Patent Publication Number: US-7213439-B2

Title: Automatic bridge balancing means and method for a capillary bridge viscometer

Description:
BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   This invention relates to a bridge balancing method and to a thermally controlled stage that is connected within one arm of a capillary bridge viscometer so that the temperature of the one arm can be controlled to a different temperature than the temperatures of the other three arms. This allows the bridge be automatically balanced to provide accurate measurement signals. 
   2. Background Art 
   An example of a capillary bridge viscometer which is adapted to accurately measure the specific viscosity of a solute in a suitable solvent is available by referring to U.S. Pat. No. 4,463,598 issued Aug. 7, 1984. Such a capillary bridge viscometer is useful in determining the molecular parameters of a polymer including molar mass and hydrodynamic radius.  FIG. 1  of the drawings illustrates this well known capillary bridge viscometer. 
   The aforementioned patented differential viscometer includes a capillary bridge  50  that must be balanced to achieve accurate test results and a wide dynamic range. A solvent is usually supplied from a reservoir to the capillary bridge  50  by means of a low pulsation chromatography pump. Typically, the sensitivity of bridge  50  is limited by the pressure amplitude of the pump pulses. First and second capillaries  52  and  54  are connected in series between supply and discharge ports  60  and  62 . Third and fourth capillaries  64  and  66  are connected in series between the supply and discharge ports  60  and  62 . The series connected capillaries  52 ,  54 , and  64 ,  66  are connected in parallel with one another between the supply and discharge ports  60  and  62  to form a fluid analog of the well known Wheatstone (i.e., resistance) bridge in the electrical art. 
   A delay volume  72  is located in the fluid arm of bridge  50  which contains the capillary  66 . The delay volume  72  is constructed so as to have a negligible flow impedance, but a large internal volume. A differential pressure transducer  74  is connected in the capillary bridge  50  to measure the differential pressure across the bridge when different fluids are flowing through the capillaries thereof. Another differential transducer  75  is connected between the supply and discharge ports  60  and  62  to measure the pressure from the inlet to the outlet sides of the bridge. Typically, a zero reading of the pressure transducer  74  provides an indication that the bridge  50  is in balance. 
   In the traditional method for mechanically tuning the bridge  50 , the length of one fluid arm of the bridge is changed by disassembling the bridge and precisely cutting off (or adding) a length of tubing. This is generally tedious and time consuming. Moreover, some fluid samples such as proteins, and the like, are known to stick to the fluid tubing which causes the original tuning to slowly drift with time. In this case, the fluid tubing must be cleaned out and flushed by the operator or a periodic rebalancing will otherwise be required. In the alternative, the viscometer will have to be returned to its manufacturer to be serviced. In either case, the viscometer will be rendered temporarily out of use with the consequence that fluid sample testing will be inefficiently delayed. What would be desirable is an improved balancing technique that is equivalent in effect to the mechanical balancing, but can be accomplished automatically and more accurately, as required, and without disassembly of the system. 
   SUMMARY OF THE INVENTION 
   Instead of varying the length of one fluid arm of a capillary bridge viscometer as has been accomplished in the past, an independently controlled thermal stage is connected within at least one arm of the bridge to achieve the desired balance. The thermal stage includes a tuning capillary tubing portion that is wrapped around a thermally conductive (e.g., brass or copper) core. The core and the tuning capillary tubing portion wrapped therearound are isolated from the other fluid arms of the bridge within an insulated thermal housing. 
   A (e.g. resistance) heater or a Peltier thermoelectric device is located within the thermal housing to lie in close thermal contact with the tuning capillary tubing portion. A temperature probe is also located within the housing so as to be responsive to the temperature of the capillary tubing portion. With the bridge of the capillary bridge viscometer initially out of balance, the power to the heater or Peltier device is adjusted to cause a change (i.e., either heating or cooling) in the temperature of the capillary tubing portion. As the temperature of the capillary rises or falls, the viscosity of the fluid in the capillary and the associated pressure drop across the fluid arm is correspondingly changed. Accordingly, the sum of the pressures in the fluid arm in which the tuning capillary tubing portion is connected is likewise changed. The temperature of the capillary tubing portion in the thermal housing of the thermally controlled stage is monitored until the pressure differential across the bridge is trimmed to 0, whereby the bridge will now be in balance so as to enable the viscometer to provide accurate measurement signals and the widest operating range. Once balanced, the temperature of the thermally controlled turning capillary is held constant. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  shows a conventional bridge of the type that is common to a capillary bridge viscometer; 
       FIG. 2  shows details of a thermally controlled stage that is added to one arm of the bridge of  FIG. 1  and that includes a heater to achieve an accurate and automatic balancing thereof; 
       FIG. 3  shows details of another thermally controlled stage that is added to one arm of the bridge of  FIG. 1  and that includes a Peltier thermoelectric device to allow either heating or cooling; and 
       FIG. 4  shows an alternate embodiment where several arms of the bridge of  FIG. 1  are independently thermally controlled. 
   

   DESCRIPTION OF THE PREFERRED EMBODIMENT 
   Disclosed herein is an automatic bridge balancing method and means for a capillary bridge viscometer. Viscosity is known to be a strong function of temperature. Therefore, it is contemplated to control the temperature of the fluid arms of the bridge viscometer to insure that the only pressure differences measured are due to changes in the composition of the sample rather than to thermally induced variations of the viscosity. The present improvement relies on using this strong temperature dependence as a tuning method. 
   Rather than attempting to mechanically tune the bridge  50  of  FIG. 1  while encountering the inconvenience and time delay associated with changing the length of one fluid arm thereof to constantly keep the bridge in balance, it has been discovered that the bridge may be balanced by heating or cooling the arm. More particularly, instead of adjusting the length of a fluid tubing line to tune the bridge, it has been found that a more efficient approach is to heat or cool one arm of the bridge, or a portion thereof, to achieve the desired balance. 
   Referring now to  FIG. 2  of the drawings, there is shown one fluid tubing arm  10  of a capillary bridge viscometer that is to be substituted for the fluid tubing arm from the bridge  50  shown in  FIG. 1  within which the aforementioned fluid sample delay volume  72  is connected. In accordance with the preferred improvement, the capillary tubing portion  66  of the bridge  50  of  FIG. 1  is replaced by a thermally controlled stage containing a thermally tuned capillary tubing portion  18 . The new capillary tubing portion  18  is manufactured from a thermally conductive material having a flow impedance. Capillary tubing portion  18  is wrapped around a thermally conductive (e.g., brass or copper) core  20  that is isolated from the other fluid tubing arms within a thermally insulated housing  22  of the thermally controlled stage. Although the core  20  is illustrated in  FIG. 2  as a cylinder, it is to be understood that the core may have any other shape (e.g., a spool, cube, plane, etc.) that will facilitate the capillary tubing portion  18  being wrapped therearound and a soon to be described heating or cooling device being anchored thereto. In this same regard, while the preferred embodiment of the capillary tubing portion  18  is shown in  FIG. 2  as a coil that is wound around the core  20 , the capillary tubing portion  18  may have other suitable configurations so as to maximize its thermal contact with the core  20 . 
   In the bridge balancing configuration and technique of  FIG. 2 , the tuning capillary tubing portion  18  is located downstream (i.e., closer to the discharge port  62  of the bridge) from the fluid sample delay volume  72 . A (e.g., resistance) heater  24  is located within the thermal housing  22  of the thermally controlled stage so as to be anchored in close proximity to the core  20 . A temperature probe  26  (e.g., a thermocouple) is also located within housing  22  so as to be responsive to the temperature of capillary tubing portion  18 . It is preferable that temperature probe  26 , like heater  24 , be anchored in close proximity to the core  20  so as to be able to accurately measure the temperature of the capillary  18 . 
   The measurement begins by establishing a flow of solvent though the viscometer bridge and waiting until the outputs of the bridge transducers (designated  74  and  75  in  FIG. 1 ) become stable. Initially, the output of the differential pressure transducer  74  is usually not zero which indicates that the bridge is out of balance. This imbalance can be caused by small imperfections of construction or changes in the inner diameter of the tubing due to the contaminating effects of previous measurements. Alternatively, the bridge can be intentionally imbalanced during construction so that thermal balancing method herein disclosed may be used to controllably bring the bridge into balance. 
   Adjusting the power to the heater  24  varies the temperature of the tuning capillary tubing portion  18  in fluid arm  10  that is wrapped around core  20  within the thermal housing  22 . As the temperature rises, the viscosity of the fluid flowing through the tuning capillary tubing portion  18  is correspondingly decreased, and the pressure drop across the arm  10  is correspondingly reduced. The bridge is brought into balance by monitoring the output of the differential pressure transducer  74  extending across the bridge  50  of  FIG. 1 . When the transducer  74  reads zero, the bridge in which the arm  10  is connected will be suitably balanced. The temperature measured by temperature probe  26  is then maintained constant by adjusting the output power of heater  24 . The bridge  50  is now ready to receive one or more test samples. After the samples have fully exited the bridge, the system may be retuned, at the operator&#39;s discretion. 
   It will now be demonstrated that this method of balancing the bridge does not negatively impact the accuracy of the measurement. In the fluid analog of the Wheatstone bridge represented by  FIG. 1 , the non-turbulent mass flow through a capillary is given by Poiselle&#39;s law: 
                   Q   =       Δ   ⁢           ⁢   p       R   ⁢           ⁢   η         ,           (   1   )               
where Q, is the mass flow rate though the each tube, Δp is the pressure across the tube, η is the viscosity of the fluid flowing through the tube, and R is the flow impedance of the tube defined by:
 
                   R   =       8   ⁢   l       π   ⁢           ⁢     r   4           ,           (   2   )               
where l is the length the tube and r is the inner radius of the tube. When connected in this configuration with all of the arms of bridge  50  having an identical flow impedance, the bridge viscometer measures the specific viscosity from measurements of the two differential transducers  74  and  75  as:
 
                     η   sp     =         η     η   0       -   1     =       4   ⁢   Δ   ⁢           ⁢   p       IP   -     2   ⁢   Δ   ⁢           ⁢   p             ,           (   3   )               
where η sp  is the specific viscosity, η is the viscosity of the sample under test, η 0  is the solvent viscosity, Δp is the measurement of the transducer  74 , and IP is the measurement of the transducer  75 .
 
   Mathematical consideration is now given in order to evaluate whether the process of thermal tuning, or the effect of connecting non-identical flow impedances in the bridge arms, affects the accuracy of the resulting measurement. It can be easily shown that when solvent is flowing through all arms of the temperature regulated bridge  50 , the ratio of the pressures measured in the two transducers  74  and  75  is given by: 
                       Δ   ⁢           ⁢   p     IP     =       1     1   +       R   52       R   54           -     1     1   +         η   0       η   T       ⁢       R   64       R   66                 ,           (   4   )               
where η T  is the viscosity of the solvent passing through the thermally controlled tuning arm R 66 .
 
When the bridge  50  is balanced, Δp=0, which implies the corresponding balance condition:
 
                       R   52       R   54       =         η   0       η   T       ⁢       R   64       R   66           ,           (   5   )               
where the ratio R 52 /R 54 ≡y, for purposes of simplification. Clearly when the temperature of the thermally controlled stage containing R 66  is identical to the rest of the bridge (i.e. θ T =η 0 ), this reduces to the traditional Wheatstone bridge balance condition. When the sample with viscosity θ s  is introduced to the viscometer, it passes through arms R 64 , R 52 , and R 54 . However, since the delay reservoir  72  is filled with solvent, R 66  is supplied with solvent at the control temperature with viscosity η T . Therefore the ratio of the transducer pressures is now given by:
 
                     Δ   ⁢           ⁢   p     IP     =       1     1   +       R   52       R   54           -       1     1   +         η   s       η   T       ⁢       R   64       R   66             .               (   6   )               
In terms of y, the Equation (6) is simplified to:
 
                     Δ   ⁢           ⁢   p     IP     =       1     1   +   y       -       1     1   +         η   s       η   0       ⁢   y         .               (   7   )               
This simplified Equation (7) can be solved for the specific viscosity, defined as η sp ≡η s /η 0 −1, as:
 
                   η   sp     =         Δ   ⁢           ⁢       p   ⁡     (     1   +   y     )       2           [     IP   -     dp   ⁡     (     1   +   y     )         ]     ⁢   y       .             (   8   )               
Accordingly, if the y parameter is known, precise measurements of the specific viscosity can be made. However, because no manufacturing process is perfect, the y parameter is typically not known a priori and is difficult to measure accurately. Assume that the resistances R 52 ˜R 54  are nearly equal so that one may write y=1+ε, were ε is a small parameter. In this case, the Equation (8) can be rewritten as:
 
                   η   sp     =         4   ⁢   Δ   ⁢           ⁢   p       IP   -     2   ⁢   Δ   ⁢           ⁢   p         +         4   ⁢   Δ   ⁢           ⁢     p   2           (     IP   -     2   ⁢   Δ   ⁢           ⁢   p       )     2       ⁢   ɛ     +       O   ⁡     (     ɛ   2     )       .               (   9   )               
This is a fundamental result. Alternatively, this same result may be written as
 
                         η   sp     ⁡     (   ɛ   )           η   sp     ⁡     (     ɛ   =   0     )         =     1   +       ɛ   4     ⁢       η   sp     ⁡     (     ɛ   =   0     )         +     O   ⁡     (     ɛ   2     )           ,           (   10   )               
where η sp (ε=0) is the true value of the specific viscosity that would be measured by an ideal bridge. This result implies that if the ε correction for a non-ideal bridge is neglected, only a percentage error in the order of εη sp /4 is incurred. Since the range of specific viscosities that are measured by online bridge viscometers is typically much less than 1 and the bridges are typically manufactured so that ε is much less than 1, this error is of a second order in magnitude and can safely be neglected. However, this analysis assumes that the bridge  50  has been thermally balanced in the manner described above.
 
   The presence of a thermally controlled tuning stage like that shown in  FIG. 2  also allows a new method of operation of the differential viscometer. Typically, the bridge is tuned before the sample has been introduced to the instrument when only solvent is flowing though both sides of the bridge. The temperatures are then held constant when the sample is introduced. The specific viscosity is measured from the imbalance pressure as described earlier in Equation (3). However, by virtue of the present improvement, it is now possible to instead adjust the temperature of the tuning element (e.g., capillary  18 ) of the bridge to keep the bridge in balance while the sample elutes. The temperature is now adjusted to servo the differential pressure transducer  74  to zero without going into saturation. In this case, the temperature difference between the bridge and the tuning length becomes a measure of the specific viscosity represented by: 
                     η   sp     =         1     η   0       ⁢       ⅆ   η       ⅆ   T         ⁢     ❘     T   0       ⁢       (     T   -     T   0       )     +       O   ⁡     (     T   -     T   0       )       2           ,           (   11   )               
where, T 0  is the original tuning temperature, T is the time dependent temperature required to maintain Δp=0. This method requires the temperature control system to be able to change the temperature of the tuning capillary  18  rapidly enough to always keep Δp=0. It also requires a priori knowledge of a new parameter
 
   
     
       
         
           
             
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   It is to be recognized that it is within the scope of this improvement to cool (rather than heat) the core  20  within the housing  22  to increase the pressure drop of the capillary  18  and the total pressure of the arm  10  so as to trim in the balance of the bridge. In this case, a Peltier thermoelectric device, rather than the heater  24  of  FIG. 2 , will be located in close thermal contact with the capillary  18  and/or the core  20  to provide thermal regulation of the capillary  18  in fluid arm  10  relative to the other bridge arms. More particularly, and turning to  FIG. 3  of the drawings, there is shown the addition of a conventional Peltier thermoelectric device  23 , one side of which lies in close thermal contact with the thermally conductive core  20  around which the thermally tuned capillary  18  is wound within the thermally insulated housing  22 . The opposite side of the Peltier device  23  is coupled to a heat sink  24  located outside housing  22  to vent excess heat to the atmosphere. 
   Such a Peltier device  23  as that shown in  FIG. 3  can also heat as well as cool the thermally controlled capillary  18 . The additional benefit that a Peltier device confers is the ability to servo the thermally controlled capillary  18  to nearly the same temperature as the rest of the bridge, whereas the heater  24  of  FIG. 2  can only regulate the temperature of the controlled capillary at a higher temperature than the rest of the bridge. The heater method therefore requires that the controlled capillary have an initially higher flow impedance than would otherwise be required for balancing, so that the heater may lower the resistance to the correct value. 
   In the bridge balancing embodiments shown in  FIGS. 2 and 3 , a single fluid arm  10  of the bridge  50  (of  FIG. 1 ) containing the fluid sample delay volume  72  is thermally controlled. In this case, a thermally controlled stage including a thermally tuned capillary  18  is connected in the arm  10  and isolated from the other arms within housing  22 . However, it is also within the scope of this invention to thermally control several arms of a bridge  50 - 1  in the manner to be described while referring to  FIG. 4  of the drawings. That is to say, and as an alternate embodiment of this invention, other thermally tuned capillaries (designated  52 , and  64  in FIG.  4 ) having equivalent flow impedances can be connected into respective other fluid arms of the bridge  50 - 1  and temperature regulated in the same manner as that described above. In this case, there will be two independently controlled thermal stages. A first independently controlled stage includes capillaries  52 ,  54  and  64  located in a thermally controlled space  76 . The second independently controlled stage includes the aforementioned capillary  18  located in thermally controlled space  22 . The relevant control parameter is the temperature difference between the two stages  22  and  76 . In this manner, the bridge stability is improved inasmuch as the flow impedances of capillaries  52 ,  54  and  64  are not subject to changes in ambient temperature. 
   Lastly, although one may thermally regulate an entire bridge arm, it is also possible to thermally regulate a section of one of the bridge arms. The remainder of the control arms is thermally anchored to the other bridge arms. In this manner, the effect of thermal noise which may be inadvertently injected into the control stage is minimized, but the analysis above is unchanged.