Abstract:
A method and device for measuring the surface tension of liquids uses the bubble pressure principle, wherein a parameter relating to a bubble formed using a defined gas mass flow rate or volume flow rate is measured at the tip of a capillary tube immersed in the liquid. The surface tension is calculated from the measured value. With a defined gas mass flow rate or volume flow rate, the time between the minimum pressure and the maximum pressure and hence a defined pressure increase in a bubble are measured, and from this the surface tension is calculated. A relatively inexpensive sensor for measuring the surface tension in an appliance, such as a washing machine, using this inventive concepts is disclosed using a piezoelectric transducer.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
   This application is a continuation of PCT/EP2006/001537, filed Feb. 21, 2006, which is based on German Application No. 10 2005 007 870.2, filed Feb. 21, 2005, of which the contents of both are hereby incorporated by reference. 

   FIELD OF INVENTION 
   The invention generally relates to a method and a device for measuring the surface tension of liquids using the bubble pressure principle, where for a clearly defined gas mass or volume flow, a bubble parameter is determined on a capillary tube tip immersed in the liquid and the surface tension is calculated therefrom. 
   BACKGROUND OF INVENTION 
   The surface tension σ indicates what work has to be effected in order to increase by a specific amount a surface at the liquid-gas interface. It therefore gives information e.g., on the concentration and effectiveness of surfactants in liquids, e.g. for the quality control of inks or waters in washing and cleaning processes. 
   With the bubble pressure principle a gas or gas mixture, usually air, is forced through a capillary tube connected to a pneumatic system into a liquid to be analyzed and the internal pressure p of the bubble forming on the capillary tube is measured. 
   In the maximum bubble pressure method the maximum bubble pressure p max  is measured. The hydrostatic pressure p h  acting on the bubble is calculated from the immersion depth h E  of the capillary tube, which has to be detected and adjusted in a complicated manner, and the liquid density. The surface tension σ is then calculated with the radius of the capillary r cap  in a first approximation according to:
 
σ= r   cap /2( p   max   −p   h )  (1)
 
   In a differential pressure method on a capillary tube derived from this (DE 197 55 291 C1, DE 203 18 463 U1) the dynamic surface tension σ is calculated using the correlation K between the surface tension σ and the differential pressure Δp between the maximum internal pressure p max  and the minimum internal pressure p min  of the bubble:
 
σ= K·Δp  with Δ p=p   max   −p   min   (2)
 
   On the basis of the same action of the hydrostatic pressure on p min  and p max , unlike in the maximum bubble pressure method, the measurement remains independent of the capillary tube immersion depth. 
   In surfactant-containing liquids the measured value of the surface tension σ is dependent on the age of the expanding surface, because with increasing bubble life surfactants can be increasingly attached to a newly formed bubble surface. Thus, the bubble pressure principle consequently determines a dynamic surface tension, so that a measured value must always be given in connection with the associated bubble formation time or bubble life t life , this being understood to mean hereinafter the time between the pressure minimum and pressure maximum of the bubble. 
   Known bubble pressure methods measure at a clearly defined bubble frequency or bubble life of the exiting gas bubbles, which must be constantly readjusted in accordance with the dynamically changing surface tension (DE 197 55 291 C1), the maximum bubble pressure or the differential pressure at a capillary tube. A controllable air pump or an air flow-controlling valve is required for this. 
   To be able to sufficiently accurately measure the surface tension, the pressure sensor used must have a high measuring accuracy compared with other applications. 
   Pressure sensors meeting these demands must be temperature-compensated and calibrated and therefore constitute the most costly component of a measuring system. 
   Alternatives to the transformation of the bubble pressure into an electrical signal are sound pressure transducers such as condenser, moving coil, crystal and carbon microphones as well as piezoelectric disks (EP 760 472 B1, EP 902 887 A1). Thus, according to EP 760 472 B1 using a cost effective sound pressure transducer the first derivation of the pressure signal after time is measured and by subsequent integration the bubble pressure and from this the surface tension is determined. It is impossible to avoid measurement errors resulting from the influence of the ambient temperature, atmospheric humidity, frequency dependence of the microphones in the transmission behaviour and drift during a measurement. Sound pressure transducers do not meet the accuracy requirements in connection with a pressure measurement without taking additional measures. 
   It is known from EP 682 588 A1, that in the case of adequately constant air flows the measured bubble frequency of the bubbles forming on a capillary tube is correlated with the surface tension. With decreasing surface tension the bubble frequency rises. The reciprocal of the bubble frequency, the bubble period time, is formed from the bubble life and the so-called bubble dead time (DE 203 18 463 U1). The bubble dead time designates the time between the pressure maximum following the passage of which the bubble collapses and is inflated and bubble detachment. Even minor flow patterns in the liquid or mechanical vibrations influence the bubble detachment in a random manner and consequently lead to high measurement errors on measuring the surface tension through the bubble frequency. The resulting measurement accuracy is not adequate e.g. for the determination of the detergent concentration in the textile cleaning sector. 
   Hitherto in the textile and dishwashing sector, particularly in the domestic field, no economic, marketable solution is known with which the surface tension can be sufficiently precisely measured for concentration determination of the detergent or washing agent and on the basis of this an automatic dosing or metering. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The invention is explained in greater detail relative to an embodiment and the attached drawings, wherein show: 
       FIG. 1  illustrates the bubble formation and the path of the bubble internal pressure based on a bubble pressure method, 
       FIG. 2  illustrates a pneumatic system for illustrating the physical bases of the invention, 
       FIG. 3  illustrates a graphical representation of bubble pressure signals of different surface tensions for a constant air mass flow, 
       FIG. 4  illustrates measurement results for different liquids, 
       FIG. 5  illustrates a diagrammatically represented piezoelectric sound pressure transducer, 
       FIG. 6  illustrates one embodiment of a function structure for the surface tension measurement in a washing machine, and 
       FIG. 7  illustrates a diagrammatic section through a compact surface tension sensor operating according to one embodiment of the invention. 
   

   DETAILED DESCRIPTION 
   On the basis of the dependence of the bubble life on the surface tension with a clearly defined gas mass or gas volume flow, one problem addressed by the invention is to give a method and device for the dynamic measurement of the surface tension of a liquid, which with comparatively limited sensor expenditure provides sufficiently accurate measurement results for most applications. 
   According to one embodiment of the invention the problem is solved with the features given in claims  1 . Advantageous further developments are provided in the other claims. 
   The method according to the invention is based on the dependence of the bubble life t life  on the surface tension in the case of a clearly defined gas mass or volume flow introduced into a system volume. 
   When a bubble is formed at the end of the capillary tube, the differential pressure between pressure minimum and pressure maximum in the bubble is correlated with the surface tension σ, such as when introducing a clearly defined gas mass or volume flow, usually an air mass or volume flow, into the pneumatic system volume, independently of the surface tension σ, during the same time period the same gas mass or volume always flows into the same. Therefore the bubble life is also dependent on the surface tension σ, because with a lower surface tension σ a lower pressure is built up in the bubble and consequently up to the reaching of the maximum pressure, less gas has to be compressed in the system volume. Therefore the point in time of the pressure maximum is more rapidly reached with a lower surface tension than with a high surface tension. The novel method, referred to as the bubble life method, at a clearly defined gas mass or volume flow measures the bubble life of a bubble forced into the liquid and from this calculates the liquid surface tension. 
   The precision requirements on a pressure to voltage signal converter are low compared with the known differential pressure measurement method, because it is only necessary to adequately precisely determine the point in time of the pressure minimum and the point in time of the following pressure maximum of a bubble from the pressure signal. The pressure to voltage signal converter does not have to be temperature-compensated or calibrated with respect to the signal amplitude and shift. 
   In place of pressure sensors it is advantageously possible to use simple and therefore inexpensive sound pressure transducers, e.g. piezoelectric disks. In the case of the direct piezoelectric effect, mechanical deformations caused by pressure changes lead to a mutual shift of the charge mass centres of the crystal atoms. Within the crystal there is an electrical polarization P and surface charges to the outside can be measured. As proportionality exists between the magnitude of the mechanical stress of the piezoelectric crystal and the surface charge quantity, the time points (e.g., points in time) of pressure minimum and pressure maximum can be readily detected as electrical signals. Simple piezoelectric sound transducers are mass produced for the reversed use in piezoelectric buzzers and are extremely inexpensive. 
   As is diagrammatically shown in  FIG. 1 , in the case of a bubble pressure method for measuring the surface tension, air or some other suitable gas or gas mixture is forced through a capillary tube  1  into the liquid to be analyzed. A pressure-voltage converter illustrated in greater detail in  FIG. 5  detects the internal pressure p of a bubble  2  forming at the tip of a capillary tube  1 . As is apparent from  FIG. 1   a , a new bubble  2  has a large radius r B &gt;&gt;r cap  and the pneumatic system connected to the capillary  1  and illustrated in greater detail in  FIG. 2 , is under the lowest pressure p min . As a result of the afterfiowing air, the pressure p in bubble  2  (in  FIG. 1   b ) rises. Bubble  2  bulges at capillary tube  1  ( FIG. 1   b ) and the radius of the bubble r B  decreases. If the bubble  2  reaches its minimum radius, which is approximately the same as the capillary tube radius r B =r cap , the pressure in the interior rises to the pressure maximum p max  (see, e.g.,  FIG. 1   b ). The time from the start of the formation of a bubble  2  up to the reaching of the pressure maximum p max  gives the surface age or bubble life t life  of a bubble. After exceeding the pressure maximum p max  the bubble  2  bursts: r B &gt;r cap  and the pressure p in the interior of bubble  2  rapidly drops through the volume expansion ( FIG. 1   c ). Then the air flow slowly inflates the bubble  2  again until it tilts upwards and is detached from the capillary tube  1  (see, e.g.,  FIG. 1   a ). The time period from the pressure maximum p max  to the detachment of the bubble  2  is called the dead time t dead . Then the process is repeated through the formation of the next bubble. The number of bubbles  2  formed per time unit is called the bubble frequency f B . 
   On introducing a clearly defined gas mass or volume flow into the pneumatic system volume, the bubble life t life  decreases more strongly than the bubble dead time t dead  with falling surface tension σ. Thus, with the bubble life it is possible to better resolve a surface tension change than with using the bubble dead time. Even minor variation in the flows in the liquid to be measured, together with mechanical vibrations, influence bubble detachment in a random manner, and therefore the bubble dead time and also the bubble frequency. It is clear that the bubble frequency is unsuitable for determining the surface tension. 
   According to one embodiment of the present invention, the bubble life t life  of a bubble is measured in such a way that it permits the attainment of adequately precise results using extremely inexpensive sensors. 
   The basic principles of the method will be explained relative to  FIGS. 2 and 3 .  FIG. 2  diagrammatically shows the pneumatic system for a bubble pressure method with the system volume V S , in which is enclosed the volume of capillary tube  1 , bubble pressure p, bubble volume V B  and an air mass flow m′ 1 . For the subsequent calculation, a constant air mass flow m′ 1  and a constant air temperature T 1  is assumed, as is air as the ideal gas and a pressure minimum p min  equal to the hydrostatic pressure p h . 
   The starting point for the analysis of the pneumatic system is the thermal equation of state of an ideal gas:
 
p V=m R G  T  (3)
 
   Into the system volume  3  flows a constant air mass flow m′ 1 . In the time t life  the pressure rises from p h  to p max =f(σ). The total volume V G  rises from V s  to V s +V B . 
   The air mass which has been received during the time t life  is calculated as follows:
 
m=m′·t life   (4)
 
   On the basis of the observations, equation (3) for the time point of maximum bubble pressure can be written as follows:
 
(Δ p+p   h )( V   S   +ΔV )=( m   0   +Δm ) R   air   T   air   (5)
 
( p   max   −p   h   +p   h )( V   S   +V   B )=( m   0   +m′·t   life ) R   air   T   air   (6)
 
m 0  is calculated using equation (3) to give
 
 m   0 =( p   h   ·Vs )/( R   air   ·T   air )  (7)
 
equation (7), inserted in (6), gives:
 
 p   max ( V   S   +V   B )=(( p   h   ·V   S )/( R   air   ·T   air )+ m′·t   life ) R   air   T   air   (8)
 
transposed according to t life , it follows:
 
 t   life =( p   max ( V   S   +V   B )− p   h   ·Vs )/ m′·R   air   T   air   (9)
 
with the hydrostatic pressure
 
 p   h =ρ w   ·g·h   E   p   0   (10)
 
and the maximum pressure as a function of the surface tension (first approximation):
 
 p max=(2 σ/r   cap )+ p   h   (11)
 
and the bubble volume at maximum bubble pressure:
 
 V   B =⅔π· r   cap   3   (12)
 
through insertion in equation (9), it is obtained:
 
 t   life =((2σ/ r   cap +ρ w    g h   e   +p   0 )( V   S +⅔π· r   cap   3 )−(ρ w    g h   E   +p   0 )· V   S )/ m′·R   air   T   air   (13)
 
   By transposing equation (13), it is obtained:
 
 t   life =(2 σ/r   cap ( V   S +⅔π· r   cap   3 )+(ρ w    g h   E   +p   0 )·⅔π· r   cap   3 )/ m′·R   air   T   air   (14)
 
   On the basis of equation (14) it can be seen that the bubble life t life  in the case of a constant air mass flow is linearly dependent on the surface tension σ of a liquid:
 
 t   life   =f (σ),  m′   air =const  (15)
 
     FIG. 3  shows the pressure gradient of a bubble at different surface tensions and unlike the normal procedure, the bubble life t life  is not kept constant and instead through the constantly introduced air mass flow m′ 1  the pressure rise in the bubble from pressure minimum p min  to pressure maximum p max1  or p max2 ; dp/dt=const. According to the invention, the bubble life t life  of a bubble is measured instead of the pressure difference Δp=p max −p min  in a bubble. As is shown in  FIG. 3 , the internal pressure  5   b  of a bubble in a liquid with a lower surface tension σ 2  reaches the pressure maximum p max2  with a shorter bubble life t life2  compared with the internal pressure  5   a  of a bubble in a liquid with a higher surface tension σ 1 , which only reaches the pressure maximum p max1  after a longer bubble life t life1 . 
     FIG. 4  is a graph with bubble pressure signals of liquids with different surface tension and a constant air mass flow. All the bubble pressure signals rise in the same way up to a maximum bubble pressure dependent on the surface tension. For the lower surface tension bubble pressure signals, the pressure minimum is lower, because following bubble detachment there is an initial covering of the surface with surfactants and consequently there is a lower surface tension at the pressure minimum. 
   The resolution of the surface tension by measuring the bubble life is dependent on the reference bubble life, which is set, e.g., by the air mass flow in water. In the case of a reference bubble life of 300 ms set in water (cf.  FIG. 4 ), there is already a sensitivity of 3.9 ms per 1 mN/m. A calibration of the surface tension sensor can take place in water with known temperature and consequently known surface tension, in that the bubble life is measured and is used as the reference bubble life. With this procedure it is advantageously possible to obviate the need for regulating the gas mass or volume flow. 
     FIG. 5  shows the use of a piezoelectric transducer as a sound pressure transducer for the aforementioned method. A piezoelectric sound pressure transducer  4  is connected to an appropriate point of the system volume  3 . The piezoelectric sound pressure transducer  4  comprises two metallic contact surfaces  6  with leads, between which is bonded a so-called piezoelectric crystal  7 . When there is a pressure change in pneumatic system  3 , the piezoelectric sound pressure transducer  4  produces a charge shift at the contact surfaces  6 . The time change to the pressure or the derivation of the bubble pressure after time dp/dt is proportional to the externally measured current. By integrating the measured current by means of an evaluating circuit it is possible to generate a voltage signal u(t), which is proportional to the pressure signal. Since, according to the invention, only the time period t life  between pressure minimum p min  and pressure maximum p max  are of interest, whereas no interest is attached to the level of the maximum pressure or maximum differential pressure, there are significant cost reductions with respect to an evaluating circuit. The t life  can be determined using, for example, an inexpensive microcontroller. 
     FIG. 6  shows a function structure for an application in an appliance, such as a washing machine, using the inventive bubble life method. 
   In the fluidic part  8  of the washing machine, in the bypass to a detergent solution container  9 , is provided a measuring vessel  10 , to which is supplied by a detergent solution pump  11  process-controlled detergent solution and thorough mixing takes place there. As the surface tension of a liquid is very highly temperature-dependent, a temperature sensor  12  measures the detergent solution temperature            .
   The pneumatics  13  comprise capillary tube  1 , system volume  3 , the pressure sensor or sound pressure transducer  14  and the constant air quantity source  15 ,  16 ,  17 . In the present embodiment an air pump  15 , e.g. a diaphragm pump with motor or piezoelectric drive, by means of a buffer volume  17  forces through a choke  16  air into the pneumatic system and to it are connected on the one hand the pressure sensor or sound pressure transducer  14  and on the other a capillary tube  1 . The choke  16  is used for setting the operating point of air pump  15  and prevents as a maximum size pneumatic resistor any effects of the bubble pressure on the operating point thereof. Another possibility is constituted by the connection of a gas pressure container. The tip of capillary tube  1  is immersed in the measurement vessel  10 . 
   Not shown are the electronics that evaluate the signals u(t) taken from the pressure sensor or sound pressure transducer  14 , as well as the signals emanating from temperature sensor  12  and controls the measurement process. The electronics interface to the washing machine control components. 
   The surface tension sensor is calibrated in water of known temperature and therefore known surface tension (σ), in that, in the above-described manner, the bubble life t life  is measured and from it is calculated the gas mass or volume flow (m′ 1 ). The measuring or calibrating process starts with the switching on of pump  15  and after a clearly defined time during which an adequately constant pressure has built up in buffer volume  17 , the bubble life t life  is determined. When using the surface tension sensor in a washing machine, it is calibrated at water intake times, the washing machine drum being stationary during the measurement and calibration processes. 
     FIG. 7  is a diagrammatic section through a compact surface tension sensor operating according to the inventive method. Into said compact surface tension sensor are integrated an air pump, a buffer volume, a choke, the system volume, the piezoelectric sound pressure transducer and the capillary tube. 
   The compact surface tension sensor comprises a base member  19  on which are formed a connection for capillary tube  1  and system volume area  3 , choke  16 , buffer volume area  17 , a pump chamber  20  and pump valves with holders for valve flaps  21 . 
   The system volume  3  is closed at one end by the piezoelectric transducer  4  described in greater detail relative to  FIG. 5 . Buffer volume  17  is sealed by a cover  22 . A piezoelectric transducer  4  comprising two metallic contact surfaces  6  with leads between which is bonded a so-called piezoelectric crystal  7 , closes the pump chamber  20  and forms the diaphragm drive of air pump  15  of  FIG. 6 . 
   Such a surface tension sensor can be extremely inexpensively manufactured by a plastic injection moulding process.