Cavitation patterns in high-pressure homogenization nozzles with cylindrical orifices: Influence of mixing stream in Simultaneous Homogenization and Mixing

High-pressure homogenization is the state of the art to produce high-quality emulsions with droplet sizes in the submicron range. In simultaneous homogenization and mixing (SHM), an additional mixing stream is inserted into a modified homogenization nozzle in order to create synergies between the unit operation homogenization and mixing. In this work, the influence of the mixing stream on cavitation patterns after a cylindrical orifice is investigated. Shadow-graphic images of the cavitation patterns were taken using a high-speed camera and an optically accessible mixing chamber. Results show that adding the mixing stream can contribute to coalescence of cavitation bubbles. Choked cavitation was observed at higher cavitation numbers σ with increasing mixing stream. The influence of the mixing stream became more significant at a higher orifice to outlet ratio, where a hydraulic flip was also observed at higher σ. The decrease of cavitation intensity with increasing back-pressure was found to be identical with conventional high-pressure homogenization. In the future, the results can be taken into account in the SHM process design to improve the efficiency of droplet break-up by preventing cavitation or at least hydraulic flip.


Introduction
High-pressure homogenization is the state of the art to produce high-quality emulsions with droplet sizes in the submicron range in the pharmaceutical, chemical, and food industry. A raw emulsion is compressed to pressures up to 1000 bar or higher and then accelerated through a disruption unit. While different kinds of disruption units such as flat valves or orifice nozzles are used in homogenizers, they all have a strong reduction of the flow cross section in common . As a result, disruptive stresses such as elongational stress, shear stress, or turbulent inertial stress causing droplet breakup are induced in laminar, transitional, or turbulent flow (Walstra, 1993;Kelemen et al., 2015).
Furthermore, hydrodynamic cavitation can occur in and after the constriction due to a local pressure drop (Franc and Michel, 2005). It is defined as the spontaneous emergence, growth, and subsequent implosion of vapor filled cavities.
The collapse of cavitation bubbles near a droplet can lead to the formation of a microjet focused at the bubble and cause droplet breakup. The occurrence of cavitation also changes the local flow conditions and effects the hydrodynamic stresses. In previous works, several cavitation patterns were observed in high-pressure homogenization nozzles (Schlender et al., 2015b;Gothsch et al., 2016). Depending on the applied pressures and the ratio of orifice diameter to outlet diameter β, jet cavitation, choked cavitation, and hydraulic flip were observed. It was found that the cavitation pattern affects the efficiency of droplet breakup in emulsification processes and the occurrence of a hydraulic flip proved to be especially harmful for the droplet breakup (Schlender et al., 2015b). By applying a back-pressure after the orifice at the same inlet pressure, visible cavitation decreases. This correlation was first shown by McKillop et al. (1955). When the ratio of back-pressure to inlet pressure described as Thoma number reaches 0.3 < Th < 0.5 depending on the geometry, cavitation disappears (Jahnke, 1998). Amongst others, Kurzhals and Reuter (1979), Freudig et al. (2003), Finke et al. (2014), andSchlender et al. (2015a) were able to enhance droplet breakup efficiency in emulsification trials by applying a back-pressure with a minimum droplet size located at 20%-30% of the inlet pressure. However, conventional high-pressure homogenization is still very energy consuming and not applicable for some material systems. By adding an additional mixing stream into the homogenization nozzle shortly after the orifice, new applications and energy reductions could be achieved (summarized in Gall et al. (2016)). This development is called simultaneous homogenization and mixing (SHM) (Köhler und Schuchmann, 2012). For example, it can be used to improve energy efficiency in milk homogenization by preventing coalescence by diluting the premix using a mixing stream of skim milk (Köhler et al., 2007). At the present time, it is not fully understood how adding the mixing stream changes the flow conditions in the SHM nozzle. So far, no cavitation investigations have been carried out including a mixing stream. Since adding the mixing stream causes an increase of the total mass flow and could lead to a local increase of pressure, it possibly changes the cavitation pattern if not reduce cavitation intensity. This assumption is supported by the fact that increasing the Th number did not affect the drop size distribution in the SHM process as strongly as in conventional HPH in milk homogenization (Köhler et al. 2009).
The aim of this work is therefore to investigate the influence of the mixing stream on the occurrence and pattern of cavitation. As a first step, it is examined whether cavitation in SHM can also be prevented by applying the same Th numbers as in conventional high-pressure homogenization. Since applying a back-pressure increases energy consumption in SHM due to the increased pressure needed for conveying the mixing stream, the influence of the mixing stream on cavitation patterns obtained without applying back-pressure is also investigated. Optical investigations of cavitation have been conducted in the past using incident lighting (de Giorgi et al., 2013), laser light induced luminescence combined with mikro-PIV (Gothsch et al., 2016), or via sono-chemiluminescence (Schlender et al., 2016).
The cavitation patterns in this study are observed taking shadow-graphic images using opposing light at several process parameters as presented by Sato et al. (2013). For the trials, a modified homogenization nozzle with optically accessible mixing chamber (OAMC) was built, which enables the visualization of cavitation after the orifice throat.

Theoretical background
In order to describe the results obtained in this study, several established approaches will be applied. Based on the continuity equation through an orifice, the mean velocity in the orifice orifice u through an orifice with diameter orifice d is calculated as follows: In this case, the mass flow rate HS M  through the orifice can be experimentally measured and l ρ represents the density of the liquid at experimental conditions. With the dynamic viscosity of the liquid l η and orifice u , the Re number in the orifice: can be calculated to estimate the flow regime.
In high-pressure processes with an increased backpressure, the ratio between the applied back-pressure 2 p and inlet pressure inlet p is often used to describe homogenization results at different parameters (Kurzhals and Reuter, 1979). It is defined as Thoma number 2 inlet p Th p = (3) In this case, the pressures are given as relative pressures resulting in Th = 0 describing a process without applied back-pressure. Especially for processes with no or low back-pressure, the cavitation number σ is much more precise to describe cavitation patterns. It describes the probability of cavitation appearance in an orifice throat and its outlet channel (Numachi et al., 1960). It is calculated on the basis of the ration between the static pressure tending to suppress cavitation and the hydrodynamic pressure tending to support cavitation (Stanley, 2012): Here, 2 p describes the pressure downstream of the orifice, which equals 2 p for trials with applied back-pressure and the atmospheric pressure otherwise, and vapor l ( ) p T is given by the vapor pressure for the used liquid at its temperature. While cavitation can initiate when falling below 1 σ = , the number of cavitation bubbles and collapses increase with decreasing σ .
The cavitation number at which the first small cavitation bubbles can be observed is characterized as cavitation inception i σ , which strongly depends on the geometrical aspects of the orifice described by outlet With decreasing σ , more cavitation bubbles occur and expand while traveling downstream with the flow (Sato and Saito, 2002;Mizuyama et al., 2010). When the cavitation bubbles are visible downstream the orifice in the shape of a jet consisting of single bubbles, the cavitation pattern is described as jet cavitation or cavitating jet (Soyama et al., 1996). The cavitation pattern in which the first coherent vapor bubble appears is called chocked cavitation and located at ch σ (Yan and Thorpe, 1990). It can be calculated using the following equations: The concentration coefficient describes the ratio between the real orifice flow area A and the effective orifice flow area eff A (Stephan et al., 2019) due to the "vena contracta" at the entrance of the orifice. Choked cavitation can merge into the cavitation pattern "hydraulic flip" by decreasing σ or increasing β (Schlender et al., 2015b), which occurs when the outlet channel is filled completely by one cohesive vapor bubble surrounded by a thin liquid film (Sou et al., 2007).

Materials
Distilled water was used as a model system for both the experiments and simulations. Schlender et al. (2015b) was able to show that adding a surfactant can prevent coalescence of single cavitation bubbles, but does not influence the length and change of cavitation patterns. Their trials also showed that adding plant oil up to 10 wt% to water with adjusted refractive index showed no influence on the cavitation pattern. Furthermore, the water used in the experiments was not degassed. This could potentially lead to the occurrence of pseudocavitation, which is described as diffusion of dissolved air due to the decrease in local pressure. While Tesch (2002) stated that pseudocavitation plays a minor part at 1 σ  , the results observed in this study could present an overlay of pseudocavitation and hydrodynamical cavitation. We decided to work with non degassed distilled water for the following reasons:  By not degassing the water, the results reflect real process conditions in high-pressure homogenizers better.


The results presented in this study can be compared to findings in literature (Gothsch et al., 2015;Schlender et al., 2015b).

High-pressure homogenization plant setup
A schematic of the experimental plant setup is given in Fig. 1. For conveying the high-pressure stream, distilled water is prepared in a storage tank (A) and then compressed by a two-piston pump with a working pressure of 1200 bar. A pulsation damper (C) compensates for pressure fluctuations. The mixing stream is conveyed by regulating the pressure in a pressure tank (E) with a nitrogen bottle (G) and a reducing valve (F). A needle valve (H) enabled to adjust the mass flow rate of the mixing stream accordingly to the high-pressure stream achieving the desired mixing ratio. Both streams are mixed in a disruption unit with optically accessible mixing chamber (OAMC). The disruption unit is made via drilling and consists of two parts as illustrated in Fig. 1.
The pipe supply of the high-pressure stream and the circular orifice are made of stainless steel to guarantee their pressure resistance. The orifice is followed by an optically accessible mixing chamber (OAMC) made of PMMA (Fig. 2). This design enables the investigation of cavitation after the orifice while cavities in the orifice throat itself remain invisible. The insertion of the mixing stream to the circular outlet is designed as a T-mixer shortly after the orifice. a T-mixer was used to prevent cavitation bubbles flowing back in and out of the T-mixer and thus changing the cavitation pattern. The geometrical aspects of the disruption unit used for the trials and the simulations are specified in Table 1. For the trials that required an increased back-pressure after the disruption unit, a needle valve (I) was used (setup a) to reduce the flow cross section. In the remaining trials, the outlet pressure after the orifice 2 p corresponded to atmospheric pressure.

Experimental procedure for capturing shadow-graphic images
The cavitation patterns were visualized using opposing light imaging (shadow-graphic) as performed in literature (Sato  combined with a 100 mm macro objective (Canan Inc., Japan) was used to take pictures of the cavitation patterns in the OAMC. The frequency of the recording was set to 10,000 fps and the exposure time ranged between 50 and 70 μs. For each set of parameters, 2000 images were taken.
Since the cavitating flow fluctuates in time, the image series was converted to gray images in MATLAB (Matlab Inc, USA) and processed to an averaged image. While representative single images are used to discuss the cavitation pattern in detail, the averaged image provides information on the average shape of the cavitation pattern, e.g., the length of the jet in jet cavitation. In order to investigate the effect of the mixing stream on different cavitation patterns, the inlet pressure inlet p of the high-pressure stream was varied between 100 and 550 bar. Since the orifice diameter orifice d = 150 μm was kept constant for all trials, an increase of the inlet pressure is directly connected to an increase of the Re numbers in the orifice orifice

Re
. The values for orifice Re were calculated and are given in Table 2. However, the discussion of the experiments will be based on the inlet pressures as these contribute to the calculation of the characteristic numbers.
A set of trails was conducted to investigate the influence of an increased Th number on the disappearance of visible cavitation. The Th number was adjusted between 0 (which equals no applied back-pressure) and 0.25. Since the Th number is only commonly used in high-pressure homogenization, the cavitation number σ was also calculated for all sets of parameters. For this, the vapor pressure vapor 20 C 0.02 ( ) 347 p  = bar was used (Stephan et al., 2019). In the trials, the temperature ranged between 20 and 40 °C. In that area, the increase of the vapor pressure in this temperature range does barely influence σ and was therefore neglected. between 0 (no mixing stream) and 20. Because the mixing stream is not considered in any of the characteristic numbers, they only depend on inlet p and 2 p . Furthermore, the trials were conducted using two outlet diameters orifice d at 2 and 4 mm, resulting in β = 0.075 and β = 0.038. The reason for this is that the increase of total mass flow with increasing MS HS M M   could affect the cavitation patterns more significant at a lower outlet diameter and therefore higher β.

Results and discussion
The results presented in this study show how the mixing stream in SHM nozzles influences cavitation. The first part deals with the question whether applying a back-pressure affects visible cavitation in the same way as described in literature for conventional HPH nozzles. First, shadowgraphic images are taken under variation of the Th number. These results are supplemented by local pressure distributions calculated in simulations in order to assess their validity with regard to predict cavitation. The second part describes in detail how increasing the mixing stream at constant highpressure homogenization stream affects different cavitation patterns and their transitions using shadow-graphic images.

Influence of back-pressure on shadow-graphic images
In order to verify that the effect of decreasing visible cavitation with increasing back-pressure is comparable to conventional high-pressure homogenization, shadow-graphic images were taken at Th = 0-0.25 for two inlet pressures. Figure  = 1 was also directly compared to trials in which no mixing stream was added in Fig. 4. In this case, β was set to 0.038.  (Schlender et al., 2016). A comparison with the images shown above also shows that the disappearance of visible cavitation does not depend on β . In summary, no influence of the mixing ratio could be observed in this case.

Influence of mixing ratio on jet cavitation
This section visualizes the impact on an increasing mixing ratio MS HS M M   on jet cavitation. Figure 5 shows the change of the cavitating jet at inlet p = 100 bar and 0.075 β = . For a better visibility of the effects, for each mixing ratio ranging between 1/5 and 20, both an instantaneous impression is given by a single image ("instantaneous") and the averaged image shows that the observations are not randomly recorded elves due to the fluctuation of the jet.
The averaged images illustrate that the average length of the jet decreases with increasing mixing ratio between  flow downstream the orifice total M  strongly increases with increasing mixing ratio. The instantaneous images also show in this context that single cavitation bubbles that are not dissolved after the orifice are carried out much faster with increasing mixing ratio. The trials do not allow determining whether the decreasing jet length is caused by a local pressure increase due to the insertion of the mixing stream or just a consequence of faster carrying out the cavitation bubbles. In either case, the reducing effect of the mixing ratio on the jet is limited, since the emergence of a The effect of the mixing ratio was also investigated at inlet p = 100 bar and 0.038 β = . The results are displayed in Fig. 6. In this case, both HS M  and total M  are equal to the flow rates at higher β , but due to the increased outlet d , the average flow velociy in the outlet channel is much smaller. Fig. 6 Influence of increasing mixing ratio on jet cavitation for 0.038 β = and inlet p = 100 bar. The cavitating jet is not influenced by the increasing mixing ratio until a second area of cavitaton is observed.
V. Gall,E. Rütten,H. Karbstein 162 The images show that the effect of the increased mixing ratio proves to be much smaller than at 0.078 β = .   Fig. 7 do not indicate a further increase of ch σ beyond doubt, while the averaged picture shows a hint of a cohesive vapor bubble just being formed at inlet p = 300 bar. It is remarkable that the vapor bubble is always oriented to the bottom half of the OAMC. The reason for this could be small irregularities in the nozzle geometry due to its mechanical production. In literature, the transition of ch σ was also observed for increasing β (Schlender et al., 2015b).

Influence of mixing ratio on hydraulic flip
Since the shadow-graphic images presented in the last section displayed that adding the mixing stream contributed to coalescence of the cavitation bubbles, this section deals with the question whether the mixing stream also affects the hydraulic flip. In Fig. 8 . The increase of the mixing ratio causes choked cavitation to occur at higher ch σ .
Cavitation patterns in high-pressure homogenization nozzles with cylindrical orifices: Influence of mixing stream in Simultaneous Homogenization and Mixing 163  Fig. 10 show that increasing the mixing stream leads to a shorter length of the outlet channel filled with the cohesive vapor bubble. Again, this effect could be ascribed to the fact that the cavitation bubbles are carried out faster.

Conclusions
In this work we investigated the influence of a mixing stream on cavitation in the disruption unit of a high-pressure homogenizer. It was shown that the mixing stream does not change the Th numbers required to reduce cavitation by applying a back-pressure. Therefore, Th numbers found in literature for conventional high-pressure homogenization can be applied to SHM nozzles in order to suppress cavitation. In addition, our investigations could show that increasing the mixing ratio of mixing stream to high-pressure stream can cause the cavitation bubbles in jet cavitation to coalesce at higher cavitation numbers σ and therefore increase ch σ where choked cavitation is first observed. The increase of the mixing stream can therefore have a similar effect than an increase of the ratio β of outlet diameter to orifice diameter. In literature, hydraulic flip is described to be harmful for droplet breakup in HPH processes. Our results suggest that β should be adjusted to counteract the effect of the mixing stream. However, the increase of the outlet diameter could also change the mixing characteristics and thus influence droplet breakup. This should be further investigated in future.