Classifications

• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
  • G01N13/00—Investigating surface or boundary effects, e.g. wetting power; Investigating diffusion effects; Analysing materials by determining surface, boundary, or diffusion effects
  • G01N13/02—Investigating surface tension of liquids
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
  • G01N13/00—Investigating surface or boundary effects, e.g. wetting power; Investigating diffusion effects; Analysing materials by determining surface, boundary, or diffusion effects
  • G01N13/02—Investigating surface tension of liquids
  • G01N2013/0241—Investigating surface tension of liquids bubble, pendant drop, sessile drop methods
  • G01N2013/025—Measuring foam stability
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
  • G01N35/00—Automatic analysis not limited to methods or materials provided for in any single one of groups G01N1/00 - G01N33/00; Handling materials therefor
  • G01N35/10—Devices for transferring samples or any liquids to, in, or from, the analysis apparatus, e.g. suction devices, injection devices
  • G01N35/1009—Characterised by arrangements for controlling the aspiration or dispense of liquids
  • G01N35/1016—Control of the volume dispensed or introduced
  • G01N2035/1018—Detecting inhomogeneities, e.g. foam, bubbles, clots

Definitions

• the invention relates to the field of evaluation and characterization of foam properties of foaming agents by using a simple and quick method.
• Foams of very different stability are commonly met in many industrial processes and everyday life. That's why there are available various tests and parameters for foam characterization.
• the methods of foam characterization differ mainly in the kind of foam formation.
• the techniques of foam generation include shaking [4], pouring [5, 6], pneumatic sparging [5-9], bubbling [10] and vibrating [1 1 ] procedures to get any surfactant solution foamed.
• Foamscan is commercially available [9, 17, 18].
• This method adopts the pneumatic technique well known for the characterization of unstable foams [5, 19, 20].
• the foam is created in a glass tube and its time dependent height is measured by image processing while the residual liquid in the foam is measured by a conductivity method.
• the foaming solutions are characterized in such way that a gas of constant flow is bubbled through the solutions until an identical foam height is reached in all cases. This maximum height is used as reference state.
• the Foamscan apparatus the gas flow and the end of sparging are defined. However, the period of sparging time required for forming the same foam volume is rather long, of the order of magnitude of a few minutes. In [17] this time amounts to 8 minutes (commercial soap solutions).
• SITA Foam Tester 2000 Recently another foam test apparatus, called SITA Foam Tester 2000, was developed [22]. In this method the input of air is performed by a rotor and the foam height is measured mechanically by various steel needles located on top of the foam. This method is applicable to very stable foams only. Measuring the foam height by some downward motion of various needles is not only inconvenient but also influences the foam as the contact of the needles with the top foam layer can make it rupture. Finally, the input of gas is not well defined.
• An object of the present invention therefore was to provide a method which allows for higher accuracy in determining foam properties and/or foam characteristics.
• an object was to provide a method in which foams can be evaluated based on measuring the foam/solution interface only.
• a further object of the present invention was to provide a simple, quick, reproducible and generally applicable procedure for the determination and evaluation of foam properties. It was a further object of the present invention to provide a relatively inexpensive procedure for testing foam stability of any foaming solution by a well-defined process under well-defined conditions. A further object was to provide a simple apparatus, which can be utilized for the foaming tests, and a procedure which can quickly discriminate foams of different stability and evaluate the stability of the foams formed by appropriate parameters that refer to physically well-defined boundary conditions. A further object was to provide an apparatus which can be utilized for characterizing both (meta)stable as well as unstable foam systems by the same procedure and by the same parameters.
• a method for determining or/and evaluating foam properties of a solution wherein a predefined volume of gas is introduced into a predefined volume of solution to be tested and foam height h f , solution height h s and/or total height H(t) are measured and wherein at an initial time t +0l when all the predefined volume of gas has been introduced into the solution, there is at least a minimum volume of solution V s mi n left, which is not contained in the foam.
• the initial conditions are modified such that one can unequivocally determine whether and at what concentration the overall volume of gas will be completely incorporated in the foam column.
• the percentage of gas in the foam related to the overall gas volume used can be measured.
• a definite amount of gas preferably air
• the gas is introduced into the solution with a definite velocity. The process can be performed manually as well as automatically.
• foam height h f , solution height h s and total height H(t) are measured independently or simultaneously in dependence on time.
• gas content per unit volume of solution adjustable and measurable (convenient for theoretical description of foamability). This is hardly possibly for other methods like Bartsch, Ross-Miles or methods using stirring, shaking, whipping, etc.
• foam stability by means of which the foam stability is characterized refer to physically reasonable and well-defined conditions. They are very sensitive to foam stability covering several orders of magnitude.
• foams and foam properties can be measured in a standardized manner, whereby the parameters to be determined are not chosen arbitrarily but have a physicochemical basis.
• a predefined volume of gas is introduced into a solution to be tested, e.g. a solution of a detergent or a surfactant or solutions for which foam properties are important, such as beer, waste water, detergent solutions, etc., whereby a predefined volume of such solution is used.
• the general set-up is in particular defined by predefining the volumes of solution and gas and by setting these volumes in a manner that h s mi n > 0 or V s min > 0, respectively.
• the ratio of solution volume to gas volume is 1 :10 to 10:1 , more preferably 1 :5 to 5:1 and, especially preferred, 1 :1 .8 to 1 :2.2.
• the use of a ratio of volume of solution to volume of gas introduced of 1 :2 proved to be particularly favorable.
• the gas is introduced into the solution at a constant rate, e.g. at a rate of from 1 to 100 l/h, more preferably from 10 to 30 l/h and, in particular, at about 18 l/h. Therefore, the amounts of gas and solution used to form the foam and also the boundary condition h s mi n > 0 and/or V s min > 0 are well-controlled according to the invention.
• foam height h f , solution height h s and/or total height H(t) are measured to characterize the foams, whereby physicochemical parameters of the foams can be derived from these measured quantities. It is to be understood that the height values can also be obtained by determining the corresponding volume of foam V f , volume of solution V s or total volume V(t). Solution height h s is measured particularly preferably.
• An essential advantage of the invention lies in that all kinds of foams, i.e. metastable and non-stable foams as well as wet foams and dry foams, can be tested quantitatively by the same procedure. The characteristic physical values to be measured provide significant values for all kinds of foams. Definite and equal boundary conditions are applied in each case.
• the foam decay can be described by three different stages of decay according to the ratio of the ruptured foam volume and the corresponding volume of drained solution:
• the method according to the invention and the parameters given allow to determine i) foamability, ii) foam stability, iii) liquid contents in foam or/and drainage rates.
• test experiments according to the invention are simple, quick and reproducible. Automatization of the test procedure is easily possible. While air is preferably used as gas, in general different kinds of gas are applicable.
• a predefined volume of gas is introduced into a predefined volume of solution to be tested, preferably with a predefined velocity.
• a certain amount of foam and, therefore, a certain foam height is formed.
• Ah f Ah s .
• Ah f /Ah s 1 in said initial stage.
• the initial stage is at least 2 s, more preferably at least 5 s and particularly preferred at least 10 s.
• the stable foams can further be discriminated by the occurence of an intermediate state.
• AhVAh 3 > 1 At longer time, that is at t > t d e V) its behavior is described by AhVAh 3 > 1 , in particular, AhVAh 5 > 10, preferably AhVAh 3 > 100.
• the latter condition means that the foam system is very stable.
• novel results of the present invention can be obtained using the pneumatic method and procedure for swift characterization of foamability and foam stability as described in [1 -3].
• H(t) total height of foam and solution, measured from frit bottom to foam/air interface
• the measurement value ..volume can also be determined accordingly.
• the cross-section of the foam column is kept constant and it is then possible in a simple manner to determine the corresponding parameters V(t) indicating total volume of foam and solution, volume of foam (V f ) and/or volume of solution (V s ).
• European Patent No. 1 416 261 [1 ] is related to the condition (2a) and (2c) with
• the parameter time of deviation, t deV) is derived from the ratio of the time dependent changes of the corresponding levels of solution/foam ⁇ +Ah s (t) ⁇ and foam/air ⁇ -Ah f (t) ⁇ .
• the parameter time of deviation, t dev refers to the end of that time interval within which
• the parameter time of deviation is related to the initial interval
• the parameter t dev is preferably determined.
• acccording to the invention to determine further parameters, independently of each other or in combination, which allow a characterization of foams.
• minimal concentration of total gas intake (cti), foam capacity, gas holding capacity of the foam, foaming efficiency, foamability, critical concentration of micelle formation (cmc), time of onset of dry foam stage (t dr y), half time of dry foam state ( ⁇ 1 ⁇ 2) and/or gas absorbing capacity of a foam are determined as further parameters.
• foam capacity is determined either as the sole parameter or as a parameter together with one or more of the other parameters given herein.
• foam capacity refers to the different volumes of foam produced by any method of foam generation.
• this parameter is not well-defined as long as it cannot be related to the quantitative volume of gas introduced. If the gas volume is measured and conditions of inequations (5) are maintained, there will always be a maximum value of "foam capacity", which cannot be overrun because of the law of conservation of matter, see equation (3e).
• foam capacity as used in [1 1 , 21], which relates to the volume of foam produced, is not convenient.
• the parameter gas holding capacity is determined, either alone or together with one or more additional parameters.
• gas holding capacity of the foam is suggested, which is given by the weight difference of unit volume of solution and of foam related to the unit volume of foam. This can serve as a relative measure only because the foam itself is taken as reference state whose boundary conditions are not well-defined.
• the parameter gas absorbing capacity of a foam is determined, either alone or together with one or more other parameters.
• the quotient of gas volume contained in the foam to the total gas volume inserted into the foamant solution during the initial stage of foam life is used as reasonable, generally applicable parameter to measure foam capacity or gas holding capacity of the foam.
• A (V 9as ) f oam (V9 as )ins *100 % at t ⁇ t dev , (6a), gives the relative amount of gas in the foam as related to the overall amount of gas inserted.
• the foam capacity has a finite limit, which is achieved at complete incorporation of inserted gas, i. e. at 100 percent. This limit is herein referred to as gas absorbing capacity of the foam, A.
• the quantity A is determined by
• the parameter cti is preferably determined according to the invention either as the sole parameter or together with one or more additional parameters given herein.
• H +0 H dev ⁇ H ma x (7b).
• the minimum concentration of total gas intake, cti indicates the surfactants' specific gas absorption efficiency.
• the cti values are related to their concentration of critical micelle formation, cmc. At the latter concentration, the surfactant's adsorption layer reaches saturation adsorption.
• the ratio cti/cmc denotes the surfactant's lowest adsorption density at which the gas intake reaches the maximum possible value.
• the cti value related to the concentration of micelle formation concerned (cmc) describes the surfactant's individual efficiency of gas intake, which can be used as quantitative measure of the surfactant's foamability.
• Surfactants are classified as highly foamable if they have a cti/cmc value of from 0.01 to 0.2, in particular, from 0.01 to 0.1 .
• Surfactants are classified as having medium formability if they have a cti/cmc value of from 0.5 to 1 , in particular, from 0.8 to 1 .
• the inverse ratio cmc/cti may be used as a measure of the surfactant's specific foaming efficiency (ef) because it refers to the minimal surface concentration enabling total gas embedding at times t ⁇ t dev .
• Fig. 3 various surfactant systems' specific foraming efficiencies are illustrated. With respect to standardization the system decyldimethylphosphine oxide has a foaming efficiency of roughly 100 percent. A surfactant system which reaches its cti value at concentration c > cmc would have a foaming efficiency lower than 100% correspondingly.
• the meaning of the foam parameter time of deviation t dev is given by equations (3a) to (3e) above.
• the time dependence of the two boundary layers foam/solution and foam/air has to be measured simultaneously.
• the parameter time of deviation, tdev can also be determined by the dynamics of the total height H(t) alone, if the conditions given by equations (3a) to (3d) leading to equation (3e) are fulfilled.
• Fig. 4 The new approach for classifying stages of foam life is exemplified in Fig. 4 by evaluating the dependence of foam height on time, h f (t), of a solution of 1 x10 "4 M decyldimethylphosphine oxide. Three different intervals are observed. The end of the initial first interval meets the onset of the intermediate, second interval. The intersection of the two curves represents the value of the parameter time of deviation, t dev . Thus, t dev is at the end of the first stage.
• the first stage of foam decay can also be discriminated by the rate of draining solution in dependence on time, h s (t).
• the limits of the intermediate second stage, in which rupture of foam bubbles and solution efflux proceed simultaneously, are well characterized according to the present invention.
• the onset of the second stage begins at the characteristic time of deviation (t dev ), whereas the end of this second stage is reached at the well-defined state of "dry foam".
• the intermediate state of foam decay covers the time interval between time of deviation and time of onset of dry foam according to:
• the behavior of foams in terms of time is thus divided into three stages of foam life.
• stage I interval I, first interval or initial stage
• H(t) constant.
• the first stage begins at t +0 and ends at t de y
• stage II In the second stage, herein also called stage II, interval II, second interval or intermediate stage, there is simultaneously efflux of solution from the foam and foam rupture.
• stage II In the second stage, herein also called stage II, interval II, second interval or intermediate stage, there is simultaneously efflux of solution from the foam and foam rupture.
• the second stage is between t dev and t dry .
• stage III In the third stage, herein also called stage III, interval III, third interval or final stage, a dry foam is present and there is negligible or no more efflux of solution but only foam rupture.
• the third stage starts at t dry .
• foam parameters can be determined which provide important information about the nature of the foam.
• Preferred parameters which are measured either alone or together with one or more other parameters are half-life of dry foam ⁇ 1 ⁇ 2 and characteristic time of foam stability
• the life time of the dry foam is reasonably described by the half-life of the decaying dry foam, denoted by ⁇ 1 ⁇ 2 .
• This parameter stands for the time interval that is needed for the dry foam to lose half of its original volume.
• Fig. 9 represents the course of foam height in dependence on time within the dry foam stage (t > t dry ) for various surfactant solutions at a logarithmic time scale. All curves exactly follow a linear course as was expected. Thus, the reasonability of the parameter of half-life of dry foam ( ⁇ 1 ⁇ 2) becomes evident.
• the overall lifetime of a foam is determined by the feature of its final stage, which is fundamentally characterized by the half-life of dry foam, ⁇ 1 ⁇ 2.
• the characteristic time ⁇ of foam stability represents the overall time from generation of the foam up to that time when the foam column has decayed down to half of the height of its dry foam.
• Fig. 10 illustrates the dependence of the characteristic time of foam stability, ⁇ , on concentration of surfactant solutions such as nonyl-a-glucopyranoside solutions.
• Foam stability increases linearly with concentration. The same dependence is shown for solutions of two homologous series of decyldimethylphosphine oxide and sodium dodecylsulfate plotted in double logarithmic scale in Fig. 1 1 .
• the latter surfactant forms extremely stable foams, revealing a roughly by one order of magnitude stronger foam stability.
• the characteristic ⁇ vs. (log c) dependence of decyldimethylphosphine oxide reveals a break at the concentration of 1 .8x10 "3 M. It occurs exactly at the critical concentration of micelle formation, cmc.
• the cmc values of micelle forming surfactants can be determined by the parameter characteristic time of foam stability ⁇ , too.
• the nature of the foam/air interface is always more rough than that of the corresponding solution/air interface.
• roughness of the foam/air interface deteriorates with increasing foam life, i.e. the higher foam stability the greater the scatter of the corresponding parameter, cf. for example, Na-dodecylsulfate, Fig. 1 1 .
• any characteristic parameter related to the foam/air (f) interface will be of less accuracy than one based on measurement of the foam/solution (s) interface.
• advantageously parameters are related to the measurement of the solution/foam interface only, which all time remains plain with much better, unchanging quality.
• the invention provides a novel method which allows using solely the solution/foam interface to determine the characteristic foam parameters.
• a further parameter which is determined according to the invention either alone or in combination with one or more additional parameters is the time of reaching the state of dry foam, t dry .
• the remaining foam column in a dry state contains a tiny amount of solution at t > t dry yet, which consists of some residual solution within the foam's Gibbs channels.
• the volume thereof is negligible, of the order of one percent or less of the total solution volume. This is smaller than the corresponding measuring error of the solution height.
• the value of t dry is easily registered when the measuring value of the initial height of the solution column (h s . 0 ) is reached.
• the amount of solution still left in the foam's dry state can be determined and the parameter t dry can be determined, for example, by the solution kinetics in the two states (stage II and stage III), which is distinctly different from each other.
• the parameter t dry is then determined by the intersection of the relationships h s (t) valid within the interval between t dev ⁇ t ⁇ t dry with that (practically) constant value of eq. (10a):
• the characteristic parameter critical micelle concentration (cmc) of surfactants can be determined based on t dry .
• Fig. 12 shows the dependence of the parameter t dry on concentration of the solutions of two different homologous series of surfactants (decyldimethyl- phosphine oxide and nonyl-a-glucopyranoside).
• the numerical values of the parameter t dry are of the same order of magnitude as those of the half time values ⁇ 1 ⁇ 2. This is due to the fact that the value t dry is the first value of the dry foam interval. Hence, due to the exponentially decaying dry foam it is evident that there is a reasonable relationship between the parameters ⁇ 1 ⁇ 2 and t dry .
• the parameter of the onset of dry foam t dry can be used as reasonable stability parameter as well. It is the more favorable parameter because it is related to the well-defined flat solution/foam interface whereas ⁇ 1 ⁇ 2 is related to the less defined, coarse foam/air interface.
• the parameter t dry is preferred compared to the previously suggested parameter of transition time t tr .
• the latter originates from the assumption of a continuously occurring transition region between the initial and the final state of foam decay which does not hold. In fact, it is the intermediate stage in which the rate of change in foam height is lowest as compared to its neighboring stages (cf. also Fig. 6).
• ⁇ 1 ⁇ 2 and t dry are related to each other.
• Fig. 13 proves that there exists a relationship between the characteristic time of foam stability ⁇ and the time of onset of dry foam stage t dry .
• solutions of medium foam stability there is a linear relationship between tdry and ⁇ , whereas solutions of strongest foam stability like sodium dodecylsulfate seem to follow a logarithmic dependence.
• a further preferred parameter by which foam characteristics can be determined is deceleration of initial efflux d 0 .
• the dynamic behavior of the solution/foam interface offers a further possibility to evaluate foam stability. As the quality of this interface is much better than that of foam/air interface and remains always completely plain independent on foam life, it can be measured with good accuracy.
• the rate of draining solution is the greatest at the very beginning of foam life, i. e. at t ⁇ +0.
• d 0 means the decrease of efflux rate within the initial interval per unit of time. According to the invention it is denoted deceleration of initial efflux do.
• Fig. 14 illustrates the dependence of d 0 vs. log c for two kinds of surfactants forming either foams of medium or of strong stability.
• the d 0 values are inversely proportional to foam stability. High do values indicate a high deceleration of efflux, in turn indicating a low foam stability.
• Equal foam stability corresponds with equal values of the parameters d 0 . Since equal numerical d 0 values stand for equal foam stability, the parameter d 0 can be used to compare foaming efficiencies of different foamant systems. As long as there are union sets of d 0 values in the d 0 vs. log c isotherms of different surfactant systems, they can be exploited as follows.
• the parameter deceleration of initial solution efflux d 0 may also be used to standardize surfactant systems with respect to their foaming efficiency.
• the present invention also provides criteria for characterizing wet and dry foam behavior. Accordingly, it can be discriminated between wet or dry foam feature.
• Fig. 15 illustrates the dynamic behavior of the total foam height H(t) of three solutions of a typical wet foam surfactant.
• the time dependence H(t) of the solutions decreases linearly from the very beginning on. There is no initial interval 0 ⁇ t ⁇ t dev detectable during which H(t) remains constant, i.e. drainage and rupture occur simultaneously from the very beginning of foam life up to its end.
• This dynamic behavior is characteristic for any wet foam.
• wet foams do never reach dry foam stage. Their foam life ends when they still contain rather high liquid content between 10 and 20 percent or even more. Foam life of wet foams is comparatively short.
• the ratio between volume of gas inserted into the foamant solution and that embedded in the foam determines the parameter of gas holding capacity of the foam and foaming efficiency, respectively.
• this ratio has a maximum possible value which is reached when the total amount of inserted gas remains enclosed within the foam during the initial stage of foam life.
• the parameter of minimal concentration of total gas intake, cti denotes that minimum surfactant concentration, which enables the complete inserted gas volume to remain absorbed during the initial stage of foam life.
• the inverse ratio cmc/cti allows to quantitatively characterizing the foaming efficiency, ef, of each surfactant. This ratio may differ by almost one order of magnitude.
• the basic parameter of (meta)stable foam is that of half-life of dry foam ⁇ 1 ⁇ 2 which allows to define foam life on a non-arbitrary basis, unlike the usually applied half-life value of the foam's initial height.
• the parameter of half-life of dry foam is the most appropriate parameter to characterize foam stability of stable foams. It sensitively depends on concentration of surfactants.
• the time when the state of dry foam will be reached represents another important parameter. It is denoted by the parameter time of onset of dry foam state, t dry .
• the parameter t dry correlates with the corresponding half- life ⁇ 1 ⁇ 2 .
• the parameter t dry constitutes another reasonable characteristic of foam stability.
• the total time consisting of the sum of time of onset of dry foam state, tdry, and half-life of dry foam, ⁇ 1 ⁇ 2, represents another preferred parameter characterizing foam stability. It is called characteristic time of foam stability ⁇ .
• time of deviation, t d e V) and time of onset of dry foam state, t dry can favorably be determined by measuring the time dependence of the solution/foam interface only. As the quality of the corresponding foam/air interface continuously deteriorates with rising time but the quality of the solution/foam interface remains of much better, unchanging quality this option is favorably applied, especially for stable foam systems.
• wet and dry foam behavior can be discriminated from each other without doubt.
• Stable (metastable) foams are of long life which exceeds that of wet foams by orders of magnitude. Their final stage is that of dry foam with negligible liquid content left. In the dry foam state the solution efflux has practically ceased. Their lifetime is most appropriately characterized by the parameter of half-life of dry foam, ⁇ 1 ⁇ 2, which is related to a well-defined scientific basis. The time of the onset of the dry foam stage, tdry, is another convenient parameter to characterize foam stability together with the sum of these two parameter values, called characteristic time of foam stability,
• Stability of dry foams can likewise be related to the velocity and/or deceleration of solution efflux at the very beginning of foam life, v s 0 and do.
• Solutions forming dry foams can absorb the entire amount of gas introduced into the solution to be foamed from certain minimal concentrations cti on, characteristic of each surfactant. At concentrations c > cti the total amount of gas remains absorbed in the foam during the initial interval 0 ⁇ t ⁇ tdev- 16.
• concentrations c > cti the total amount of gas remains absorbed in the foam during the initial interval 0 ⁇ t ⁇ tdev- 16.
• the apparatus consists of a glass column of 42 mm inner diameter and 25 cm length with a fritted glass G 2 at the bottom for gas dispersing, and a syringe for supplying a definite amount of gas (air) into the solution to be foamed.
• Beneath the frit is a stopcock, which is connected to a small pump the piston of which is driven automatically at a preset gas flow rate of e.g. 18 l/h. Volumes of 50 ml of solution and 90 ml of gas were used.
• the gas from the syringe was introduced into the solution through the sintered glass, applying gas flow rate of 18 l/h.
• the stopcock was locked when the solution (50 ml) was poured into the column in such manner that no foam was formed.
• the filled foam column is fixed between optical sensors of the foam test system (FTS) originally developed by the firm Paar. After having positioned the filled glass column appropriately between the sensors, the stopcock was opened and subsequently 90 cm 3 of air were bubbled via the frit into the surfactant solution by a connected RTU Dosierpumpe (firm Paar). Then foam and solution height were recorded simultaneously. Due to the certain size of the fotodiodes the minimal measurable difference of the height of the foam and/or the solution column was 2.5mm. The experiments were performed at room temperature (22 ⁇ 1 °C).
• Total foam height H 0 ⁇ H max of various surfactant solutions in dependence on concentration The concentration of total gas intake, cti value, denotes the lowest required concentration at which the complete gas volume pressed into the solution remains dispersed unchanged in the foamant solution during the initial range of foam life, i. e. during the interval 0 ⁇ t ⁇ t dev .
• the onset of the dry foam region is denoted by t dry .
• ⁇ 1 ⁇ 2 stands for the half-life of the dry foam interval, when h f equals 1 ⁇ 2xh dry .

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• 2014
  • 2014-06-30 WO PCT/EP2014/063833 patent/WO2016000739A1/en active Application Filing

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