BACKGROUND OF THE INVENTION In a scanning capillary tube viscometer, a U-shaped tube is used where one portion of the U-shaped tube is formed by a flow restrictor, e. g., capillary tube. One leg of the U-shaped tube supports a falling column of fluid and the other leg supports a rising column of fluid Furthermore, movement of either one or both of these columns is monitored, hence the term"scanning."See Fig. 1. It should be understood that the term"scanning,"as used in this Specification, also includes the detection of the change in mass (e. g., weight) in each of the columns. Thus, all manners of detecting the change in the column mass, volume, height, etc. is covered by the term "scanning." In order to measure liquid viscosity using a U-shaped scanning capillary tube viscometer, the pressure drop across the capillary tube has to be precisely estimated from the height difference between the two fluid columns in the respective legs of the U-shaped tube. However, under normal circumstances, the height difference, th (t), contains the effects of surface tension and yield stress. Therefore, the contributions of the surface tension (that) and yield stress (ry) to th (t), have to be taken into account, or isolated. Here, Ah (t) is equal to h1 (t)-h2 (t).

The magnitude of the surface tension of a liquid in a tube differs greater depending on the condition of the tube wall. Normally, the surface tension reported in college textbooks are measured from a perfectly wet tube. However, in reality, the falling column has a perfectly wet surface while the rising column has a perfectly dry surface. When the tube is completely dry, the value of the surface tension from the same tube can be substantially different from that measured from a perfectly wet tube.

Hence, there is a pronounced effects of the surface tension on the overall height difference between the two columns. The height difference caused by the surface tension can be significantly greater than the experimental resolution required for the accuracy of viscosity measurement. For example, the difference between surface tensions of two columns in the U-shaped tube can produce the height difference, Ahst, of 3.5 mm where the height difference, Ah (t), must be measured as accurately as 0.1 mm. Thus, it is extremely important to isolate the effect of the surface tension from the viscosity measurement.

Similarly, the effect of yield stress, ry, must be isolated from the viscosity measurement.

Thus, there remains a need for accounting for, or isolating, the surface tension and yield stress in viscosity measurements when using a scanning capillary tube viscometer.

SUMMARY OF THE INVENTION A method for isolating the effect of surface tension on a fluid that is flowing in a U-shaped tube having a flow restrictor (e. g., a capillary tube) forming a portion of said U-shaped tube. The fluid forms a falling column of fluid, having a first height that changes with time, in a first leg of the U-shaped tube and a rising column of fluid, having a second height that changes with time, in a second leg of said U-shaped tube.

The method comprises the steps of: (a) detecting the difference between the first and second heights overtime; and (b) subtracting a term representing surface tension from the difference.

A method of isolating the effect of surface tension on a fluid and the effect of yield stress of a fluid that is flowing in a U-shaped tube having a flow restrictor forming a portion of said U-shaped tube. The fluid forms a falling column of fluid, having a first height that changes with time, in a first leg of said U-shaped tube and a rising column of fluid, having a second height that changes with time, in a second leg of said U- shaped tube. The method comprises the steps of: (a) detecting the difference between the first and second heights over time for generating falling column data and rising column data; (b) curve fitting an equation using the falling column data and the rising column data to determine: (1) a term representing surface tension; and (2) a term representing the yield stress.

DESCRIPTION OF THE DRAWINGS The invention of this present application will be readily appreciated as the same becomes better understood by reference to the following detailed description when considered in connection with the accompanying drawings wherein: Fig. 1 is a functional diagram of a test fluid flowing in a U-shaped tube having a flow restrictor therein and with column level detectors and a single point detector monitoring the movement of the fluid ; and Fig. 2 is a graphical representation of the height of the respective columns of fluid over time in the two legs of the U-shaped tube.

DESCRIPTION OF THE PREFERRED EMBODIMENT OF THE INVENTION Referring now in detail to the various figures of the drawing wherein like reference characters refer to like parts, there is shown at 20 a U-tube structure comprising a first leg (e. g., a first riser tube) R1, a flow restrictor 22 (e. g., a capillary tube) and a second leg (e. g., second riser tube) R2. It should be understood that the preferred embodiment of the U-tube structure has the flow restrictor forming the horizontal portion at the bottom of the U-tube that connects the two legs together.

However, it is within the broadest scope of this invention to include the positioning of the flow restrictor in either one of the legs themselves.

The apparatus 20 uses column level detectors 54/56 for detecting the movement (e. g., the heights, h) of the columns of fluid in the legs of the U-tube: a falling column of fluid 82 and a rising column of fluid 84, as indicated by the respective arrows 83 and 85. The details of such types of detectors are disclosed in A. S. N.

09/439,795, filed on November 12,1999 and A. S. N. 09/573, 267, filed on May 18, 2000, both of which are entitled DUAL RISER/SINGLE CAPILLARY VISCOMETER, both of which are assigned to the same Assignee of the present invention, namely Visco Technologies, Inc. and both of whose entire disclosures are incorporated by reference herein. Thus, the details of these detectors are not repeated here.

Furthermore, although not shown in Fig. 1, but disclosed in these other applications, the column level detectors 54/56 communicate with a computerfor processing the data collected by these detectors.

It should be understood that it is within the broadest scope of this invention to include the monitoring of only one of the columns of fluid 82 or 84 while obtaining a single point from the other one of the columns of fluid 82 or 84 using a single point detector 954 (which also communicates with the computer mentioned previously). In particular, as shown in Fig. 2, since the rising and falling columns 82/84 exhibit a symmetry about a horizontal axis, it is possible to monitor only one of the columns of fluid while obtaining a single data point from the other column. For example, as shown in Fig. 1, the column level detector 56 can be used to monitor the rising column 84 while the single point detector 954 can be used to detect any one point of the falling column 82 in R1.

In the preferred embodiment, the U-tube structure 20 is in an upright position; the test fluid is entered into the top of one of the legs (e. g., R1) while the top of the other leg (e. g. R2) is exposed to atmospheric pressure. Using this configuration, the test fluid is subjected to a decreasing pressure differential that moves the test fluid through a plurality of shear rates (i. e., from a high shear rate at the beginning of the test run to a low shear rate at the end of the test run), which is especially important in determining the viscosity of non-Newtonian fluids, as set forth in A. S. N. 09/439,795 and A. S. N. 09/573,267. However, it should be understood that it is within the broadest scope of this invention to include any other configurations where the test fluid can be subjected to a decreasing pressure differential in order to move the test fluid through a plurality of shear rates.

As disclosed in those patent applications, the height vs. time data that was generated is shown in Fig. 2, where as time goes to infinity a constant separation between the column heights, known as Ah-can be attributed to surface tension Ah, t and/or yield stress zy. The present application provides a method for determining the individual effects of these two parameters. In particular, the present application discloses a mathematical method to isolate both the effects of surface tension and yield stress of a test fluid from the pressure drop created by the height difference between the two columns of test fluid in respective legs of the U-shaped tube.

The method begins with the conservation of energy equation which can be written in terms of pressure as follows : P1+1/2#V12+#gh1(t)=P2+1/2#V22+#gh2(t)+#Pc+#g#hst (1) where Pi and P2 : hydro-static pressures at fluid levels at the two columns 82/84 in the U- shaped tube ; p : density of fluid ; g: gravitational acceleration ; V1 and V2 : flow velocities of the two columns of fluid 82/84 in the U-shaped tube; h, (t) and h2 (t): heights of the two columns of fluid 82/84 in the U-shaped tube; , (t): pressure drop across the capillary tube 22; #hst : additional height difference due to surface tension; Since P1 and P2=Patm and |VI V2|, equation (1) can be reduced to the following : #Pc(t)=#g[h1(t)-h2(t)-#hst] This last equation demonstrates that the effect of the surface tension is isolated by subtracting Aht from the height difference, h1 (t)-h2 (t), between the two columns of fluid 82/84 in the U-shaped tube; the yield stress #y will be addressed later. Thus, the pressure drop across a capillary tube 22 can be determined as shown in Equation (2).

Later, Ah, t is determined through curve fitting of the experimental data of h, (t) and h2 (t).

It should be understood that Equation 2 is valid regardless of the curve-fitting model selected, i. e., power-law, Casson, or Herschel-Bulkley model. Furthermore, as used throughout this Specification, the phrase"curve fitting"encompasses all manners of fitting the data to a curve and/or equation, including the use of"solvers", e. g., Microsoft's Excel Solver that can solve for a plurality of unknowns in a single equation from data that is provided.

When a fluid exhibits a yield stress (#y), the height difference between the two fluid columns of the U-shaped tube is greatly affected by the yield stress particularly at low shear operation. Accordingly, the effect of the yield stress also must be taken into account (i. e., isolated) in orderto accurately estimate the pressure drop across the capillary tube. In order to handle the yield stress term, one needs to start with a constitutive equation such as the Casson or Herschel-Bulkley model. These constitutive models have a term representing the yield stress as set forth below : Casson model : y = 0, when z < where z is shear stress, y is shear rate, #y is the yield stress, and k is a constant.

Herschel-Bulkley model : #=#y+k#n when ###y y = 0, when # <#y where k and n are model constants.

It should be noted that the power-law model does not have the yield stress term.

Thus, it does not have the capability of handling the effect of yield stress.

For both the Casson and Herschel-Bulkley models, the pressure drop across the capillary tube 22, AP, (t), can be expressed as follows : #Pc(t)=#g[h1(t)-h2(t)-#hst] As time goes to infinity, this equation can be written as #Pc(#)=#g[h1(#)-h2(#)-#hst] where APc (#) represents the pressure drop across the capillary tube 22 as time goes to infinity, which can be attributed to the yield stress, #y, of the test fluid. There is a relationship between the yield stress, #y, and APc (#), which can be written as: <BR> <BR> <BR> <BR> <BR> <BR> <BR> #y = #Pc (#) # (5)<BR> <BR> <BR> <BR> <BR> 2L where R and L are the radius and the length of the capillary tube 22, respectively.

To obtain the AhSt and ry, two alternative approaches can be used. In the first approach, these two parameters are obtained sequentially, i. e., Equation 4 is curve- fitted using the experimental data of h1 (t) and h2 (t) data and solved for Ahst ; then the determined value for Ahst is plugged into Equation 5 and solved for #y.

Alternatively, in the second approach, both Ah, t and the yield stress ry can be determined directly from the curve fitting of the experimental data of h, (t) and h2 (t), as set forth below. As mentioned previously, in order to handle the yield stress #y, a constitutive equation is required, which has a term representing the yield stress.

Examples of such a constitutive equation include Casson and Herschel-Bulkley models, although these are only by way of example and not limitation. In particular, the procedure for curve-fitting the column height data with either a Casson model or a Herschel-Bulkley model is as follows : From the falling column of fluid 82, hi (t), and the rising column of fluid 84, h2 (t), one can obtain the flow velocities of the two columns by taking the derivative of each height, i.e., <BR> <BR> <BR> dh1(t)<BR> <BR> V1= and (6) dt <BR> <BR> <BR> <BR> <BR> dt<BR> <BR> dt Since the flows in the two columns of the U-shaped tube move in the opposite directions, one can determine the average flow velocity at the riser tube, by the following equation: Since the scanning capillary tube viscometer collects h, (t) and h2 (t) data over time, one can digitize the h1 (t) and h2 (t) data in the following manner to obtain the average flow velocity at the riser tube: d(h1(t)-h2(t)) (h1(t+#t)-h2(t+#t))-(h1(t-#t)-h2(t-#t))<BR> =<BR> <BR> <BR> <BR> dt 2#t In order to start a curve-fitting procedure, a mathematical description of Vr is required for each model : 1. Casson model #=0, when #<#y where # is shear stress, # is shear rate, #y is the yield stress, and k is a constant.

Wall shear stress (#w) and yield stress (#y) can be defined as follows: <BR> <BR> <BR> <BR> <BR> #Pc(t)#R<BR> <BR> <BR> <BR> #w=,<BR> <BR> <BR> <BR> <BR> <BR> <BR> <BR> <BR> <BR> 2L<BR> #Pc(t)#ry(t) #Pc(#)#R<BR> <BR> #y= (evaluated as time goes to #) =,<BR> 2L 2L where R and L are the radius and length of a capillary tube, respectively, and ry(t) is the radial distance, where shear stress (#) is bigger than yield stress (#y).

Using the above equations, the velocity profile at the capillary tube 22 can be calculated as follows: According to the definition of shear rate, y, the expression of the shear rate is defined as: In order to calculate the average flow velocity at either riser tube (Vr), the flow rate at a capillary tube 22 needs to be determined first. The flow rate at the capillary tube 22 can be obtained by integrating the velocity profile over the cross-section of the capillary tube 22 as: Since Q (t) = zRr2Yr, the mean flow velocity at the riser tube can be calculated as follows : where Rr is the radius of either riser tube. Thus, a mathematical description for Vr for Casson model case is obtained.

Using a curve-fitting model (e. g., the Microsoft Excel Solver), the unknown variables can be determined. For the Casson model, there are three unknown variables, which are the model constant, k, the contribution of the surface tension Ahst and the yield stress #y. It should be noted that the unknown variables are constants, which will be determined from the curve-fitting of experimental data of AP, (t). It should also be noted that APc (t) essentially comes from h, (t) and h2 (t) 2. Herschel-Bulkley model #=#y+k#n when ###y y = 0, when #<#y where k and n are both model constants.

In a similar method as for the case of Casson model, the velocity profile at the capillary tube 22 can be derived for the Herschel-Bulkley model as follows : The flow rate at capillary tube 22 can be obtained by integrating the velocity profile over the cross-section of the capillary tube 22 as: ry(t)<BR> whereCy(t)=, which is used for convenience.<BR> <BR> <BR> <BR> <P> R Since Q(t) = #Rr2#r, where Rr is the radius of either riser tube. Thus a mathematical description for Vr for the Herschel-Bulkley model case is obtained. Using a curve-fitting model (e. g., Microsoft Excel Solver), the unknown variables can be determined. For the Herschel- Bulkley model, there are four unknown variables, which are the two model constants, n and k, the contribution of the surface tension, Ah, t, and yield stress zy. Again, it should be noted that the unknown variables are constants, which will be determined from the curve-fitting of experimental data of AP, (t) essentially comes from/ (t) and h2 (t).

It should be understood that the above disclosed methodology, including the equations, curve fitting, etc., can be implemented on the computerthat communicates with the column level detectors 54/56 and/or the single point detector 954.

It should also be understood that the actual position of the flow restrictor 22 is not limited to the horizontal portion of the U-shaped tube; the flow restrictor 22 could form a portion of either leg of the U-shaped tube as shown in A. S. N. 09/439,795 and A. S. N. 09/573,267.

Without further elaboration, the foregoing will so fully illustrate our invention that others may, by applying current or future knowledge, readily adopt the same for use under various conditions of service.