Abstract:
A method for harvesting algae according to embodiments of the present invention includes filling a reservoir at least partially with a liquid, submerging a bag at least partially in the liquid, the bag containing media, the media comprising algae, the bag comprising a first end, a second end, a harvesting port located closer to the first end than to the second end, and a gas port, delivering gas into the bag through the gas port, and raising the second end of the bag by accumulating the gas at the second end to flow the media toward the harvesting port.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit of U.S. Provisional Patent Application Ser. No. 61/220,136, filed on Jun. 24, 2009, which is incorporated by reference herein for all purposes. 
    
    
     TECHNICAL FIELD 
     Some embodiments of the present invention relate generally to algae harvesting, and more specifically to algae harvesting from film photobioreactor bags. 
     BACKGROUND 
     Removing algae from photobioreactors for harvesting and eventual processing, such as, for example, biofuels processing, often involves complex, time-consuming, and costly mechanisms. Pumps, as well as mechanical systems designed to mechanically squeeze algae or algae-containing media from a photobioreactor often use large amounts of energy, thereby increasing the cost of algae harvesting and/or biofuels production. 
     SUMMARY 
     A method for harvesting algae according to embodiments of the present invention includes filling a reservoir at least partially with a liquid; submerging a bag at least partially in the liquid, the bag containing media, the media comprising algae, the bag including a first end, a second end, a harvesting port located closer to the first end than to the second end, and a gas port; delivering gas into the bag through the gas port; and raising the second end of the bag by accumulating the gas at the second end to flow the media toward the harvesting port. An embodiment of the method may further include tethering the bag to the reservoir closer to the first end than to the second end. In some cases, the bag includes an elongated support member, and tethering the bag to the reservoir includes tethering the elongated support member to the reservoir. Tethering the elongated support member to the reservoir may include pivotally coupling the elongated support member to the reservoir. Raising the second end may include raising the second end up to an upper level of the liquid in the reservoir. 
     Methods for harvesting algae according to embodiments of the present invention may further include arranging multiple submerged bags in the reservoir and emptying different bags at different times or in different ways. For example, methods for harvesting algae according to embodiments of the present invention may include emptying every second bag simultaneously and re-submerging them before emptying the remaining bags. 
     A system for harvesting algae according to embodiments of the present invention includes a reservoir at least partially filled with a liquid; a media bag containing media, the media including algae, the bag at least partially submerged in the liquid, the bag including a first end and a second end and a harvesting port located closer to the first end than to the second end; and an inflation bag, the inflation bag coupled to the media bag and located closer to the second end than to the first end. In some cases, the inflation bag may be separate from the media bag. 
     While multiple embodiments are disclosed, still other embodiments of the present invention will become apparent to those skilled in the art from the following detailed description, which shows and describes illustrative embodiments of the invention. Accordingly, the drawings and detailed description are to be regarded as illustrative in nature and not restrictive. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  illustrates a side elevation view of a photobioreactor and algae-harvesting system, according to embodiments of the present invention. 
         FIG. 2  illustrates a cross-sectional view of a photobioreactor bag, according to embodiments of the present invention. 
         FIG. 3  illustrates a side elevation view of a photobioreactor and alternative algae-harvesting system, according to embodiments of the present invention. 
         FIG. 4  illustrates a side elevation view of a submerged photobioreactor bag and algae-harvesting system prior to harvesting, according to embodiments of the present invention. 
         FIG. 5  illustrates the photobioreactor bag of  FIG. 4  during a harvesting procedure, according to embodiments of the present invention. 
         FIG. 6  illustrates the photobioreactor bag of  FIGS. 4 and 5  during a harvesting procedure, according to embodiments of the present invention. 
         FIG. 7  illustrates the photobioreactor bag of  FIGS. 4-6  during a harvesting procedure, according to embodiments of the present invention. 
         FIG. 8  illustrates a cross-sectional view of a photobioreactor bag and alignment groove with the photobioreactor bag in a raised position, according to embodiments of the present invention. 
         FIG. 9  illustrates a cross-sectional view of a photobioreactor bag and alignment groove with the photobioreactor bag in a lowered position, according to embodiments of the present invention. 
         FIG. 10  illustrates a combined partial top view and partial side view of a series of photobioreactor bags and an algae harvesting system, according to embodiments of the present invention. 
         FIG. 11  illustrates a combined partial top view and partial side view of a series of photobioreactor bags and an alternative algae-harvesting system, according to embodiments of the present invention. 
         FIG. 12  illustrates a side elevation view of an alternative photobioreactor and algae-harvesting system, according to embodiments of the present invention. 
         FIG. 13  illustrates a cross sectional view of the photobioreactor of  FIG. 12 , according to embodiments of the present invention. 
     
    
    
     While the invention is amenable to various modifications and alternative forms, specific embodiments have been shown by way of example in the drawings and are described in detail below. The intention, however, is not to limit the invention to the particular embodiments described. On the contrary, the invention is intended to cover all modifications, equivalents, and alternatives falling within the scope of the invention as defined by the appended claims. 
     DETAILED DESCRIPTION 
       FIG. 1  illustrates a side elevation view of a photobioreactor bag  101  and algae-harvesting system  100 , according to embodiments of the present invention.  FIG. 2  illustrates a cross-sectional view of a photobioreactor bag  101 , according to embodiments of the present invention. The photobioreactor bag  101  includes a media  102  which may include water and/or algae or other microorganisms, and a head space  103  above the media within the bag  101 , which may include air, carbon dioxide, and/or other gases, according to embodiments of the present invention. The bag  101  may also be coupled to a weight member  108  via a weight member interface  202 ; the weight member interface  202  may be a channel and/or one or more loops formed in the bag  101  and configured to receive a weight member  108 . Weight member  108  may be a pipe or other device for providing weight to the bag  101  to prevent the bag from moving and/or floating to the top due to the buoyancy created by the gases in the head space  103 , according to embodiments of the present invention. Weight member  108  may be a PVC pipe filled with concrete, or other sufficiently stiff and/or heavy ballast material, according to embodiments of the present invention. Weight member interface  202  may be formed by welding the sides of the bag  101  together at location  204 , for example. According to some embodiments of the present invention, weight member  108  is a pipe or strut, such as a pipe with a weight of approximately three hundred forty pounds per one hundred feet. 
     As used herein, the term “coupled” is used in its broadest sense to refer to elements which are connected, attached, and/or engaged, either directly or integrally or indirectly via other elements, and either permanently, temporarily, or removably. As used herein, the term “pivotally coupled” is used in its broadest sense to refer to elements which are coupled in a way that permits one element to pivot with respect to another element. As used herein, the terms “fluidly coupled” or in “fluid communication” are used in their broadest sense to refer to elements which are coupled in a way that permits fluid flow between them. 
     The bag  101  may be at least partially submerged in a reservoir, the bottom of which is indicated at least partially at reference numeral  140 , and the top level of the liquid (e.g. water) in the reservoir is indicated by reference numeral  110 , according to embodiments of the present invention. The reservoir may be any natural or artificial container capable of holding liquid, according to embodiments of the present invention. The bag  101  includes a harvesting port  116 , and a harvesting tube  118  in fluid communication with the bag  101  via the harvesting port  116 , according to embodiments of the present invention. The harvesting tube  118  may also include a valve  122  which, during harvesting, may be opened to permit the media  102  within the bag  101  to flow toward the harvesting port  116 , through the harvesting tube  118 , and out of the end  120  of the harvesting tube  118 . The harvested media may then be stored and/or further processed to separate the algae from the water, for example, for further processing steps. 
     As illustrated in  FIG. 1 , the weight member  108  may be coupled with the bag  101  along some or all of the length of the bag, from one end  104  of the bag  101  to another end  106  of the bag  101 , according to embodiments of the present invention. The weight member  108  may be coupled to the reservoir  140  or other underlying surface; for example, the weight member  108  may be pivotally coupled to the reservoir  140  at location  142 , according to embodiments of the present invention. According to some embodiments of the present invention, the weight member  108  may be pivotally coupled to the reservoir  140  with a zip tie connection or the like. 
     A blower  124  is in fluid communication with the bag  101  via line  126 , according to embodiments of the present invention. Another line  128  fluidly connects the blower  124  with another end  104  of the bag  101  via line  130 . Line  128  may be referred to as a filler bypass line, according to embodiments of the present invention. Exhaust lines  132  and  138  are also in fluid communication with lines  126 ,  128 , and  130 , according to embodiments of the present invention. Line  126  is in fluid communication with the bag  101  via gas inlet port  112 , and line  130  is in fluid communication with the bag  101  via gas exhaust port  114 , according to embodiments of the present invention. Although port  112  is shown as being located toward end  106  and port  114  is shown as being located toward end  104 , one of ordinary skill in the art, based on the disclosure provided herein, will recognize the various other possible locations of ports  112  and/or  114 . Valve  134  is located inline between pump  124  and line  128 , and valve  136  is located inline between line  128  and line  132 , according to embodiments of the present invention. 
     During normal operation, valve  134  is closed and blower  124  blows gas through line  126 , into gas inlet port  112 , and into the photobioreactor bag  101 , according to embodiments of the present invention. The gas may be carbon dioxide, air, and/or a mixture of gases. For example, blower  124  may blow air into the bag  101  to provide a certain air pressure sufficient to maintain a desired head space  103  and thus maintain the photobioreactor bag  101  in an upright position submerged within the reservoir or tank  140 . During normal operation, valve  136  is open, and because end  144  of line  132  is under the liquid (e.g. water) level  110 , the blower  124  supplies the air to the bag  101  at or above the pressure at end  144  in order to maintain the head space  103 . If blower  124  supplies air at a flow rate sufficient to raise the pressure in the bag  101  higher than the pressure at the depth of end  144 , air will flow through the bag  101  and exhaust out of end  144 . In such a scenario, the air will not exhaust out of end  146  of line  138  because end  146  is at a greater depth, and thus a higher pressure, than end  144 . This normal operating pressure may be, for example, equivalent to three or four inches of water (e.g. the end  144  may be three or four inches below level  110 ). 
     During a harvesting operation, valve  134  is opened and valve  136  is closed. This causes the air supplied by the blower  124  to reach a higher pressure before exhausting, because the closure of valve  136  requires a higher pressure within the line  128  and photobioreactor bag  101  before the air exhausts through end  146 , according to embodiments of the present invention. The air (and/or combination of gases) from blower  124  accumulates within the bag  101  and the end  104  begins to raise toward the surface level  110 , according to embodiments of the present invention. According to some embodiments of the present invention, the harvesting port  116  is located closer to end  106  than end  104  so that, as gas accumulates at the second end  104 , the end  104  is raised, thus flowing the media  102  toward the harvesting port  116 . 
     According to some embodiments of the present invention, the harvesting cycle may be initiated in different ways. For example, in some systems, line  132  and valve  136  may be eliminated, and the pressure at the end of line  138  may be varied between a normal operating pressure and a harvesting pressure (e.g. the pressure at which gas accumulates to raise the bag  101 ) by mechanically moving the end  146  from a normal operating depth below level  110  to a deeper, harvesting depth below level  110 . This may be done, for example, by building line  138  as a PVC pipe extending through a frictional gasket or grommet, whose vertical position with respect to the water level  110  may be adjusted by manually lifting up or pushing down on the line  138 , according to embodiments of the present invention. 
       FIG. 3  illustrates a side elevation view of a photobioreactor  101  and alternative algae-harvesting system  300 , according to embodiments of the present invention. During normal operation of system  300 , valve  334  is closed, and blower  124  blows air (or any other gas or mixture of gases) into bag  101 , and the air exhausts through line  303  out of end  144 , which is submerged below level  110  to pressurize the head space  103 . According to some embodiments of the present invention, level  144  is at the same distance below level  110  as level  105  is below  110 . Valve  334  is inline with line  328  which is in fluid communication with flotation bag  301  via gas port  302 , according to embodiments of the present invention. According to some embodiments of the present invention, the flotation bag  301  is separate from the photobioreactor bag  101  (e.g. is not in fluid communication with bag  101 ), but may also be coupled to weight element  108  and/or bag  101 , according to embodiments of the present invention. During a harvesting operation, valve  334  is opened and valve  136  is closed, which causes inflation of bag  301 , causing end  104  to rise toward the surface level  110 , according to embodiments of the present invention. This raising of end  104  and the pressure difference between end  144  and end  146  causes enhanced accumulation of gas inside the bag  101  near end  104 , which in turn further raises the bag  101  and directs media  102  flow toward the harvesting port  116 , according to embodiments of the present invention. Once the harvesting operation is complete, the inflation bag  301  may be deflated through an exhaust line (not shown), and valve  334  may be closed, to permit re-submergence of the bag  101 , according to embodiments of the present invention. 
     An exhaust port for the inflation bag  301  may be included in several different ways. For example, valve  334  may be a three-way valve which fluidly couples blower  124  with line  328  during harvesting and fluidly couples line  328  with an exhaust line or atmosphere during a deflation of bag  301 , according to embodiments of the present invention. Alternatively, the bag  301  may include one or more small leak orifices formed therein, such that gas within the bag  301  leaks out of bag  301  more slowly than the rate at which blower  124  can supply gas to the bag  301 . This permits the bag  301  to fill when connected with blower  124 , while also permitting the bag to slowly deflate when blower  124  is turned off or disconnected, according to embodiments of the present invention. Based on the disclosure provided herein, one of ordinary skill in the art will recognize various other ways to exhaust bag  301 . 
       FIGS. 4-7  illustrate side elevation views of the photobioreactor bag  101  of  FIG. 1  in various stages during a harvesting operation, in which the blower  124 , lines  126 ,  128 ,  130 ,  132 , and the harvesting line  118  are omitted from the drawings for clarity, according to embodiments of the present invention. As shown in  FIG. 4 , the bag  101  begins submerged under water level  110 , due to the weight of the weight member  108  offsetting the buoyancy force created by the head space  103  and the bag  101 , according to embodiments of the present invention. 
     Once the valve  134  is opened and valve  136  closed, the end  104  of the bag  101  begins to accumulate air and floats further toward the top surface  110 , as illustrated in  FIG. 5 . According to some embodiments, this occurs when the buoyancy force of the air within the bag  101  exceeds the weight of the bag  101  and the weight member  108 . As shown in  FIG. 5 , the weight member, or support member,  108  is pivotally coupled to pivot  142 , which permits end  104  to rise while leaving end  106  submerged. When the end  104  rises toward and eventually floats at or above the water level  110  in the tank or reservoir  140 , the difference in height between end  104  and end  106 , and/or the dynamic motion of the end  104  swinging upward toward the surface  110 , creates a “dumping” effect which causes flow of the media  102  from end  104  toward end  106 , and thus toward the harvesting port  116  near or at end  106 , according to embodiments of the present invention. Furthermore, if any media  102  within the bag  101  were to end up above the water level  110 , enough media  102  will be displaced within the bag to cause the media level  105  to lower to a level at or near the surface liquid level  110 , according to embodiments of the present invention. Such media  102  will be displaced by draining through harvesting port  116 , according to embodiments of the present invention. 
     During or after the gravitational and/or dynamic “dumping” and fluid displacement occurs, the bag  101  begins to fill with air until the pressure within the bag  101  reaches the pressure at the depth of end  146  of exhaust line  138 , according to embodiments of the present invention. As illustrated in  FIG. 6 , the air accumulates within the bag  101  and increases the air pressure within the bag  101 , thereby displacing the media  102  below the surface level  110  and pushing it out of harvesting port  116 . Placing the end  146  of the exhaust line  138  at a depth at or below the depth of the harvesting port  116  from the surface  110  may enhance this air displacement effect during harvesting, because the air pressure in the bag  101  will build up to a degree sufficient to displace the media  102  until the depth difference between the media level  105  and the surface level  110  is at or near the depth difference between the end  146  and the surface level  110  (due, for example, to the pressure of the water in the reservoir surrounding the bag  101 ), according to embodiments of the present invention. 
     Placing the end  120  of the harvesting tube  118  at an atmospheric depth below the harvesting port  116  and/or the bottom of the bag  101  (or at a pressure otherwise lower than the pressure at the harvesting port  116 ) may enhance the harvesting process by creating a siphon effect for outward flow of media  102  through the harvesting line  118 , according to embodiments of the present invention. According to some embodiments of the present invention, a vacuum source such as, for example, a shop vac, may be placed in fluid communication with end  120  of harvesting tube  118  to enhance the siphoning or pressure differential effect, to facilitate harvesting. According to some embodiments of the present invention, the same pump or blower  124  used to blow gas into the bag  101  may also be used, simultaneously for example, to create a suction or negative pressure on the harvesting tube  118 . 
     According to alternative embodiments of the present invention, the weight member  108  may be releasably tethered to pivot  142  by a tether line  702 , which permits the entire end  106  of the bag  101  to float to the surface  110 , as illustrated in  FIG. 7 . The tether line  702  may instead be a mechanical linkage, such as, for example, a single bar pivotably coupled to base  142  and weight member  108 , according to embodiments of the present invention. Using a tether line or linkage may further enhance the gravitational displacement effect and require less air pressure for the harvesting process (e.g. lower depth of end  146  and/or lower power blower  124 ), according to embodiments of the present invention. According to some alternative embodiments of the present invention, the linear weight density of the weight member  108  varies between ends  104  and  106 , such that the weight member  108  is heavier toward end  106  and remains at or near the bottom  140  of the tank throughout the harvesting process while permitting end  104  to rise, even with or without a connection or tethering between weight member  108  and bottom  140 . According to some embodiments of the present invention, the linear weight density of the weight member  108  varies between ends  104  and  106 , such that the weight member  108  is heavier toward end  106  and remains at or near the bottom  140  of the tank throughout the harvesting process while permitting end  104  to rise, until the media  102  is almost completely drained from the bag  101 , at which point the buoyancy of the bag  101  lifts the entire weight member  108  toward the surface (similar to that depicted in  FIG. 7 ). 
     Once the media  102  has been drained and/or harvested from within the bag  101 , and/or once the bag  101  is empty or near empty, the bag  101  may be lowered back to the normal operating position by closing valve  134  and opening valve  136  to permit the accumulated air to exhaust through exhaust line  132 , according to embodiments of the present invention. The bag  101  may be refilled with media  102  such as, for example, through harvesting port  116  and/or through another port. The refilling of the bag  101  with media  102  may be done while the bag  101  is sinking back toward the bottom  140  of the tank to speed up the sinking process, or it may be added after the bag  101  is back to its original position, according to embodiments of the present invention. 
     As illustrated in  FIGS. 8 and 9 , a guide device  402  may be used below the weight member  108  and photobioreactor bag  101  to guide the bag  101  back into a desired position as it sinks. Multiple guide devices  402  (or a continuous guide groove or guide device) may be used along the length of, or at intervals along the length of, the weight member  108  from end  104  toward end  106 , according to embodiments of the present invention. Multiple guide devices  402  may also be used in parallel to guide more than one bag  101  back into place where the bags  101  are arranged in multiples next to each other, as illustrated in  FIGS. 10 and 11 . A linkage attached to the bottom of bag  101  and/or weight member  108  further assists the bag  101  in descending to its original or desired position, according to embodiments of the present invention. 
     According to some embodiments of the present invention, the bag  101  remains coupled with the bottom  140  of the reservoir along its length, and remains partially or wholly submerged throughout the harvesting process. Such a harvesting process may be accomplished by adding gas to the inside of the bag  101  to achieve a pressure that is high enough to push the media level  105  down and push the media  102  out of the harvesting tube  118 , according to embodiments of the present invention. According to other embodiments of the present invention, a combination of pressurizing of the inside of the bag  101  and floating the bag  101  upwards towards surface  110  may be used. 
       FIG. 10  illustrates a combined partial top view and partial side view of a series of photobioreactor bags  101  connected in parallel and an algae harvesting system  1000 , according to embodiments of the present invention. The exhaust system  1050  is shown in partial side view in  FIG. 10 . The bags  101  may be arranged in parallel in a tank (not shown) to maximize production and harvesting density, according to embodiments of the present invention. Algae harvesting system  1000  is capable of initiating the harvesting process of multiple bags  101  simultaneously. A common gas header  1002  connects each gas inlet line  126 , and a common exhaust header  1004  connects each exhaust line  130 , according to embodiments of the present invention. Line  1008  connects the header  1004  with exhaust system  1050 , which includes the exhaust lines  132  and  138 . Exhaust lines  132  and  138 , as described above, extend to different depths within tank  1006 , which may in some embodiments be the same tank in which the photobioreactor bags  101  are submerged, according to embodiments of the present invention. As described above with respect to FIGS.  1  and  4 - 6 , during normal operation valve  134  is closed and valve  136  is opened, and during harvesting, valve  134  is opened and valve  136  is closed. 
       FIG. 11  illustrates a combined partial top view and partial side view of a series of photobioreactor bags  101 ,  1101  and an alternative algae-harvesting system  1100 , according to embodiments of the present invention. The exhaust system  1150  is shown in partial side view in  FIG. 11 . Bags  101  and  1101  are arranged in parallel similarly to the bags  101  of  FIG. 10 ; however, two different back end systems permit the staggered harvesting of different groups of bags. During normal operation, valves  134  and  1134  are closed, and valves  136  and  1136  are open, and each bag  101  and  1101  operates as described with respect to  FIG. 1 . To harvest bags  101 , valve  134  is opened and valve  136  closed. To harvest bags  1101 , valve  1134  is opened and valve  1136  is closed. Harvesting adjacent bags in a staggered fashion may permit a higher degree of precision in returning the bags  101  and  1101  to their original starting positions and locations; for example, the bags  101  on either side of bag  1101  act as a kind of guide as bag  101  is deflated and permitted to sink back to its original position. Harvesting adjacent bags in a staggered fashion may also have less of an impact on the overall liquid level in the tank, and/or may facilitate harvesting with a harvesting tube  118  that has a limited flow rate, according to embodiments of the present invention. 
     Staggered and/or selective harvesting may also permit different bags to be harvested in different stages of algae growth and/or at different times. For example, bags  101  may contain an algae culture that is ready for harvesting, while bags  1101  may contain a young algae culture that still needs to grow. Although system  1100  is shown for staggered harvesting of two sets of bags  101 ,  1101 , one of ordinary skill in the art will appreciate that more than two sets of bags may be configured for staggered and/or selective harvesting, according to embodiments of the present invention. According to some embodiments of the present invention, one bag  101  at a time is selected for initiation of a harvesting cycle. 
       FIG. 12  illustrates a side elevation view of an alternative photobioreactor and algae-harvesting system  1200 , according to embodiments of the present invention. System  1200  is similar to system  100 . However, in system  1200 , line  128  is absent. System  1200  further includes a sparge tube  1202 , which may be a separate tube or formed integrally with bag  101 , and which is configured to deliver gas from blower  124  into the media  102  via bubbles  1204 , according to embodiments of the present invention. The gas bubbles  1204  may be delivered through apertures formed or cut into an outer surface of the sparge tube  1202 , according to embodiments of the present invention. Line  126  fluidly couples blower  124  with sparge tube  1202 , and line  130  is in fluid communication with another end of the sparge tube  1202 , according to embodiments of the present invention.  FIG. 13  illustrates a side cross sectional view of system  1200 , according to embodiments of the present invention. 
     To initiate a harvesting cycle, valve  136  is closed, thereby increasing the pressure at the end of the sparge tube  1202  nearest end  104 , and thereby causing the delivered gas  1204  to accumulate in the head space  103 . The accumulated gas eventually creates a buoyancy force which lifts end  104  toward the surface  110 , thereby causing the media  102  to begin flowing out of the harvesting tube  118 , as described with respect to  FIGS. 4-7 , according to embodiments of the present invention. Line  128  (see  FIG. 1 ), while optional, may be helpful in situations in which the flow rate of gas from the sparge tube  1202  into media  102  is not sufficient to cause a sufficiently rapid accumulation of gas within the bag  101 . 
     Although some embodiments of the present invention include pressure regulation systems that involve lines  132 ,  138  submerged to different depths under water in order to control the pressure within the photobioreactor bag  101 , one of ordinary skill in the art will recognize various other ways to control and/or vary the pressure on the exhaust end  104  of the photobioreactor bag  101 , according to embodiments of the present invention. However, using submerged lines  132 ,  138  at different depths also provides a built-in pressure relief feature, such that an air pressure within the bag that exceeds the pressure at the submerged end  146  will simply cause excess air to flow harmlessly out of the end  146 , while still maintaining the pressure (e.g. the depth) at end  146 , according to embodiments of the present invention. According to some embodiments of the present invention, ports  112 ,  114 , and/or  116 , though described as single ports, may be multiple ports and/or be connected to multiple gas sources and/or multiple exhaust lines. For example, line  126  may split into two lines and may enter bag  101  at two different ports  112 , one of which may be closer to end  106  than the other. 
     Various modifications and additions can be made to the exemplary embodiments discussed without departing from the scope of the present invention. For example, while the embodiments described above refer to particular features, the scope of this invention also includes embodiments having different combinations of features and embodiments that do not include all of the described features. Accordingly, the scope of the present invention is intended to embrace all such alternatives, modifications, and variations as fall within the scope of the claims, together with all equivalents thereof.