Static and Dynamic Stickiness Tests to Measure Particle Stickiness †

Sticking of particles has a tremendous impact on powder-processing industries, especially for hygroscopic amorphous powders. A wide variety of experimental methods has been developed to measure at what combinations of temperature and moisture content material becomes sticky. This review describes, for each method, how so-called stickiness curves are determined. As particle velocity also plays a key role, we classify the methods into static and dynamic stickiness tests. Static stickiness tests have limited particle motion during the conditioning step prior to the measurement. Thus, the obtained information is particularly useful in predicting the long-term behavior of powder during storage or in packaging. Dynamic stickiness tests involve significant particle motion during conditioning and measurement. Stickiness curves strongly depend on particle velocity, and the obtained information is highly relevant to the design and operation of powder production and processing equipment. Virtually all methods determine the onset of stickiness using powder as a starting point. Given the many industrial processes like spray drying that start from a liquid that may become sticky upon drying, future effort should focus on developing test methods that determine the onset of stickiness using a liquid droplet as a starting point.


Introduction
Sticking of particles has a tremendous impact on numerous industries that process powders. Sticking can cause several issues, such as fouling and blockage of equipment, or caking of stored powder. It can also be used advantageously to produce agglomerates with beneficial properties. Why, how, and when particles stick together are critically important questions. In this review, we focus on the 'when' question by reviewing the experimental methods commonly used to determine the conditions under which sticking occurs. We hereby focus on the stickiness of hygroscopic amorphous powders, which play a major role in the food industry (Boonyai et al., 2004). Crystalline materials, which may also stick, but through a different mechanism (Kamyabi et al., 2017), are beyond this review's scope.
Whether two particles stick depends on their material and a wide variety of parameters, including their temperature, and moisture content. A common way to characterize the stickiness of a material is to map the stickiness based on the environmental temperature and the moisture content. The moisture content can be described in terms of the particle's water mass fraction (x w ), or the equilibrium environmental relative humidity (RH). The part of the parameter space for which the material is sticky is called the sticky region, which is bounded by the so-called sticky-point curve, T 1 (x w ), and the so-called tack boundary, T 2 (x w ), as illustrated in Fig. 1. Besides the environmental parameters, this map also illustrates the particle's material properties in the form of a boundary between the glassy state and the rubbery state, known as the glass transition temperature, T ɡ (x w ). The rubbery state has some overlap with the sticky region, and with further hydration becomes the liquid state (Roos, 2002). While particles are non-sticky in the glassy state, material properties, especially viscosity, drastically change upon transitioning to the rubbery state. Hence, the curves represented by the differences T 1 (x w ) -T ɡ (x w ) and T 2 (x w ) -T ɡ (x w ) are two meaningful measurements of the sticky-region that include the influence of temperature, moisture content, as well as the material. The distance between the sticky-point curve T 1 (x w ) and the glass transition curve T ɡ (x w ) often slightly depends on x w (Palzer, 2005). Therefore, the onset of stickiness is commonly reported as a constant critical deviation from T ɡ (x w ), denoted as (T -T ɡ ) c .
Experimental stickiness tests generally aim to determine the sticky-point curve or the tack boundary by measuring stickiness for different temperatures and moisture contents. While most methods approach the sticky region from the glassy state to find T 1 (x w ) -T ɡ (x w ), a limited number of methods approach the sticky region from the liquid state to find T 2 (x w ) -T ɡ (x w ). Although the tack boundary is less well understood, it is known that the change in behavior is less sharp than near the sticky-point curve (Kudra, 2003). While the measured parameter may differ between the experimental methods, what all methods have in common is that they follow two steps: (1) a conditioning step, where the material is subjected to a specified temperature T and humidity RH for a certain time window and (2) a measurement step where the stickiness of the powder is measured (Boonyai et al., 2004). Whereas these steps are separated for some methods, they are intertwined for others. Hence, not only the duration of conditioning influences the sticky region's boundaries but also the used measurement method. While the influence of conditioning time is well understood (Kamyabi et al., 2017), the influence of particle motion in the conditioning and/or measurement step on the boundaries of the sticky region is still unclear. For skim milk powder, one of the most abundantly tested materials, a wide range for T 1 (x w ) -T ɡ (x w ) has been reported. For particles that are static during the conditioning step, values as low as 8 °C were reported for T 1 -T ɡ (Verdurmen et al., 2006). By contrast, values as high as T 1 -T ɡ = 63 °C were reported for particles moving at tens of meters per second (Walmsley et al., 2014).
Following Verdurmen et al. (2006), we therefore distinguish between two classes of methods in this review. The first class is where the particles can be considered static during conditioning (not set in continuous motion through external means). The second class is where the particles are moving during conditioning. We refer to the first class of methods as static stickiness tests and to the second class as dynamic stickiness tests.
This review aims to provide an overview of the available methods to measure stickiness. As static stickiness tests, we describe various visual observation tests, the shear test, the penetration test, and the blow test. As dynamic stickiness tests, we describe the sticky-point test, the fluidized bed test, the particle gun, the cyclone test, the optical test, and the probe test. For each method, we describe how it can be used to determine either the sticky-point curve T 1 (x w ) or the tack boundary T 2 (x w ) of the sticky region. Additionally, we describe what we view to be the method's best application in industry. The overview of methods shows that particle velocity plays a significant role in the measured boundaries of the sticky region, illustrating the importance of choosing the most appropriate method for the application in mind.

Glass transition temperature
The glass transition temperature T ɡ marks the temperature where an amorphous material transitions from a glassy state to a rubbery state upon increasing temperature. While both states are fundamentally a liquid, the behavior of the glassy state is solid-like, being hard and brittle, and the rubbery state behaves like a highly-viscous liquid. The nature of the glass transition is the molecular freedom of movement, which is restricted in the glassy state (Roos, 2002).
The most common method to experimentally determine T ɡ is using differential scanning calorimetry (DSC), although several other methods are available (Li et al., 2019). In DSC, the T ɡ is found by subjecting the material in the glassy state to a temperature ramp and measuring the specific heat capacity. The specific heat capacity shows a characteristic change during the glass transition Roos, 2010). By repeating the experiment at different x w , the curve for T ɡ (x w ) shown in Fig. 1 can be experimentally constructed. Similarly, dynamic vapor sorption (DVS) can be used to measure the vapor sorption characteristics by applying a ramp in relative humidity at a fixed T while measuring the sample's mass. In the glassy state, water sorption only occurs at the surface, while the rubbery state also allows for bulk sorption, such that a characteristic change in the water sorption rate is observed at T ɡ (Burnett et al., 2004).
The glass transition temperature can also be estimated theoretically, for example using the Gordon-Taylor or Couchman-Karasz equation. The Gordon-Taylor equation can be used to determine the influence of water on the glass transition temperature T ɡ (x w ) of a dry powder, based on the glass transition temperature of the anhydrous powder (T ɡ,s ) Fig. 1 Map of temperature and moisture content showing the region in which a material is considered sticky. This region is enveloped by the sticky-point curve (T 1 (x w )), the tack boundary (T 2 (x w )), and the temperature above which the material decomposes. The sticky-point curve and tack boundary are often reported with respect to the glass transition temperature of the material (dashed line), which separates its glassy state from its liquid state. The difference T 1 (x w ) -T ɡ (x w ) is in literature more commonly referred to as (T -T ɡ ) c . Figure is modified from Lockemann (1999) and Kudra (2003). and pure water (T ɡ,w ), and the weight fraction of moisture, with T ɡ,w = -135 °C (Roos, 2002). The constant k is often calculated from the densities ρ, T ɡ,s , and T ɡ,w as k = (ρ s T ɡ,s )/ (ρ w T w,s ) (Katkov and Levine, 2004;Simha and Boyer, 1962). The Couchman-Karasz equation, while similar to Eq. (1), is based on thermodynamic additivity of specific heat capacity. Although different versions are reported, the so-called 'modified' version is found when using k = ∆C p,w /∆C p,s in Eq. (1). The changes in heat capacity ∆C p at T ɡ can be found using DSC (Sochava, 1997). For ∆C p,w , 1.94 J K -1 g -1 is often used (Katkov and Levine, 2004;Roos, 2002). Katkov and Levine 2004 showed that the modified version of the Couchman-Karasz equation overestimated the T ɡ of mixtures and underestimated the plasticizing effect of water while they obtained a better fit using the so-called 'original' Couchman-Karasz equation While the Gordon-Taylor and Couchman-Karasz equations are suitable for most simple systems and can be used to construct the curve for T ɡ (x w ) in Fig. 1, they should be used with caution when considering complex mixtures (Katkov and Levine, 2004).
The glass transition temperature servers as a natural reference in the stickiness map and allows one to compare the stickiness of different type of materials. Similarly, the T ɡ serves as a reference in an attempt to come to a universal predictive equation of the dynamic viscosity in the rubbery state. The Williams-Landel-Ferry (WLF) equation relates the viscosity of a material to the distance from the T ɡ -curve (T -T ɡ ) as with C 1 and C 2 two constants and η ɡ the viscosity at the glass transition temperature. While the WLF equation is often considered to be valid for temperatures up to T ɡ + 100 °C (Lomellini, 1992;Williams et al., 1955), it is only valid if correct values for the constants and η ɡ are chosen. Values of η ɡ are typically in a range between 10 11 Pa s to 10 14 Pa s (Downton et al., 1982;Katkov and Levine, 2004;Murti et al., 2010;Palzer, 2005;Paterson et al., 2015;Wallack and King, 1988). Recently, the glass viscosity of freeze dried amorphous lactose was measured to be 1.1 × 10 14 Pa s, although the authors suggest that further confirmation is required (Paterson et al., 2015). The wide variety of reported constants suggests that there is no universal set valid for different types of materials and different temperatures.
Nevertheless, (C 1 , C 2 ) = (-17.44, 51.6 K) as originally reported by Williams et al. (1955), are often considered to be universal (Aguilera et al., 1993;Murti et al., 2010;Palzer, 2005;Schulnies and Kleinschmidt, 2018;Wallack and King, 1988). Peleg (1992) found that these constants give large deviations when T -T ɡ > 20 °C, and suggested (C 1 , C 2 ) = (-10.5, 85.6 K), which better matched the experimental trend for the η ɡ of amorphous lactose measured by Paterson et al. (2015). However, (C 1 , C 2 ) = (-8.86, 101.6 K) also provided a good fit to other experimental data (Dagdug and Garcıá-Colıń, 1998;Ferry, 1980). Others use material-specific constants, such as (C 1 , C 2 ) = (-14.5, 36.4 K), which were fitted for skim milk powder (Walmsley et al., 2014). Since the WLF equation is exponential, care should be taken in the choice of the constants when using the WLF equation to predict the dynamic viscosity. To illustrate the importance of this choice for a prototypical case (T -T ɡ = 20 °C and η ɡ = 10 12 Pa s), the constants by Williams et al. (1955) give η = 1.3 × 10 7 Pa s, while the constants by Peleg (1992) gives η = 1.0 × 10 10 Pa s, which is a difference of three orders of magnitude. As there are currently no clear rules of thumb on the selection of constants, we suggest that best practice would be to fit C 1 and C 2 to experimentally measured viscosity data. The direct relation between viscosity and T -T ɡ through the WLF equation leads to the natural question whether viscosity can be used as a predictor for stickiness. The success of viscosity as a predictor is expected to depend on the dominant mechanism of adhesion. For hygroscopic amorphous powders close to T ɡ , sticking is expected to occur primarily through immobile liquid bridging or viscoelastic deformation (Palzer, 2005). In case immobile liquid bridging primarily causes sticking, we generally expect viscosity to be more meaningful than when viscoelastic deformation primarily causes sticking. More specifically, using sintering theory by Frenkel (1945) and classic viscoelastic contact models, Palzer (2005) could predict the critical T -T ɡ needed for sticking. However, this model did not successfully predict sticking of high velocity particle gun experiments (Murti et al., 2010). A contact model for adhesive elastic particles showed better results when predicting the critical T -T ɡ for high velocity collisions (Walmsley et al., 2014). The mentioned works strongly suggest that viscoelasticity should be accounted for when predicting (T -T ɡ ) c for collisions of particles in motion, and that the observed (T -T ɡ ) c is a result of the colliding material's rheological behavior and the collision's kinetics.

Static stickiness tests
Testing stickiness of powders using static stickiness tests follows a general protocol. First, a powder bed is compressed under a stress σ to cause a certain amount of consolidation (Fig. 2a). Second, the powder is conditioned by exposing it to an environment of controlled temperature and relative humidity (Fig. 2b). The duration of this conditioning step can be adjusted. When sufficiently long, the powder's moisture content is in thermodynamic equilibrium with the moisture in the environment such that x w and RH are related through a vapor sorption isotherm. Third, a measurement is performed on the conditioned powder (Fig. 2c). Prior to the measurement, the powder can be considered static with little movement of the particles. Therefore, we refer to this class of tests as static stickiness tests, which are deliberately different from the dynamic stickiness tests in which the particles are actively set in continuous motion during the conditioning and measurement step. Next, we describe the different static stickiness tests.

Visual observation
The most straightforward form of analysis is through visual observation. Typically, a sample with a specified dry matter content is placed in a closed container. After conditioning it at a given temperature, the container is turned upside down to see whether any particles are stuck to the bottom. This procedure is repeated at different temperatures until particles noticeably stick to the bottom, which is identified as the sticky-point temperature (Palzer, 2005). By repeating this procedure for different moisture contents, the sticky-point curve T 1 (x w ) in Fig. 1 can be constructed. An alternative visual observation test is one in which the powder's temperature is increased stepwise while observing changes in the appearance of the powder bed (Tsourouflis et al., 1976;Verdurmen et al., 2006).

Shear test
Shear tests are used to characterize powder stickiness by measuring the powder's response to shear stress. Two common approaches are uniaxial compression and shearing in shear cells. The uniaxial compression approach consolidates the bed with normal stress σ and then compresses along one axis until failure. The failure stress σ f for different values of σ gives a yield locus that can be used to find the unconfined yield strength σ c by drawing a Mohr circle starting at σ = 0 Pa (Schulze, 2008). The unconfined yield strength σ c is used as the parameter for bed strength and can be determined for different environmental T and RH (Fitzpatrick et al., 2007b;Hartmann and Palzer, 2011). In order to find a sticky-point curve T 1 (x w ), a critical bed strength, which is characteristic for a sticky powder, must be determined first. It can be empirically determined before testing using the same or comparable materials (Palzer and Zürcher, 2004).
Similarly to uniaxial compression, shear cells can be used to determine σ c and acquire T 1 (x w ) by defining a critical σ c for the bed strength of a sticky powder (Hartmann and Palzer, 2011; Schulnies and Kleinschmidt, Fig. 2 An overview of the static stickiness tests. a) In the consolidation step, the powder is compressed under a stress σ. b) In the conditioning step, the powder is subjected to temperature T and relative humidity RH for a specified duration. c) The measurement of stickiness proceeds differently per test. 2018). However, shear cells improve on result consistency by preshearing before measuring the failure stress. Preshearing to steady-state at normal stress σ 1 eliminates any stress history, for example, due to filling (Schulnies and Kleinschmidt, 2018). After preshearing, the shear stress is reversed to reduce the shear stress to zero. Subsequently, the sample is sheared to failure while measuring shear stress σ τ under normal stress σ 2 so that σ 1 < σ 2 (overconsolidation), which ensures a peak is observed for the failure stress (Schulze, 2008). By shearing to failure at different σ 2 while preshearing at identical σ 1 a yield locus can be found. From this point on, the acquisition of σ c and T 1 (x w ) is similar to uniaxial compression.
Besides acquiring the sticky-point curve, shear tests have other commonly used applications related to stickiness and powder cohesion. Shear tests are commonly used to quantify the powder flowability. The flowability is described in terms of the flow function, which is the inverse slope in a plot of unconfined yield strength σ c versus normal stress σ (Fitzpatrick et al., 2007b;Jenike, 1964;Papadakis and Bahu, 1992;Schulze, 2008). Shear cells can also be used to measure wall friction. This is done by replacing the bottom ring of a shear cell with the wall material. When choosing the wall material similar to industrial surfaces or packaging materials, the adhesion of powder to these substrates can be measured (Papadakis and Bahu, 1992;Schulze, 2008).
Commonly used examples of shear cells are the manual Jenike shear cell (Jenike, 1964), the automated Schulze ring shear test (Schulnies and Kleinschmidt, 2018), or the more recent Freeman FT4 Powder Rheometer (Freeman, 2007) and Anton Paar MCR rheometers (Anton Paar GmbH, 2020; Groen et al., 2020). Conveniently, both the Freeman and Anton Paar powder rheometers can quickly change environmental T and RH independently through powder bed aeration with conditioned airflow (Freeman, 2007;Groen et al., 2020;Mitra et al., 2017). Besides uniaxial compression and shear cells, other types of shear tests for measuring flowability have been reported (e.g., Warren Spring cohesion tester, Peschl shear cell). These were not described as their application to find T 1 (x w ) was not found in literature (Pasley et al., 1995).

Penetration test
Penetration tests are similar to the uniaxial compression tests, but use a puncher with a diameter of 1 mm to 2 mm to penetrate the powder bed to a preset depth (Knight and Johnson, 1988). Measurement of the required penetration force F p , which is a measure for bed strength (Özkan et al., 2002; 2003), is done after conditioning at a fixed T and RH for a given time. Through repetition, while varying these conditions, the sticky-point curve T 1 (x w ) is found for the combinations of T and RH, where the measured F p equals a predetermined critical value for which the powder is considered sticky (Özkan et al., 2003).

Blow test
The blow test uses a small thin tube to blow air at a powder bed surface. The tube is placed millimeters above the surface at an angle of 45°. The airflow through the tube is increased until particles dislodge from the surface of the conditioned powder bed, which is the endpoint of the blow test. The flow rate of air at which particles start dislodging is a measure for bed strength (Paterson et al., 2001). The sticky-point curve T 1 (x w ) is found at the T and RH where the airflow to dislodge particles reaches a predetermined critical value for which the powder is considered sticky Paterson et al., 2005).
A benefit of the blow test is the ability to test multiple times without needing to repeat the consolidation and conditioning step. The powder bed sits on a distributor plate, which sections the powder into multiple parts with an equal amount of powder. Each section of powder is conditioned with the same T and RH and can be measured separately by rotating the thin tube. Therefore, the blow test is convenient when interested in temporal measurements, such as determining the rate of bed strength increase .

Comparison of tests
While simplicity is a strength of the visual observation tests, it is also their greatest weakness. The accurate detection of the sticky-point temperature relies on the observer's experience. Based on caking theory, we expect that visible changes in powder properties occur after a high degree of agglomeration has taken place (Kamyabi et al., 2017). Hence, human observers can miss the onset of stickiness, which would cause an over-prediction of the sticky-point temperature. The onset of stickiness can be more precisely quantified with the other tests. Based on the literature, we find that shear tests are more accurate than penetration tests, with less scatter of data and time consolidation effects that are easier to detect (Knight and Johnson, 1988;Schwedes, 2003). Based on these findings, we recommend using uniaxial compression or shear cells instead of penetration tests, in line with Knight and Johnson (1988), who recommended to only use penetrometry in support of shear cell experiments. While shear tests are applied to the bulk of the powder, the blow test is applied to the powder's surface, suggesting that the blow test mostly tests the surface conditions. Blow tests nevertheless create channels in the powder bed (Billings et al., 2006;Paterson et al., 2005), indicating that the bulk is strongly affected by blow test. Hence, we expect that blow tests can be used to determine (bulk) stickiness, similarly to the shear tests. An advantage of the shear tests over the blow test is that the compression during consolidation can be maintained during conditioning, while an advantage of the blow test over the shear tests is that multiple measurements can be performed without having to repeat the consolidation and conditioning steps.
The shear, penetration, and blow tests can be used to quantify bed strength for different T and RH based on the measured parameter (yield strength, penetration force, flow rate). To, in turn, relate bed strength to stickiness, a predetermined value of the critical bed strength is required at which the powder of interest is considered sticky. A way to overcome having to predetermine a critical bed strength is by considering the temporal behavior. Experiments with the blow test, for example, show an initial linear increase of bed strength with time (Foster et al., 2006;. Similar experiments with shear cells are timeconsuming since each test requires repetition of consolidation and conditioning, but suggest a similar linear increase of bed strength with time (Fitzpatrick et al., 2007a;2008). By measuring the rate (i.e., slope) of increase for a range of T -T ɡ , one can infer the sticky-point curve T 1 (x w ) by plotting the rate versus T -T ɡ and extrapolating to arate of zero. In case the critical bed strength is not available a priori, studying the temporal behavior to determine the rate of bed strength increase as a function of T -T ɡ provides a means to construct the sticky-point curve T 1 (x w ).

Application areas of static stickiness tests
Generally, the static stickiness methods are useful in predicting the long-term behavior of powder during storage, transport, or in packaging. In these situations, particles may stick together under the influence of humidity in a process known as caking. This process comprises multiple steps. Firstly, environmental conditions cause particle surfaces to become viscous. Contacting liquid particle surfaces become connected through liquid bridges. Secondly, the liquid bridges that formed grow in size, increasing powder cohesion. Thirdly, the pores that existed between particles disappear as the liquid fills up the pores (Kamyabi et al., 2017). During the caking process, the bed strength initially increases with time until a maximum value is achieved. As the process continues, the bed strength starts to decrease, attributed to partial crystallization of material to non-sticky crystals (Fitzpatrick et al., 2007b), as well as a decreased liquid bridge viscosity due to increased liquid adsorption (Hartmann and Palzer, 2011). Static stickiness tests are particularly suitable for assessing the progress of caking by monitoring bed strength as a function of time. Shear tests are particularly useful because they can emulate storage environment conditions in a warehouse or transport vehicle by maintaining a certain level of compression during conditioning and measurement. Using shear cells where the powder can be sheared against a wall material is also applicable to measure powder stickiness in food packaging.

Dynamic stickiness tests
The class of dynamic stickiness tests covers the tests where particles are not static during conditioning, but set in continuous motion through external means. This introduces particle velocity or contact time between particles as an additional relevant parameter. An overview of dynamic stickiness tests is listed in Table 1, showing the measured parameter and the most suitable application. Most dynamic stickiness tests approach the sticky region from the glassy state, while just a few approach it from the liquid state.

Sticky-point test
The sticky-point test is the earliest reported method to measure stickiness, hence the name (Lazar et al., 1956). This test has also been referred to as a propeller-driven test (Boonyai et al., 2004). As shown in Fig. 3, the device uses a container in which a powder with known moisture content x w is placed. The sample container is submerged in a heating medium to control the powder's temperature.
The sample is continuously stirred at fixed angular velocity with a stirring device, and the required torque τ is measured. Typically, a temperature ramp is imposed where the temperature is slowly increased until the powder transitions from the glassy to the rubbery state. Above T ɡ , the cohesive forces increase. Further increase of the temperature leads to particles sticking together, leading to a sharp increase in the required τ. The temperature where this sharp increase is observed is identified as the sticky-point temperature. By repeating the test with different x w , the sticky-point curve T 1 (x w ) can be found. Detection of the sticky-point in the earliest versions relied on manual stirring. When the stirring had become noticeably more demanding, the sticky-point was reached (Downton et al., 1982;Lazar et al., 1956). More accurate detection methods use automatic stirrers or shear cells equipped with stirrers, which record the τ required for stirring (Özkan et al., 2002;Wallack and King, 1988). Recently, the method has been further improved by utilizing aeration in an Anton Paar rheometer equipped with a propeller (Groen et al., 2020). The option to aerate the powder is used to fluidize the powder, which occurs at a sufficiently high airflow velocity. The powder conditions are controlled by changing the T and RH of the airflow, instead of using a heating medium surrounding the container. The propeller stirs the fluidized powder and measures the required τ. The required τ is substantially smaller than without fluidization, although the rheometers are sufficiently sensitive (Groen et al., 2020). The benefit of aeration or fluidizing is that environmental conditioning occurs rapidly by changing the air's temperature and humidity. In our view, this makes the sticky-point test combined with fluidizing the powder a promising method for measuring dynamic stickiness, both in terms of accuracy and a shorter experimental time.
Besides applying the sticky-point test to free-flowing powder, it has also been used to measure the stickiness of drying liquids. Hence, instead of determining the stickypoint curve T 1 (x w ), the tack boundary T 2 (x w ) is determined. Kudra (2003) used a laboratory batch dryer equipped with a stirrer to measure the stickiness of drying sludge. They found that the temperature where the torque substantially increased was different from the T 1 (x w ) that is found when approaching from the glassy state. The conclusion was that most materials have a sticky-region in which they are sticky (Kudra, 2003).

Fluidized bed
As discussed for the sticky-point test, the fluidization of powder reduces the required conditioning time. However, because powder fluidization is highly sensitive to powder cohesiveness, the fluidized bed in isolation is also suitable to measure stickiness. In a fluidized bed, which is shown in Fig. 4, a powder bed sits in a column while airflow is applied at the bottom. Fluidization causes expansion of the powder bed so that the powder displays fluid-like behavior with a high degree of mixing. The sticky-point curve's acquisition goes as follows: The T or RH of the fluidizing air is increased stepwise. Most commonly, a RH ramp is used at a fixed T by increasing the airflow's humidity. As the cohesiveness increases, there is a point where the fluidized bed collapses (defluidization). The conditions where the collapse of the powder bed is observed, visually, or using pressure drop measurements, is the sticky-point T 1 (Palzer, 2005;Verdurmen et al., 2006). By repeating the RH ramp at different temperatures, the sticky-point curve T 1 (x w ) can be drawn.
In many cases, fluidized bed collapse is detrimental when it occurs. Hence, much research has been done on the detection and prevention of bed collapse (Bartels et al., 2008). Methods such as the attractor comparison method can be used to detect early changes in the bed that indicate an upcoming collapse (Van Ommen, 2001) and have been used to determine the sticky-point curve T 1 (x w ) (van Fig. 3 A sticky-point test. A powder with known moisture content is placed in a temperature-programmable water bath. The powder is stirred at a fixed angular velocity, and the required torque τ is measured. Fig. 4 A fluidized bed test. The humidity or temperature of the conditioned airflow is increased stepwise until the powder bed collapses. der Knaap, 2006;Verschueren et al., 2007). When such detection methods are implemented, the sensitivity of the fluidized bed as a stickiness test is expected to be high.

Particle gun
The particle gun has been designed to measure the sticking of high-velocity particles to a wall and is shown in Fig. 5. It is a duct through which conditioned air is flowing at high velocity with a target plate at the far end of the duct. For each experiment, a sample of approximately 25 g powder is introduced into the duct. The particles become entrained in the conditioned air-jet shortly until eventually impacting the target plate. Due to the short exposure of particles to the air, the particle gun relies heavily on the rapid acclimation of the powder surface to environmental conditions. The short acclimation time has consequences for liquid bridge formation as the thin surface region that has adsorbed vapor limits their potential width (Murti et al., 2010). The measured parameter is the percentage of injected powder deposited on the target plate. Plotting this parameter versus T -T ɡ shows negligible 0 % deposition until a critical value of T -T ɡ is reached. Above this temperature, deposition is observed and increases linearly with T -T ɡ . The temperature where deposition starts increasing is taken as T 1 (x w ) (Zuo et al., 2007).

Cyclone test
The cyclone test, shown in Fig. 6, uses a cyclone in which conditioned air is circling (Boonyai et al., 2002). When the air is at a steady-state, approximately 1 g of powder is injected at the top of the cyclone. When conditions are such that the powder becomes sticky, particle lumps and powder deposition on the cyclone are observed within minutes. Longer experimental times lead to full immobilization of the powder. The experiment starts at a low RH of the air and is increased stepwise until lumping and deposition are observed visually, which marks a point on the sticky-point curve T 1 (x w ). Lockemann (1999) proposed an optical test, shown in Fig. 7, which uses changes in reflectivity to determine the sticky-point curve. The proposed optical test consists of a rotating test tube containing the free-flowing powder with known (x w ). The tube is inserted into an oil bath with a programmable temperature. A near-infrared source emits light to the sample while a fiber-optical sensor records the back-scattered signal. The sensor is also immersed in the oil-bath to prevent any refraction of the signal. When particles in the tube stick together, the powder flowability changes, which is observed as a sudden change in reflectivity. This marks the sticky-point temperature T 1 (Lockemann, 1999). The experiment has to be repeated for different x w to determine T 1 (x w ).

Probe test
The probe test is the only method that is solely applicable to measure stickiness when starting from the liquid state. Hence, instead of the sticky-point curve T 1 (x w ), the tack boundary T 2 (x w ) is found. The probe test can be applied to liquid films or droplets (J. Chen et al., 2008;Werner et al., 2007a). The approach for either is similar. Fig. 5 The particle gun. Conditioned air flows with high velocity through an air duct. The powder is introduced through a funnel, and the entrained particles hit the target plate. Particles either bounce off or deposit on the plate.

Fig. 6
A cyclone stickiness test. Conditioned airflow is used to circulate a powder sample through the cyclone. Non-sticky particles remain entrained in the cyclone, while sticky particles can agglomerate or stick to the cyclone wall. Fig. 7 The optical test. A rotating sample tube is placed in a heated water bath. A fiber-optical sensor illuminates the sample and receives scattered light. Redrawn from Lockemann (1999). Fig. 8 and goes as follows. Droplet evaporation is monitored gravimetrically by placing the droplet on a scale (Werner et al., 2007a(Werner et al., , 2007b. At some point during evaporation, a probe is lowered with a fixed speed to touch the droplet's surface and then retracted, also with a fixed speed, while the required force for retraction is measured. Hence, this approach is similar to a force measurement with Atomic Force Microscopy (Fabre et al., 2016). The peak tensile force F TU is then determined, which is a measure of the tack, or stickiness, of the sample (Hammond, 1965;Kambe and Kamagata, 1969). By plotting F TU versus drying time, a point is found where F TU increases substantially, marking the tack boundary T 2 (x w ) with x w determined gravimetrically based on the initial solids concentration and the measured weight loss. It should be noted that the measured F TU is influenced by the probe speed and material (Adhikari et al., 2007;Green, 1942). Besides x w , the sample's temperature T also changes during evaporation, which should be accounted for when determining T 2 (x w ) (Schutyser et al., 2019).

Comparison of tests
The particle gun, fluidized bed, cyclone test, and optical test use a powder as a starting point, approaching the sticky region from the glassy state to find the sticky-point curve T 1 (x w ). The probe test starts from the liquid state and hence can be used to determine the tack boundary T 2 (x w ). The sticky-point test can be used starting from the glassy or liquid state and is hence suited for determining both boundaries. The influence of inter-particle contact time was already observed for the static stickiness tests investigating caking. The longer the powder bed is subjected to environmental conditions where the powder will cake, the stronger the powder bed becomes. Control over particle motion and contact time in the dynamic stickiness tests provides a means to investigate the influence of motion within a sample on the boundaries of the sticky region.
Particle motion depends on the angular velocity of the stirrer or the container in the sticky-point and optical tests, on the air velocity in the fluidized bed, cyclone test, and particle gun, and the probe speed in the probe test. A key challenge, in comparing these tests or studying the influence of particle motion on the boundaries of the sticky region, is that particle motion largely differs in all these tests. Even for a single test at a single condition, particle motion may be heterogeneous. In a sticky-point test, for example, stirring can cause the powder to distribute inhomogeneously in the stirring vessel, e.g., due to the stirrer digging channels in the powder. Similarly, in a fluidized bed, the particle velocities are inhomogeneous, mostly due to the common occurrence of bubbling (Seville et al., 2000). Hence, quantification of the relative velocity between the particles, and the resulting inter-particle contact time, presents a challenge, apart from the particle gun where the particle impact velocity may be controlled and quantified (Murti et al., 2010;Walmsley et al., 2015;Zhao, 2009).
The clearest influence of particle motion has been observed with the particle gun, as shown in Fig. 9. The data by Murti et al. (2010) shows a minimal increase for (T -T ɡ ) c with increasing v i . The data by Walmsley et al. (2015) shows a sharp increase of (T -T ɡ ) c with increasing v i , although, at v i > 20 m s -1 , the effect appears to level off. A similar trend was observed by Zhao (2009) where v i ranged from 10 m s -1 to 45 m s -1 . These particle gun experiments show that a larger v i shifts T 1 (x w ) to higher temperatures so that (T -T ɡ ) c is increased.
The influence of particle motion also becomes apparent when different methods are compared with each other. A static method where the visual change of an SMP bed was used to find (T -T ɡ ) c was compared with a dynamic fluidized bed method where the pressure change was used to find (T -T ɡ ) c (Verdurmen et al., 2006). Over an Fig. 8 The probe test. A probe is lowered until it touches the evaporating droplet. The probe retracts, and the required tensile force F TU is measured. The droplet evaporation is monitored gravimetrically. Redrawn from Boonyai et al. 2004. Fig. 9 Velocity-dependence of (T -T ɡ ) c using skim milk powder and the particle gun. Triangles ▲ are data by Walmsley et al. (2015); circles • are data by Zhao (2009), and squares □ are data by Murti et al. (2010). Note that the data cannot be directly compared between authors as different experimental settings were used. Error bars indicate the experimental range for (T -T ɡ ) c that was reported by the respective authors. The dashed trendlines are to guide the eye. experimental range of RH = 12 % to 30 %, the average offset of the sticky-point curve to the T ɡ was determined. The static test resulted in an average offset of T -T ɡ = 13 °C and the dynamic stickiness test resulted in an average offset of T -T ɡ = 18 °C. Another example is a comparison between the dynamic fluidized bed and particle gun tests. The (T -T ɡ ) c was obtained for both methods using various types of skim and whole milk powder. While the results varied, for 6 out of 8 samples, the (T -T ɡ ) c was lower for the fluidized bed by ≈ 10 °C to 15 °C. For the other two samples, the two methods provided similar results (Murti et al., 2010;Zuo, 2004). Based on these results, we strongly recommend matching the velocity of the particles in the dynamic stickiness test to the application in mind to achieve the most accurate T 1 (x w ).
In an attempt to further clarify the influence of particle motion on (T -T ɡ ) c , data from dynamic stickiness tests was gathered in Table 2. No data was found for the optical test and data for the probe test could not be used to find (T -T ɡ ) c . For each experiment, the impact velocity v i of particle collisions was estimated. For the particle gun, the v i was chosen as the air jet velocity. For the sticky-point test, v i was estimated as the maximum angular velocity of the stirrer. For the fluidized bed, an average particle velocity p v [11] was estimated using Eq. (4), with U the superficial velocity and U mf the minimum fluidization velocity (Ennis et al., 1991). The constant α was estimated from Seville et al. (2000) to be α = 0.53.
For the data where v i could be estimated, no clear trend with (T -T ɡ ) c could be found. Nonetheless, a wide range of (T -T ɡ ) c = -5 °C to 90 °C has been reported. Further analysis indicated that, besides v i , material and experimental differences can also play a substantial role in determining (T -T ɡ ) c , some of which is highlighted below. Some outliers can be explained by material differences, e.g. the (T -T ɡ ) c = 90 °C is for a skim milk powder (SMP) with 80 % protein, which is known to decrease stickiness . Another example is the low value of -5 °C for a fluidized bed experiment using amorphous lactose. Using a range of RH = 7 % to 32 %, the results were (T -T ɡ ) c = -5 °C to 3.8 °C with a single outlier of (T -T ɡ ) c = 21 °C for RH = 53 %, the highest humidity tested. Amorphous lactose is known for its early onset of stickiness (Zuo et al., 2007) and crystallization (Schulnies and Kleinschmidt, 2018). We expect the latter could have played a role in the outlier as crystallization reportedly reduces liquid bridge strength (Fitzpatrick et al., 2007b).
However, even for similar materials, the deviation can be quite large. Using SMP in a particle gun with a velocity of 15 m s -1 the (T -T ɡ ) c was found to be 34 °C to 36 °C by Murti et al. (2010) and 57 °C to 61 °C by Walmsley et al. (2014). Two experimental differences explained this deviation. In the experiment of Walmsley et al. (2014), the deposition was only measured for the air jet's impingement location, not for the entire target plate. Particles that stray from the jet direction move through the air with undefined T and RH. Hence, the surface conditions of stray particles cannot be accurately determined. Additionally, the target plate was heated to match the temperature of the air jet. The plate temperature T p can play an important role and is often a relevant industrial parameter, e.g., in dryers, pneumatic ducts, fluidized beds, and cyclones (Walmsley et al., 2014). A higher T p is known to reduce the amount of wall deposition (X.D. Chen et al., 1993). Walmsley et al. (2014) found reduced deposition for higher T p , which was consistent regardless of the used v i . Such wall temperature effects are also found outside of food processing, such as cold spray deposition (Khalkhali and Rothstein, 2020). The improvements of the particle gun made by Walmsley et al. (2014) show that the experimental conditions influence the resulting T 1 (x w ). Hence, the experimental conditions need to be accurately chosen when stickiness tests are used for predicting powder processing parameters.

Application areas of dynamic stickiness tests
The moving nature of the particles in dynamic stickiness tests makes these tests useful for predicting the behavior of powder in most of powder production and processing equipment. However, it makes them unsuitable for measuring powder caking. The application of the dynamic tests will depend on the impact velocity v i of collisions and whether particle-particle or particle-wall collisions are tested.
The particle gun can measure the highest impact velocity of all the reviewed methods and involves particle-wall collisions. Initially, an impact velocity of 20 m s -1 was chosen for its similarity to industrial cyclones (Zuo et al., 2007). The high impact velocity makes it a useful method to predict stickiness for high-velocity pneumatic handling, dried material colliding with spray dryer walls, or industrial cyclones. Additionally, by changing the target plate's material or dimensions, the influence of wall material or impact angle can also be investigated (Murti et al., 2010;Walmsley et al., 2015).
The sticky-point test and fluidized bed have continuously moving powder, making these tests useful for various industrial applications involving moving powders such as powder mixing, blending, and milling. Since many industrial processes incorporate a fluidized bed, a stickiness test using fluidized powder will be most applicable to the fluidized bed itself. Limitations of the stirrer's angular velocity and the velocity of fluidization airflow make the sticky-point test and fluidized bed ill-suited for high-velocity processes such as spray drying or pneumatic handling. Further work on the influence of the intensity of continuous mixing on the sticky-point is required to choose experimental conditions for specific applications when using the sticky-point test and the fluidized bed. Using the sticky-point test with a fluidized powder solves some of the issues of the individual methods. However, sensitive equipment is necessary to measure the smaller increase of torque at the sticky-point, compared to without fluidization, which is possible with advanced rheometers (Groen et al., 2020).
The cyclone test was proposed as an alternative for the fluidized bed test, while we expect it to achieve sufficient particle motion to be an alternative for the particle gun as well. Boonyai et al. (2004) suggested that the cyclone test's primary advantage over the fluidized bed is that the cyclone test measures both adhesion and cohesion while the fluidized bed measures only cohesion. Therefore, the cyclone test would be more suitable to predict stickiness in spray drying, fluidized beds, and pneumatic handling of powders (Boonyai et al., 2004). However, it is difficult to judge this statement since, besides the original paper by Boonyai et al. (2002), we only found one application of the cyclone test in literature (Intipunya et al., 2009).
The optical test can be used if the tested material scatters near-infrared light (Boonyai et al., 2004). Since it was proposed, no further experiments using this method have been reported to our knowledge. Hence, no judgment of its applicability can be made momentarily. Still, commonly tested powders such as amorphous lactose and various milk powders are all opaque, indicating that this method could be applied to these powders.
The most prominent application for the probe test is the droplet evaporation phase of spray drying. However, the use of a bulk moisture content severely limits this application. Werner et al. (2007a) measured the stickiness of an evaporating droplet with the probe test. The onset of stickiness occurred much earlier than expected based on the droplet's bulk moisture content, which indicated solute had accumulated at the droplet surface. Hence, the gravimetrically determined droplet water content is an unhelpful parameter for determining T 2 (x w ), which makes the probe test not applicable to industrial processes involving rapid evaporation. Crucially, this includes spray drying, for which there is no adequate method to predict droplet stickiness in the initial evaporation phase. Future methods should focus on the drying droplet's surface conditions for finding the tack point T 2 (x w ), either through direct measurement or by modeling the gradient formation under the influence of evaporation (Adhikari et al., 2005).

Conclusion
In this review, we provided an overview of methods that measure the stickiness of amorphous powders relevant in the food industry. The reviewed methods included visual observation tests, shear tests, the penetration test, the blow test, the sticky-point test, the fluidized bed, the particle gun, the cyclone test, the optical test, and the probe test. For each method, we described how either the sticky-point temperature T 1 (x w ) or the tack boundary T 2 (x w ) can be determined. We have classified the methods based on the particle mobility during the conditioning and measurement steps into static stickiness tests and dynamic stickiness tests.
Static stickiness tests have limited particle motion during the conditioning step, which can be as long as desired. Therefore, these tests are particularly suitable to measure the caking rate of powder beds. Hence, industrial applicability is predominantly in predicting the long-term behavior of powder during storage or in packaging. Static stickiness tests have shown that the caking rate can be related to T -T ɡ when T -T ɡ > (T -T ɡ ) c , although the nature of the relation is dependent on the used method. Nonetheless, this approach gives much insight into the stability of stored powders.
Dynamic stickiness tests involve particles with significant particle motion during the conditioning and measurement step. The particle gun is a good method to measure stickiness during particle-wall impacts, while the combination of the sticky-point test and fluidized bed measure stickiness for particle-particle collisions and continuously mixed systems. A wide range of testing conditions can be achieved by varying the impact velocity or contact time between particles. Hence, information from dynamic stickiness tests is highly relevant to the design and operation of powder production and processing equipment. Dynamic stickiness tests have shown that velocity plays an important role in the location of the sticky region, with larger velocity shifting the sticky-point curve T 1 (x w ) to higher temperatures so that a larger (T -T ɡ ) c is obtained.
An essential type of stickiness test that is lacking is a dynamic test that measures particle stickiness when moving from the liquid state to the sticky-region, hence, finding the tack boundary T 2 (x w ). Much unclarity exists for when evaporating solute containing droplets are sticky, while this is hugely relevant for spray drying, which is one of the most used processes in the food processing industry. The probe method does approach the sticky-region from the liquid state, but the reliance on the droplet's bulk properties makes it unable to determine values for T 2 (x w ). Further work in predicting the surface stickiness, either through direct measurement or by modeling the gradient formation under the influence of evaporation, is required to predict droplet stickiness.