thickness of the closed first sidewall  403  can differ at the first portion  619  from the second portion  621 , such that a greater amount of the first cooling fluid  407  can undergo the phase change within the first portion  619 . In further embodiments, to enable the phase change, the second tube  431  can comprise a differing thickness at the first portion  619  than at the second portion  621 , such that differing cooling capacities of the first tube  401  can be achieved, thus allowing for the portion of the first cooling fluid  407  to undergo the phase change. 
     In some embodiments, methods can comprise extracting the first cooling fluid  407  by suction after the first cooling fluid  407  has been directed from the end of the first tube  401  and through the nozzle  311 . For example, in some embodiments, the first cooling apparatus  303  can comprise a suction nozzle  651  positioned adjacent to the nozzle  311 . The suction nozzle  651  can define an opening into which fluid can be drawn (e.g., illustrated with arrow  653 ) into the suction nozzle  651 . In some embodiments, the suction nozzle  651  can remove air from the environment  603  near the area  325  and near the nozzle  311 . By removing air, the suction nozzle  651  can reduce the pressure in the environment  603  near the nozzle  311 , which can cause the gas  322  and the one or more coolant particles  315  to be drawn along a path (e.g., illustrated with arrow  653 ) into the suction nozzle  651 . While one suction nozzle  651  is illustrated in  FIG.  6   , in some embodiments, a plurality of suction nozzles  651  may be provided in proximity to the nozzle  311 . The suction nozzle  651  can provide several benefits. For example, due to the phase change of the first cooling fluid  407  upon exiting the nozzle  311 , a density of the environment  603  can change. This density change can affect a pressure within the environment  603 , which may have unwanted effects upon the ribbon of glass-forming material  103 . To reduce any unwanted effects, the suction nozzle  651  can draw the gas  322  and the one or more coolant particles  315 . 
     Referring to  FIGS.  7 - 8   , additional embodiments of a first cooling apparatus  701  are illustrated. The first cooling apparatus  701  illustrated in  FIGS.  7 - 8    can be similar to the first cooling apparatus  303  illustrated in  FIGS.  3 - 6   . For example, referring to  FIG.  7   , the first cooling apparatus  701  can comprise the cooling tube  307  comprising the first tube  401  and the second tube  431  surrounded by the refractory material  461 . In some embodiments, the first tube  401  can comprise a non-constant cross-sectional size between the first end  411  and the second end  413 , wherein the non-constant cross-sectional size is measured between an inner surface of the first tube  401 . For example, the first tube  401  can comprise a first cross-sectional size  703  at a first location  705  between the first end  411  and the second end  413 , and a second cross-sectional size  707  at a second location  709  adjacent to the second end  413 . In some embodiments, the cross-sectional size can comprise a maximum distance separating an inner surface of the first tube  401  along a direction that is perpendicular to the longitudinal axis  415 . For example, when the first tube  401  comprises a circular cross-sectional shape, the first cross-sectional size  703  and the second cross-sectional size  707  can comprise a diameter (e.g., a linear distance) of the first tube  401 . In some embodiments, the cross-sectional size can comprise an area of the first tube  401  along a plane perpendicular to the longitudinal axis  415 . 
     The first location  705  can be located within the second portion  621  of the first tube  401  at a location between the first end  411  and the first portion  619 . The second location  709  can be located within the first portion  619  of the first tube  401  at a location between the second end  413  and the second portion  621 . In some embodiments, the first cross-sectional size  703  (e.g., at the first location  705 ) can be different than the second cross-sectional size  707  (e.g., at the second location  709 ), for example, wherein the first cross-sectional size  703  can be greater than the second cross-sectional size  707 . For example, the first tube  401  can comprise a decreasing cross-sectional size, wherein a cross-sectional size of the first tube  401  at the first end  411  may be greater than the cross-sectional size of the first tube  401  at the second end  413 . The non-constant cross-sectional size can be achieved in several ways. For example, in some embodiments, the closed second sidewall  433  can comprise a larger thickness at the first portion  619  than at the second portion  621 , such that the first tube  401  can comprise the reduced second cross-sectional size  707  at the first portion  619 . 
     Referring to  FIG.  8   , in some embodiments, methods of manufacturing a glass ribbon can comprise controlling a phase change of the first cooling fluid  407  within the first tube  401  by accelerating a flow of the first cooling fluid  407  within the first portion  619  of the first tube  401  prior to reaching the second end  413 . For example, accelerating the flow of the first cooling fluid  407  can comprise reducing a cross-sectional size of the first portion  619  of the first tube  401  relative to the flow direction  601  of the first cooling fluid  407 . The reduction in cross-sectional size may comprise a static reduction in the dimensions of the first tube  401  and not an active reduction, for example, wherein an active reduction may comprise applying a force to an outer surface of the first tube  401  to temporarily reduce the cross-sectional size of a portion of the first tube  401 . Rather, the reduction in cross-sectional size can comprise a reduced dimension of the first tube  401  relative to the flow direction  601  from the first end  411  to the second end  413 . In some embodiments, the first tube  401  may comprise the closed first sidewall  403  of a non-constant thickness, wherein at one location (e.g., the second portion  621 ), the closed first sidewall  403  can comprise a lesser thickness than at another location (e.g., the first portion  619 ). The differing thickness of the closed first sidewall  403  can achieve the reduction in cross-sectional size due to a narrowing of the first tube  401  from the second portion  621  to the first portion  619 . 
     In addition, or in the alternative, in some embodiments, an auxiliary structure may be positioned within the first tube  401  at the first portion  619  to achieve the reduction in cross-sectional size. In some embodiments, due to the reduction in cross-sectional size, a flow rate of the one or more coolant particles  315  flowing through the first tube  401  can increase when flowing through the first portion  619  due to the second cross-sectional size  707  being greater than the first cross-sectional size  703 . By accelerating the flow of the first cooling fluid  407  within the first portion  619 , an amount of time that the first cooling fluid  407  spends within the first portion  619  can be reduced as compared to embodiments in which the flow of the first cooling fluid  407  within the first portion  619  is not accelerated. In some embodiments, a temperature of the first portion  619  of the first tube  401  may be greater than a temperature of the second portion  621 . To reduce the likelihood of the first cooling fluid  407  undergoing a phase change within the first portion  619 , the reduced cross-sectional size of the first portion  619  can facilitate a reduction in the amount of time that the first cooling fluid  407  spends within the first portion  619 . As a result, a phase change of the first cooling fluid  407  within the first portion  619  may be limited, thus providing for a greater amount of coolant particles  315  passing through the nozzle  311  prior to converting to the gas  322 . 
     Referring to  FIG.  9   , additional embodiments of a first cooling apparatus  901  are illustrated. The first cooling apparatus  901  may be similar in some respects to the first cooling apparatus  301 ,  701  illustrated in  FIGS.  3 - 8   . However, in some embodiments, the first cooling apparatus  901  can comprise an opening  905  in the first tube  401  that can define a flow path  903  for the first cooling fluid  407 . For example, adjacent to the second end  413  of the first tube  401 , one or more openings (e.g., the opening  905 ) may be formed in the closed first sidewall  403 . As such, a portion of the first cooling fluid  407  can exit the second end  413  and pas through the nozzle  311 , while another portion of the first cooling fluid  407  can travel along the flow path  903  and through the opening  905 . The opening  905  may be in fluid communication with the second channel  435 . The first cooling fluid  407  can pass through the opening  905 , whereupon the first cooling fluid  407  can function as the second cooling fluid  441  by cooling the first tube  401  and flowing toward the outlet  455 . In some embodiments, a benefit of the first cooling apparatus  901  is that the inlet  451  (e.g., illustrated in  FIGS.  5 - 8   ) may not be provided, such that a second, independent, cooling fluid may not be supplied to the second channel  435 . Rather, the first cooling fluid  407  can function as the second cooling fluid  441  of  FIGS.  5 - 8    by cooling the first tube  401 . 
     The cooling tube  307  illustrated and described herein can yield several benefits. For example, by positioning the first tube  401  within the second tube  431 , the first channel  405  of the first tube  401  can be maintained as a separate atmosphere from the second channel  435 . For example, the first tube  401  may comprise the closed first sidewall  403  that is void of openings, while the second tube  431  may comprise the closed second sidewall  433  that is void of openings. As such, the first tube  401  can receive and transmit the first cooling fluid  407  while the second tube  431  can receive and transmit the second cooling fluid  441 . The first cooling fluid  407  and the second cooling fluid  441  may not commingle or mix, such that the first cooling fluid  407  can be emitted from the first tube  401  toward the ribbon of glass-forming material  103  to cool the area  325 , and the second cooling fluid  441  can contact the closed first sidewall  403  to cool the first tube  401 . The second cooling fluid  441  can therefore cool the first tube  401  and thermally shield the first cooling fluid  407  from the elevated temperatures of the surrounding environment. By cooling the first tube  401 , the likelihood of an unintended phase change of the first cooling fluid  407  while within the first channel  405  may be avoided. By limiting the unintended phase change of the first cooling fluid  407 , the first cooling fluid  407  can be emitted from the first tube  401  in the form of the one or more coolant particles  315 , which can undergo a phase change from solid or liquid to the gas  322  adjacent to the ribbon of glass-forming material  103 , thus cooling the area  325 . 
     In addition, in some embodiments, the cooling tube  307  can facilitate an acceleration of the flow of the first cooling fluid  407  at a location near the second end  413 , for example, within the first portion  619  of the first tube  401 . For example, at a location closer to the ribbon of glass-forming material  103 , a temperature of the surrounding environment  603  may be higher as compared to a temperature near the first end  411 . To reduce the amount of time the first cooling fluid  407  spends within the first portion  619 , the first tube  401  can comprise a reduced cross-sectional size (e.g., the second cross-sectional size  707  at the second location  709 ) compared to the second portion  621  (e.g., the first cross-sectional size  703  at a first location  705 ). In some embodiments, to reduce the amount of time the first cooling fluid  407  spends within the first portion  619 , a phase change of a portion of the first cooling fluid  407  can be enabled within the first portion  619 . The phase change can result in a change in density, which can accelerate the first cooling fluid  407 . In addition, the first tube  401  can comprise a cross-sectional size, for example, a diameter, that can facilitate a pressure drop between the first end  411  and the second end  413 . For example, in some embodiments, the diameter of an interior of the first tube  401  can be within a range from about 0.25 mm to about 0.75 mm. When the pressure drop is too great, then a flow rate of the first cooling fluid  407  within the first tube  401  may be too low at the second end  413 . For a smaller pressure drop, a desired flow rate of the first cooling fluid  407  can be maintained while limiting a phase change (e.g., liquid phase or solid phase to gas phase) within the first tube  401  at a certain temperature. 
     It should be understood that while various embodiments have been described in detail relative to certain illustrative and specific examples thereof, the present disclosure should not be considered limited to such, as numerous modifications and combinations of the disclosed features are possible without departing from the scope of the following claims.