Abstract:
A method and apparatus for monitoring during dynamic processes that determines when effective measurements of thermal effusivity and/or thermal conductivity can be made during a portion of a cycle during a calibration phase, then measures thermal effusivity and/or thermal conductivity during a subsequent dynamic process in dependence upon the time delay value and the measurement duration value until a desired value is obtained. A sensor having a measurement period of between one of two seconds allows monitoring of materials during dynamic processes such as tumbling, blending, mixing, and rocking. For example, measurements can be made until a value indicative of a desired mixture condition is obtained.

Description:
FIELD OF THE INVENTION 
       [0001]    The present invention relates to methods and apparatuses for monitoring materials and is particularly concerned with monitoring during dynamic processes. 
       BACKGROUND OF THE INVENTION 
       [0002]    A sensor for monitoring materials is taught in the applicant&#39;s U.S. Pat. No. 5,795,064, issued Aug. 18, 1998 to Mathis, the entire disclosure of which is hereby incorporated by reference. This sensor provides a non-destructive test due to the surface measurement and interfacial nature of the sensor interaction with the sample. The sensor measures a materials effusivity (the square root of thermal conductivity, density and heat capacity). 
         [0003]    The sensor of the above identified patent can also be used for direct measurement of thermal conductivity as taught is the applicant&#39;s U.S. Pat. No. 6,676,287, the entire disclosure of which is hereby incorporated by reference. 
         [0004]    Referring to  FIG. 1  there is illustrated a known material monitoring sensor. The sensor  10  includes a hot wire  12  and guard heaters  14 . 
         [0005]    Referring to  FIG. 2  there is illustrated heat flow from the sensor of  FIG. 1 . 
         [0006]    In operation, a known quantity of electrical current is passed through the heating elements  12  and  14  of the sensor for a known time. This results in a temperature rise at the sensor/sample interface and, over time, a heat flow from the sensor into the sample. The sensor functions by measuring the temperature rise at the sensor/sample interface over time. The heat transfer properties of the sample profoundly affect the rate of this temperature rise. If the sample is a good thermal insulator, then as heating continues, very little heat is conducted away from the sensor/sample interface and the temperature at the interface rises very quickly. If the sample is a good heat conductor, then as the heating continues, the heat is conducted away from the sensor/sample interface and the temperature at the interface rises very slowly. 
         [0007]    The heating elements and control mechanisms are designed to keep the sensor/sample interface temperature rise within certain boundaries. Temperature rise can also be controlled by adjusting the test time. A calibration curve is constructed by performing tests on standard materials with known thermal effusivity and/or thermal conductivity. Once the calibration curve is determined, samples are tested under identical experimental conditions, and the rate of temperature change at the sensor/sample interface is translated directly into thermal effusivity and/or thermal conductivity. 
         [0008]    The sensor for  FIG. 1  uses tightly controlled heating at the surface of a sample to make direct measurements of thermal effusivity and/or thermal conductivity. The apparatus applies a known quantity of heat for a known time to the surface of a sample. During testing, three basic things happen to the applied heat: some of the heat goes into the backing material, most of the heat goes into the sample, and some of the heat goes nowhere and causes a localized temperature increase at the sensor/sample interface. The magnitude of the temperature rise at the sensor/sample interface can be quantitatively converted to thermal effusivity and/or thermal conductivity because the rise is completely dependent on the heat transfer properties of the material. As shown in  FIG. 2 , the heat flow from the hot wire  12  into a material being tested is initially straight as indicated by an arrow  16 , due to the heat flow from the guard heaters  14  as indicated by curved arrows  18 . However, the heat flow then diverges as indicated by arrows  20 . 
         [0009]    Consequently, the sensor is highly suitable for static measurements as the sensor must remain in stable contact with the material being measured. Unfortunately, many processes in which material measurements are desirable are dynamic in nature. 
         [0010]    While providing a valuable tool for sample measurement, the sensor&#39;s structure and geometry result in a measurement period in the order of two to ten seconds. For processes such as mixing, using for example a V blender, the blender must be stopped in a particular orientation to allow the material being mixed to settle and to contact the sensor in order to take a reading. This results in a time delay for each measurement, which cumulatively adds to the total mixing time and actually disturbs the mixing process. 
         [0011]    Consequently, there is a need in the prior art for a method and apparatus for monitoring materials during dynamic processes. 
       SUMMARY OF THE INVENTION 
       [0012]    An object of the present invention is to provide an improved method and apparatus for monitoring materials. 
         [0013]    In accordance with an aspect of the present invention there is provided apparatus for monitoring during a dynamic process comprising: means for measuring effusivity during a portion of a rotation period; means for determining inflection points therefrom; means for determining a time delay value and a measurement duration value from the inflection points; and means for measuring effusivity during a subsequent dynamic process in dependence upon the time delay value and the measurement duration value until a value indicative of a desired mixture condition is obtained. 
         [0014]    In accordance with another aspect of the present invention there is provided a method of monitoring during a dynamic process comprising the steps of: measuring effusivity during a portion of a rotation period; determining inflection points therefrom; determining a time delay value and a measurement duration value from the inflection points; and measuring effusivity during a subsequent dynamic process in dependence upon the time delay value and the measurement duration value until a value indicative of a desired mixture condition is obtained. 
         [0015]    In accordance with another aspect of the present invention there is provided an apparatus for monitoring during a dynamic process comprising: means for measuring thermal conductivity during a portion of a cycle; means for determining inflection points therefrom; means for determining a time delay value and a measurement duration value from the inflection points; and means for measuring thermal conductivity during a subsequent dynamic process in dependence upon the time delay value and the measurement duration value until a value indicative of a desired condition is obtained. 
         [0016]    In accordance with another aspect of the present invention there is provided a method of monitoring during a dynamic process comprising the steps of: measuring thermal conductivity during a portion of cycle; determining inflection points therefrom; determining a time delay value and a measurement duration value from the inflection points; and measuring thermal conductivity during a subsequent dynamic process in dependence upon the time delay value and the measurement duration value until a value indicative of a desired condition is obtained. 
         [0017]    The present invention advantageously provides a method and apparatus for monitoring materials dynamically during dynamic processes. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0018]    The present invention will be further understood from the following detailed description with reference to the drawings in which: 
           [0019]      FIG. 1  illustrates a known material monitoring sensor; 
           [0020]      FIG. 2  schematically illustrates heat transfer from the sensor of  FIG. 1 ; 
           [0021]      FIG. 3  illustrates a material monitoring sensor in accordance with an embodiment of the present invention; 
           [0022]      FIG. 4  schematically illustrates heat transfer from the sensor of  FIG. 3 ; 
           [0023]      FIG. 5  graphically illustrates an example of a TCR calibration curve; 
           [0024]      FIG. 6  graphically illustrates an example of a voltage versus √{square root over (t)} measurement; 
           [0025]      FIG. 7  graphically illustrates an example of a sensor effusivity calibration curve using vacuum and other materials; 
           [0026]      FIG. 8  graphically illustrates an example of early dynamic measurements before 1-point calibration; 
           [0027]      FIG. 9  graphically illustrates an example of early dynamic measurements after 1-point calibration; 
           [0028]      FIG. 10  schematically illustrates a V blender having the sensors of  FIG. 3 ; 
           [0029]      FIG. 11  schematically illustrates a top view of the V blender of  FIG. 10 ; 
           [0030]      FIG. 12  schematically illustrates an end view of the V blender of  FIG. 10 ; 
           [0031]      FIG. 13  schematically illustrates the end view of  FIG. 12  with two rotational positions thereof superimposed; 
           [0032]      FIG. 14  schematically illustrates an inverted end view of  FIG. 12  with two rotational positions thereof superimposed; 
           [0033]      FIG. 15  graphically illustrates an example of a five-second measurement with one of four sensors is shown in  FIG. 11 ; and 
           [0034]      FIG. 16  there is illustrated a system for measuring thermal effusivity in accordance with an embodiment of the invention. 
       
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
       [0035]    Referring to  FIG. 3  there is illustrated a material monitoring sensor in accordance with an embodiment of the present invention. The sensor  24  has a circular geometry, a spiral heater  26  and an outer guard heater  28 . Electrical power is provided to the sensor  24  via connections  30 ,  32  and  34 . Hence, power to the spiral heater  26  is applied to connections  30  and  32 , and power to the guard heater  28  is applied to connectors  32  and  34 . The guard heater provides another heat source and may take the form of a separate wire or be integrated as part of the spiral heater. 
         [0036]    When integrated, there are three inflection points on the heater wire. One in the center  30 , another some distance away from the centre  32 , representing an end of the spiral heater  26  and the start of the guard heater  28 , and the last at the end of the wire  34  denoting the other end of the guard heater  28 . For simplicity of the drawing and to take into account that the guard heater  28  may take different forms, the guard heater  28  is shown as a annular ring surrounding the spiral heater  26 . 
         [0037]    The sensor  24  can be made as a thin film resistor or thick film resistor material on ceramics or other substrate material. This resistor material typically has a resistance in the range of a few ohms up to hundreds of ohms and thus requires a current in the range of 50-150 milliamps, for example. The resistance can be changed by varying the density of the geometry of the coils, the width and other process parameters. The coiled configuration of the sensor provides greater depth for sensing. For example the sensor  24  can be made using thick film technology, having an alumina (aluminum oxide) base, and platinum wires enclosed in glass cover (not shown in  FIG. 3 ). Optionally, the sensor includes a low-adhesion coating, for example Teflon (a trademark of DuPont) to provide encapsulation and resistance to acids and other materials. 
         [0038]    While a circular sensor with a spiral heater is shown in the drawings, the sensor can have other shapes, for example, a rectangular, hexagon, octagon, or other similar closed polygons. Similarly the particular arrangement of heater tracks can also be changed from spiral to serpentine or similar arrangements. The main consideration is provision of a substantially uniform distribution over the area of the heater. 
         [0039]    In operation, the guard heater  28  provides more heat (to compensate for the heat loss in two directions), hence is tuned to do so regardless of whether its form is separate or integrated as an extension of the spiral heater. 
         [0040]    Referring to  FIG. 4  there is illustrated schematically heat transfer from the sensor of  FIG. 3 . In operation, the sensor  24  generates heat flow as represented by arrows  36  from the spiral heater  26  and heat flow as represented by curved arrows  38  from the guard heater  28 . The spiral heater acts as a distributed heat source providing a substantially parallel heat flow  36  to a much greater depth than the prior art sensor  10  before dispersing as represented by arrows  40 . 
         [0041]    As a result of the configuration of the sensor  24 , this type of sensor can be used for measuring the thermal effusivity of solids as well as powders, liquids, and gases. The sensor  24  is also able to measure the effusivity of a vacuum. Consequently, calibration can be done with just two measurements, vacuum and only one material. This leads to less errors because the sensor calibration is no longer distorted by environmental factors (humidity, barometric pressure), material (impurities in the sample) and quality of the contact between the sensor and the material (true for vacuum only). This also reduces the number of materials required for calibration to one. 
         [0042]    The temperature coefficient of resistivity (TCR) calibration is calibration of sensor resistance versus temperature, and is given in this equation (assuming perfect linearity): 
         [0000]        R=R   0   +A·T   (1)
 
         [0043]    Where:
       R=resistance of sensor at a given temperature (ohms)   R 0 =resistance of sensor at 0° C. (ohms)   T=temperature (° C.)   A=slope (ohm/° C.)       
 
         [0048]    An example of a TCR calibration curve is shown in  FIG. 5 . For a sensor  24  the following are typically observed: 
         [0049]    Range of A˜0.05-0.15 ohm/° C. 
         [0050]    Range of R 0 ˜20-25 ohm 
         [0051]    The slope A is equal to: 
         [0000]        A=R   0 ·TCR  (2)
 
         [0000]    Where: TCR=Temperature Coefficient of Resistivity, assumed to be constant over the measured temperature range. 
         [0052]    The slope depends on sensor resistance in general, and on R 0  in particular. Therefore, even if two sensors have the same TCR, their temperature calibration lines will still have different slopes if their resistance at a given temperature is not the same. The higher slope, the more sensitive is the sensor. In other words, higher TCR and higher sensor resistance provide higher sensitivity. 
         [0053]    For platinum used in the sensor  24 , the TCR is approximately 0.0035° C. −1 , or 0.35% for each ° C. 
         [0054]    To calculate the surface temperature of the sensor from (1) use: 
         [0000]    
       
         
           
             
               
                 
                   T 
                   = 
                   
                     
                       R 
                       - 
                       
                         R 
                         0 
                       
                     
                     A 
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
         [0055]    The resistance may be measured directly by the electronics (using very low current and short time to avoid sensor heating), or calculated from the initial voltage, V 0 , or from the applied power P (if applied power is the same for all sensors). 
         [0000]    
       
         
           
             
               
                 
                   R 
                   = 
                   
                     
                       V 
                       0 
                     
                     I 
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
             
               
                 
                   R 
                   = 
                   
                     
                       V 
                       0 
                       2 
                     
                     P 
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Where R is the measured sensor resistance at the said temperature, I is the current and P is the power. 
       Basic 2 or 3-Point Effusivity Calibration 
       [0056]    The theoretical solution of the heat equation in the case of pure one-dimensional flow of heat from the sensor (material 1) to the measured material (material 2) at the interface between the materials follows this equation: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       Δ 
                        
                       
                           
                       
                        
                       T 
                     
                     ∝ 
                     
                       
                         G 
                          
                         
                           t 
                         
                       
                       
                         
                           Eff 
                           1 
                         
                         + 
                         
                           Eff 
                           2 
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       Where 
                        
                       
                         : 
                       
                        
                       
                           
                       
                        
                       Δ 
                        
                       
                           
                       
                        
                       T 
                     
                     = 
                     
                       change 
                        
                       
                           
                       
                        
                       in 
                        
                       
                           
                       
                        
                       surface 
                        
                       
                           
                       
                        
                       temperature 
                        
                       
                           
                       
                        
                       
                         ( 
                         
                           
                             
                                 
                               ° 
                             
                              
                             
                                 
                             
                              
                             C 
                           
                           . 
                         
                         ) 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     G 
                     = 
                     
                       power 
                        
                       
                           
                       
                        
                       flux 
                        
                       
                           
                       
                        
                       supplied 
                        
                       
                           
                       
                        
                       to 
                        
                       
                           
                       
                        
                       sensor 
                        
                       
                           
                       
                        
                       
                         ( 
                         
                           W 
                            
                           
                             / 
                           
                            
                           
                             m 
                             2 
                           
                         
                         ) 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     t 
                     = 
                     
                       time 
                        
                       
                           
                       
                        
                       measured 
                        
                       
                           
                       
                        
                       from 
                        
                       
                           
                       
                        
                       start 
                        
                       
                           
                       
                        
                       of 
                        
                       
                           
                       
                        
                       process 
                        
                       
                           
                       
                        
                       
                         ( 
                         sec 
                         ) 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       Eff 
                       1 
                     
                     = 
                     
                       equivalent 
                        
                       
                           
                       
                        
                       effusivity 
                        
                       
                           
                       
                        
                       of 
                        
                       
                           
                       
                        
                       sensor 
                        
                       
                           
                       
                        
                       
                         ( 
                         
                           
                             W 
                              
                             
                               s 
                             
                           
                           
                             
                               m 
                               2 
                             
                              
                             k 
                           
                         
                         ) 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       Eff 
                       2 
                     
                     = 
                     
                       effusivity 
                        
                       
                           
                       
                        
                       of 
                        
                       
                           
                       
                        
                       measured 
                        
                       
                           
                       
                        
                       material 
                        
                       
                           
                       
                        
                       
                         ( 
                         
                           
                             W 
                              
                             
                               s 
                             
                           
                           
                             
                               m 
                               2 
                             
                              
                             k 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Assumption: Both sensor and measured material are in equilibrium and at the same temperature when the measurement starts.
 
Note: Constants are ignored in equation (6).
 
         [0057]    In the previous section we saw the connection between sensor temperature and resistance. The resistance change of the sensor is: 
         [0000]      Δ R=R−R   0   =A·ΔT   (7)
 
         [0000]    And the voltage change on the sensor is: 
         [0000]      Δ V=I·ΔR=I·A·ΔT   (8)
 
         [0000]    Using equation (6) we can write: 
         [0000]    
       
         
           
             
               
                 
                   
                     Δ 
                      
                     
                         
                     
                      
                     V 
                   
                   ∝ 
                   
                     
                       
                         I 
                         · 
                         A 
                         · 
                         G 
                       
                        
                       
                         t 
                       
                     
                     
                       
                         Eff 
                         1 
                       
                       + 
                       
                         Eff 
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
         [0058]    A example of voltage versus √{square root over (t)} measurement is graphically illustrated in  FIG. 6 . 
         [0059]    Equation (9) can be written (in the linear zone) as: 
         [0000]      ΔV∝m√{square root over (t)}  (10)
 
         [0000]    Where m is the slope, 
         [0000]    
       
         
           
             
               
                 
                   m 
                   = 
                   
                     
                       
                         I 
                         · 
                         A 
                         · 
                         G 
                       
                       
                         
                           Eff 
                           1 
                         
                         + 
                         
                           Eff 
                           2 
                         
                       
                     
                      
                     
                         
                     
                      
                     
                       ( 
                       
                         V 
                         / 
                         
                           s 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
             
               
                 
                   
                     1 
                     m 
                   
                   = 
                   
                     
                       
                         
                           Eff 
                           1 
                         
                         + 
                         
                           Eff 
                           2 
                         
                       
                       
                         I 
                         · 
                         A 
                         · 
                         G 
                       
                     
                      
                     
                         
                     
                      
                     
                       ( 
                       
                         
                           s 
                         
                         / 
                         V 
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
         [0000]    If Eff 2  is 0, i.e. sensor response is measured in vacuum, then: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       1 
                       m 
                     
                      
                     
                       ( 
                       vacuum 
                       ) 
                     
                   
                   = 
                   
                     
                       Eff 
                       1 
                     
                     
                       I 
                       · 
                       A 
                       · 
                       G 
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
         [0060]    The expression Eff 1 /IAG is a sensor/system expression of merit, and depends only on sensor characteristics and supplied power, and may be used for calibration. 
         [0061]      FIG. 7  graphically illustrates an example of sensor effusivity calibration curve using vacuum and other materials. The calibration line shows very good linearity. 
         [0062]    The calibration line can be written as: 
         [0000]    
       
         
           
             
               
                 
                   
                     1 
                     m 
                   
                   = 
                   
                     
                       M 
                       · 
                       
                         Eff 
                         2 
                       
                     
                     + 
                     C 
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Where M is the slope of the effusivity calibration and is equal to: 
         [0000]    
       
         
           
             
               
                 
                   M 
                   = 
                   
                     
                       1 
                       
                         I 
                         · 
                         A 
                         · 
                         G 
                       
                     
                      
                     
                       ( 
                       
                         
                           m 
                           2 
                         
                         · 
                         
                           
                             
                               
                                   
                                 ° 
                               
                                
                               
                                   
                               
                                
                               C 
                             
                             . 
                           
                           / 
                           W 
                         
                         · 
                         Amp 
                         · 
                         Ω 
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
       And C is: 
       [0063]    
       
         
           
             
               
                 
                   C 
                   = 
                   
                     
                       
                         Eff 
                         1 
                       
                       
                         I 
                         · 
                         A 
                         · 
                         G 
                       
                     
                      
                     
                         
                     
                      
                     
                       ( 
                       
                         
                           s 
                         
                         / 
                         V 
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Note that C is the 1/m value when Eff 2  is zero, i.e. for vacuum. 
         [0064]    To calculate the effusivity of the measured materials from (14) we use: 
         [0000]    
       
         
           
             
               
                 
                   
                     Eff 
                     2 
                   
                   = 
                   
                     
                       
                         1 
                         m 
                       
                       - 
                       C 
                     
                     M 
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Where 1/m is the inverse of the voltage versus √t slope measured for this material, and M &amp; C are the slope and intercept of the effusivity calibration curve for that sensor. 
         [0065]    Range typical for this present sensor design and system.
       M=0.07-0.1 (m 2 ·° C./W·Amp·Ω)   C=40-80 (√{square root over (s)}/V)       
 
       1-Point Effusivity Calibration 
       [0068]    We have mentioned above that vacuum is used in the sensor effusivity calibration process. But a single point is not enough, so one or more materials are used as well (PDMS (polydimethylsiloxanes) and possibly water gel) to create the calibration line. The vacuum measurement is relatively stable because it is not prone to material variations. However, the other calibration points may be affected by temperature and other environmental conditions. Since different sensors may be calibrated at different times and conditions, offset errors in calibration lines are quite common between sensors. These offset errors may be typically in the order of 1-5%. 
         [0069]    We can reduce the relative measurement errors (or % RSD) between sensors measuring the same material by applying a 1-point calibration process. 
         [0070]    Since the sensor calibration curve has two parameters, M &amp; C, we may recalculate either one of them to match all sensors such that the calculated effusivities of all sensors, measuring the same uniform material at the same time and conditions, are identical. Since the parameter C is inherent to the sensor/system, and is the measured 1/m value in vacuum, it is inherently more accurate than the parameter M, which is created from both C and measurements of the calibration materials. Therefore, we are inclined to alter M for the 1-point calibration rather than altering C. 
         [0071]    The 1-point calibration process takes a few measurements, done by different sensors on the same material at the same time, recalculates each sensor&#39;s M such that all sensors provide the same calculated effusivity number, and displays the new calculated effusivities for each sensor. 
         [0072]    If sensor (1) has calibration parameters M 1  and C 1  and measures 1/m 1 , from equation (17) the calculated effusivity will be: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       ( 
                       
                         Eff 
                         2 
                       
                       ) 
                     
                     1 
                   
                   = 
                   
                     
                       
                         1 
                         
                           m 
                           1 
                         
                       
                       - 
                       
                         C 
                         1 
                       
                     
                     
                       M 
                       1 
                     
                   
                 
               
               
                 
                   ( 
                   26 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Similarly for sensor (2) with M 2 , C 2 , and 1/m 2 : 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       ( 
                       
                         Eff 
                         2 
                       
                       ) 
                     
                     2 
                   
                   = 
                   
                     
                       
                         1 
                         
                           m 
                           2 
                         
                       
                       - 
                       
                         C 
                         2 
                       
                     
                     
                       M 
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   27 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Because of the reasons mentioned above, (Eff 2 ) 1  differs somewhat from (Eff 2 ) 2 . To equalize them to the latest value we may change only M 1 , or alternatively we may change both M 1  and M 2  to bring the effusivity value to another desired value, or to the average between the values of (Eff 2 ) 1  and (Eff 2 ) 2 . Once the effusivities are recalculated with the modified M(s), both sensors show the same number. 
         [0073]    The 1-point calibration corrects only the offset error between sensors, but cannot correct the variance of each individual sensor. Therefore, the improvement provided by the 1-point calibration is limited by this variance (excluding the case where the variance of different sensors is correlated). 
         [0074]    The 1-point calibration corrects the variance between sensors at certain measurement conditions and material, by altering the effusivity calibration line. One must be careful to not apply the new calculated slopes from one material to another, as this may increase the variance between sensors and adversely affect the accuracy. Rather, the 1-point calibration process must be repeated for different materials and conditions. 
         [0075]    Calibration can be done on a major component of the mix or on the expected value of the mix. 
         [0076]      FIGS. 8 and 9  show early dynamic measurements before and after 1-point calibration. RSD of 3-11% improved to 1-5%, approximately two times tighter. 
         [0077]    Referring to  FIG. 10  there is graphically illustrated a V blender having the sensors of  FIG. 3 . In a typical implementation of a measurement system using the sensors of  FIG. 3  a plurality of sensors are placed in different positions on the V blender  50 . For example, on the blender lids  52  and  54  outer sensors  56  and  58  could be positioned along with inner sensors  60  and  62 . Optionally other sensors  64 ,  66 ,  68 , and  70  could be placed within the V blender. While a V blender is shown in  FIG. 10 , the sensors can also be fitted to other types of blenders, for example a bin blender. 
         [0078]    Referring to  FIG. 11  there is illustrated schematically a top view of the V blender of  FIG. 10 . This view shows the blender lids  52  and  54  with outer sensors  56  and  58  and inner sensors  60  and  62 . 
         [0079]    Referring to  FIG. 12  there is illustrated schematically an end view of the V blender of  FIG. 10 . 
         [0080]    Referring to  FIG. 13  there is illustrated schematically the end view of  FIG. 12  with two rotational positions thereof superimposed. The V blender is illustrated rotating from a first position along axis  74  through a second position with axis  76  to a third position with axis  78  during a clockwise rotation through a arc  80 . If sensors are located in the lids  52  and  54  as sensors  56 ,  58 ,  60  and  62  are, or if positioned as shown by optional sensors  64  and  66 , then the arc  80  represents a period of time when the sensors would likely be covered by stable material. The arc  80  therefore represents a potential measurement period for sensors  56 ,  58 ,  60 ,  62  and optional sensors  64  and  66 . 
         [0081]    Similarly, referring to  FIG. 14  there is illustrated schematically illustrates an inverted end view of  FIG. 12  with two rotational positions thereof superimposed. The V blender is illustrated rotating clockwise through a arc  90 . If sensors are located as sensors  68 , and  70  are, then the arc  90  represents a period of time when the sensors would likely be covered by stable material. The arc  90  therefore represents a potential measurement period sensors  68  and  70 . 
         [0082]    A synchronization map of delays from a known point in the rotation to turning on of a sensor or group of sensors can be used to take full advantage of measurement periods during a given rotation. Such a mapping can be generated based on rotation speed and sensor location. 
         [0083]    However, the precise positioning of a usable measurement period also depends upon percentage fill of the blender and the properties of the materials being mixed. 
         [0084]    Hence it is desirable to measure a long sensor response, and show the inflection points caused by, for example, moving powder. In order to do this a reproducible blender orientation signal is required that provides a per rotation reference point to initiate timing of the sensor delays. For example an accelerometer chip can be used to generate a pulse for a particular orientation of the blender. The computer then uses this pulse as a reference point. This helps to establish an exact synch map and other useful parameters of the particular blender, fill level and RPM. 
         [0085]    Referring to  FIG. 15 , there is graphically illustrated an example of a five-second measurement (˜80% of a complete revolution at 10 RPM) of a blender in motion with four sensors is shown in  FIG. 11 . For one sensor there are two inflection points about 3 seconds apart, caused by the moving powder, as indicated by lines  94  and  96 . These measurements can then be used to manually establish delay values in a synchronization map or can be used by a computer programmed to determine the inflection points and then automatically calculate an appropriate measurement period. 
         [0086]    Referring to  FIG. 16  there is illustrated a system for measuring thermal effusivity in accordance with an embodiment of the invention. The system  100  comprises an instrument response receiver  110 , an instrument response analyzer  120  and a thermal effusivity calculator  130 . 
         [0087]    The instrument response receiver  110  receives instrument responses from a sensors  140 . The instrument response analyzer  120  analyzes the received instrument responses. The thermal effusivity calculator  130  calculates thermal effusivity based on the output of the analyzer  120  as described herein above with regard to  FIGS. 5-7 . 
         [0088]    The instrument response analyzer  120  has a calibration factor determiner  122  for determining a calibration factor, a compensator  124  for calibrating the sensor to compensate instrument responses by the calibration factor and a delay mapper  126  for determining sensor delay values referenced to a sync pulse from a synch pulse generator  150 . The compensator also includes a fixed power algorithm to compensate for rising sensor temperature and therefore resistance. 
         [0089]    The present invention has been described in the context of a mixing process and in particular a V blender mixing process having rotational motion. However, the present invention can be applied to any dynamic process having predictable patterns of motion, in which there exist relatively short periods (1-2 seconds) of relative stability between material and sensor. For example in addition to rotational motion, the motion can be oscillatory, pendular, rocking, i.e. generally periodic. 
         [0090]    Numerous modifications, variations and adaptations may be made to the particular embodiments of the invention described above without departing from the scope of the invention, which is defined in the claims.