Laminar Shear Flow Research Articles

Molecular recognition on the surface of concentrated hydrochloric acid: Hydration configuration-driven preferential recognition of Rh (III) anions with inner-coordinated water molecules

Comprehension of selective recognition of anions is confined to a phenomenological list of solvents, hardly surpassing Pedersen’s empirical observations of cationic-crown ether binding. In this work, a novel strategy employing thin-layer oil membrane extraction (TOMX) on the surface of concentrated hydrochloric acid is proposed for controllable recognition and separation of anions with different hydration configurations. Four typical chloric-complexing anions, RhCl63−, PdCl42−, PtCl62− and FeCl4−, usually coexisting in the concentrated hydrochloric acid leaching solutions of precious metal concentrates were focused. A surprising phenomenon was noticed that the octahedral RhCl5(H2O)2− anions with inner-coordinated water molecules were preferentially recognized by 18C6 macrocyclic molecule. However, the planar quadrilateral Pd (II) chloric-complexing anions with a hydration configuration via water molecules attacking the central Pd (II) atoms along the Z-axis direction can be separated subsequently. The Pt (IV) and Fe (III) chloric-complexing anions respectively with an octahedral and tetrahedral outer-coordinated hydration shell configuration were the last to be recognized. Such an order in extracting Rh (III) > Pd (II) > Pt (IV) > Fe (III) anions depends on their hydration capacity and the preferential affinity towards the interface, which is almost impossible during the conventional stirring and oil droplet dispersed extraction. Because of a lower concentration of dissociated hydrogen ions on the surface of concentrated hydrochloric acid compared to its bulk concentrations, the hydration of those chloric-complexing anions was enhanced. The Rh (III) anions with inner-coordinated water molecules exhibit a higher interfacial affinity than other anions. The water molecules entering the inner coordination layer of Rh (III) chloric-complexing anions, cooperating with its outer-coordinated hydration shell, act as a hydrogen bond “water bridge” to interact with 18C6 molecules, which makes it easier to feel the influence from the aqueous laminar shear flow under the thin-layer oil membrane, thereby driving the preferential recognition of easily hydrated Rh (III) anions at the interface. The controllable “water bridge” interactions driven by shear flow can be activated or deactivated on the surface of concentrated hydrochloric acid by adjusting the shear flow rate. This work lays a foundation for the future development of a controllable flexible molecular recognition technology at liquid–liquid interfaces.

MATHEMATICAL MODELLING ELECTRICALLY DRIVEN FREE SHEAR FLOWS IN A DUCT UNDER UNIFORM MAGNETIC FIELD

We consider a mathematical model of two-dimensional electrically driven laminar free shear flows in a straight duct under action of an applied uniform homogeneous magnetic field. The mathematical approach is based on studies by J.C.R. Hunt and W.E. Williams [10], Yu. Kolesnikov and H. Kalis [22,23]. We solve the system of stationary partial differential equations (PDEs) with two unknown functions of velocity U and induced magnetic field H. The flows are generated as a result of the interaction of injected electric current in liquid and the applied field using one or two couples of linear electrodes located on duct walls: three cases are considered. In dependence on direction of current injection and uniform magnetic field, the flows between the end walls are realized. Distributions of velocities and induced magnetic fields, electric current density in dependence on the Hartmann number Ha are studied. The solution of this problem is obtained analytically and numerically, using the Fourier series method and Matlab.

Mimicking kidney flow shear efficiently induces aggregation of LECT2, a protein involved in renal amyloidosis

Aggregation of leukocyte cell-derived chemotaxin 2 (LECT2) causes ALECT2, a systemic amyloidosis that affects the kidney and liver. Previous studies established that LECT2 fibrillogenesis is accelerated by loss of its bound zinc ion and stirring/shaking. These forms of agitation create heterogeneous shear conditions, including air-liquid interfaces that denature proteins, that are not present in the body. Here, we determined the extent to which a more physiological form of mechanical stress—shear generated by fluid flow through a network of narrow channels—drives LECT2 fibrillogenesis. To mimic blood flow through the kidney, where LECT2 and other proteins form amyloid deposits, we developed a microfluidic device consisting of progressively branched channels narrowing from 5 mm to 20 μm in width. Shear was particularly pronounced at the branch points and in the smallest capillaries. Aggregation was induced within 24 h by shear levels that were in the physiological range and well below those required to unfold globular proteins such as LECT2. EM images suggested the resulting fibril ultrastructures were different when generated by laminar flow shear vs. shaking/stirring. Importantly, results from the microfluidic device showed the first evidence that the I40V mutation accelerated fibril formation and increased both size and density of the aggregates. These findings suggest that kidney-like flow shear, in combination with zinc loss, acts in combination with the I40V mutation to trigger LECT2 amyloidogenesis. These microfluidic devices may be of general use for uncovering mechanisms by which blood flow induces misfolding and amyloidosis of circulating proteins.

Aggregation and breakage dynamics of alumina particles under shear by coupled Computational Fluid Dynamics – Discrete Element Method

HypothesisShear affects simultaneous aggregation and fragmentation of fine particles. Understanding the effect of shear on the dynamics of particle aggregation and break-up is important to predict aggregate size and structure. It is hypothesized that there is a transition from pure breakage of large aggregates to regimes where restructuring and aggregation also play a role as aggregates become smaller. SimulationsHere, aggregation and fragmentation dynamics of alumina particles are investigated under laminar shear flow using Discrete Element Method (DEM) coupled with Computational Fluid Dynamics (CFD). The effect of the shear rate on the aggregation and breakage rates is quantified accounting for particle–particle and particle–fluid interactions. FindingsHigh shear rates promote the formation of small, compact aggregates. The collision efficiency decreases with increasing shear rate following a power law for shear rates higher than 1250 s−1. The transition from the pure breakage limit to the region dominated by breakage and restructuring has been observed for the first time. The breakage rate decreases significantly as the transition occurs upon decreasing aggregate size. CFD-DEM-derived collision efficiency and breakage rate equations are proposed that can be readily employed in detailed population balance equation models for industrial particle process design.

Growth of Floc Structure and Subsequence Compaction into Smaller Granules through Breakup and Rearrangement of Aluminum Flocs in a Constant Laminar Shear Flow.

We have constructed an outer-cylinder-rotating Couette device for high-speed shear flow in laminar flow conditions and visualized the structure formation and subsequent rearrangement of PACl (flocculant made of aluminum hydroxide gel) and kaolinite flocs by visible light imaging. In a previous report, we analyzed the case of relatively low shear rate (G-value = 29 1/s) and confirmed that the flocculation process could be separated into two stages: a floc growth stage and a breakup/rearrangement stage. Once the large bulky flocs that reached the maximum size appeared, they rearranged and densified through structural fracture and rearrangement. In this report, this process was further investigated by conducting experiments under two different high shear rates (58 and 78 1/s) at which breakup and rearrangement became more pronounced, and three different aluminum kaolinite ratios (ALT ratios) that were over and under the optimum dosage (neutralization point by Zeta potential). Visualization results confirmed that, during the growth stage, the flocculation rate could be approximated by a scaling relationship between floc size and elapsed time, which depended on the ALT ratio. After reaching the maximum size, the floc rapidly became compact and dense following adsorption of the gel, incorporating fine fragments from erosion breakup. The over and under dosages created a lot of fragments of erosion breakup, but less so in the optimum dosage. In the optimum ALT ratio, fragments did not remain because they were incorporated into the flocs and densified, and the floc size was thought to be maintained. The floc circularity distribution peaked at around 0.6 and 1, suggesting that the flocs were spherical in shape due to erosion breakup.

Cohesive bond strength of marine aggregates and its role in fragmentation

Marine aggregates are one of the main contributors to carbon sequestration in the deep sea through the gravitational settling of biogenic particles formed from the photosynthetic products of phytoplankton. The formation of large particles due to aggregation processes has been the focus of studies in the past, but recent findings on the spatio-temporal distribution of particles suggests that the fragmentation of aggregates plays an important role in aggregate dynamics. Here, we assessed the yield strength of aggregates derived from natural planktonic communities in order to analyze the cohesive bond strength and further understand fragmentation. The experimental approach was designed around the use of a Couette device, which produces a constant laminar shear flow of water. Aggregates were found to have a higher yield strength (~289 ± 64 nN) during phases of nutrient depletion than those of mineral particles such as montmorillonite. Based on an estimated cohesive bond strength of 96 nN a numerical model to predict the temporal variation of aggregate size was created. The output of this model indicates that cohesive bond strength is a major determinant of the size of aggregates in motion. Our findings suggest that the dynamics of marine aggregates are greatly influenced by cohesive bond strength and the role in fragmentation.

Controllable molecular orientation at the interface and coordination with second hydration-sphere to enhance separation of Pt(IV) and Pd(II) in hydrochloric acid solutions: Mass transfer based separation and molecular dynamics

In conventional liquid-liquid extraction, Pt(IV) and Pd(II) chloride complex anions PtCl62− and PdCl42− in concentrated hydrochloric acid cannot be separated using simple amine extractants according to the ion association mechanism based on the thermodynamic difference in the interaction of their inner sphere coordinated chloride ions with protonated amine. This study exhibits a novel strategy for enhancing the separation of PtCl62− and PdCl42− anions using thin-layer organic membrane-based laminar flow (TOMLF) extraction by controlling the acidified primary amine N1923 (A-N1923) molecular orientation on the surface of concentrated hydrochloric acid with a laminar shear flow. Experiments revealed that the separation selectivity is primarily determined by the interaction of A-N1923 molecules with the outer sphere-bound water molecules around PtCl62− and PdCl42− anions, and is easily controlled by regulating the A-N1923 molecular orientation on the surface of laminar flow. It is a new phenomenon that has not been previously documented. The evolution of A-N1923 molecular orientation and complexation sites induced by laminar shear flow would result in a controllable spatial geometry recognition, therefore promoting or inhibiting the separation of PtCl62− and PdCl42− anions in concentrated hydrochloric acid. This work is expected to provide new insight into the development of hydration-sphere coordination strategies based upon shear-switch laminar flow for controllable host-guest molecule recognition at a flowing liquid-liquid interface.

Controlling lipid crystallization across multiple length scales by directed shear flow.

The crystallization behavior of lipids is relevant in many fields such as adipose tissue formation and regeneration, forensic investigations and food production. Using a lipid model system composed of triacylglycerols, we study the formation of crystalline structures under laminar shear flows across various length scales by polarized light-, scanning electron-, and atomic force microscopy, as well as laser diffraction spectroscopy. The shear rate during crystallization γ̇cryst influences the acyl-chain length structure and promotes domain growth into the flow direction thereby transforming the crystallites from oblate into prolate particles. Concentration dependent aggregation of crystallites into clusters is the rate limiting step for floc and floc network formation. At high γ̇cryst, fast crystallite cluster formation at smaller equilibrium diameters is promoted. The high crystallite cluster concentration induces their aggregation into flocs which form weak networks. At low γ̇cryst, floc generation is limited by the low amount of crystallite clusters leading to slow growth of larger flocs and forming of strong networks. The findings in this work have potential implications ranging from the design of injectable soft tissue fillers for adipose tissue regeneration, to the crystalline network formation in microorganism derived lipids, up to a more energy-efficient production of chocolate confectionery.

Electrically driven free shear flows in a duct under a transverse uniform magnetic field

A mathematical model of two-dimensional electrically driven laminar plane free shear flows in a straight duct under the action of an applied spanwise uniform magnetic field is considered. The mathematical approach is like that used in the research of Hunt and Williams (J. Fluid. Mech., 31, 705, 1968) and Kolesnikov and Kalis (Magnetohydrodynamics, vol. 57, 2021, no. 2). A system of stationary partial differential equations with two unknown functions of velocity and induced magnetic field is solved. The electric current is injected into the liquid by means of two couples of linear electrodes located vis-à-vis on opposite duct walls, perpendicular to the magnetic field. Three cases are considered. One pair of electrodes is current supplied and, depending on the direction of electric current injection on the electrode pair, two coinciding or two counter flows are also driven. At Hartmann numbers Ha >> 1, quasi-potential cores are formed in these flows, bounded by lateral Shercliff free boundary layers parallel to the field and two Hartmann layers on the walls perpendicular to the field. As a result, almost all of the injected current passes through these layers. An increase of the magnetic field leads only to an internal rearrangement of the potential cores of the flows. The Hartmann number varies in the range from 1 to 100. Figs 15, Refs 11.

Direct observation of deformation of individual red blood cells in oscillatory fluid flow produced using a generator of precise sinusoidal shear flow

We report the development of a precision sinusoidal shear flow generator that creates an oscillatory shear flow in the narrow gap between two parallel glass plates moving in opposite directions, thereby allowing direct observation of the cyclical deformation and recovery of a single red blood cell (RBC). The system is used to demonstrate that RBCs change their shape with cyclical elongation and shape recovery and align with the fluid streamlines in the direction of laminar Couette shear flow. From six repetitions, it can be seen that the curvature showing the time series of the elongation index (EI) of an RBC in sinusoidal shear flow in the present device was highly symmetrical and there were no significant differences at a 95% confidence interval. Moreover, the system provides details about the deformation characteristics of an RBC, which have four phases: (i) low deformation, in which the EI is minimal and the RBC mostly retains its original circular shape; (ii) shape elongation, in which the RBC loaded with shear forces begins to change its shape dynamically from circular to oval; (iii) steady deformation, in which the EI is constant and the shape of the RBC is elliptical throughout; and (iv) shape recovery, in which the EI decreases and the RBC becomes oval with trailing endpoints. Along with this information, the developed measurement system has potential application in clinical and biological analyses of RBC deformability.

On Escherichia coli Resistance to Fluid Shear Stress and Its Significance for Water Disinfection

Alternative water treatment techniques are needed to overcome the limitations of chemical disinfectants. Stemming from recent findings which point to high levels of shear stress induced by flow as the cause of microbial removal in water, we conducted systematic experiments on bacterial solutions in well-controlled hydrodynamic conditions to evaluate the effect of different levels of shear stress on the viability of Escherichia coli. We investigated a wide range of shear stresses (57–4240 Pa) using viscous substrates prepared by mixing a bacterial solution with thickeners (2-hydroxyethyl cellulose and/or guar gum). Substrate samples were tested for up to 60 min in a laminar shear flow at a constant temperature using a rotational rheometer equipped with a cone-plate measuring system so that the whole sampling volume was exposed to the same shear stress. Results show that, contrary to previous studies, high shear stresses (i.e., of order 103 Pa) do not induce inactivation or lysis of E. coli, even for prolonged exposure times. Stemming from our results and a thorough discussion of the literature on E. coli mechanical lysis and modeling cell dynamics, we infer that E. coli can resist high shear forces because of stress relaxation in a wide range of hydrodynamic conditions.

Stress- and process model for dispersing of nanoparticulate suspensions in laminar shear flow

This work presents a stress model and a process model for dispersing processes in laminar shear flow, which are performed in devices such as kneaders, extruders and three roller mills. Based on deep investigations of two kneaders (lab- and pilot-scale) a methodology is presented, which allows modelling the dispersing process by applying a stress model along with a population balance model to the given task. Stress models describe how often particles are stressed during the process and which energy is transferred to the particles. For dispersing in laminar shear flow, it is crucial to distinguish between dispersing-effective and ineffective stress events based on whether the stress intensity is high enough to overcome the particle strength. Results suggest, that the effective specific energy input determines the dispersing progress independent of the process scale. A process model in form of a population balance was required to obtain otherwise unknown parameters for the stress model. The applied population balance model accounts for the acting working principles during dispersing. For such a mechanistic depiction of the dispersing progress, the trilateral dependency between particle size, resulting viscosity, particle stressing and fragmentation must be modelled. It was found that based on the models, the process behaviour on both scales can be depicted, which offers the perspective of a knowledge-based scale-up of machines and processes, process control and process design based on these results.

Oil droplet breakup during pressure swirl atomization of emulsions: Influence of emulsion viscosity and viscosity ratio

The atomization of oil-in-water emulsions for spray drying is a common task in food engineering. During atomization with pressure swirl atomizers, the emulsions are subjected to high stresses that can lead to deformation and breakup not only of the liquid itself but also of the disperse oil droplets therein. In this study, the effect of the viscosity ratio λ of the emulsion (0.2–33) and of the emulsion viscosity (5–50 mPa⋅s) on oil droplet breakup during atomization was investigated at atomization pressures between 50 and 250 bar. A systematic influence of λ on the oil droplet size was observed with maximum oil droplet breakup for λ between 0.2 and 1.2. At a constant viscosity ratio of ∼ 1, the resulting oil droplet size was almost independent of the emulsion viscosity, even when volume flow rates and spray droplet sizes during atomization showed a clear dependence on this parameter. A model based on existing knowledge on droplet breakup in laminar shear flow is developed, by which oil droplet sizes after atomization can be predicted. This model may serve as a tool to control oil droplet size after atomization by defining appropriate atomization conditions and emulsion formulation. This is especially relevant for spray drying applications in which the oil droplet size in the powder is an important quality parameter. • Viscosity ratio λ influences oil droplet breakup during pressure swirl atomization. • At λ ∼ 1 the emulsion viscosity per se has little influence on oil droplet breakup. • Oil droplet breakup follows the theory of droplet breakup in laminar shear flow. • A model is proposed that serves as a tool to predict oil droplet breakup.

Rheology of mobile sediment beds in laminar shear flow: effects of creep and polydispersity

Classical scaling relationships for rheological quantities such as the $\mu (J)$ -rheology have become increasingly popular for closures of two-phase flow modelling. However, these frameworks have been derived for monodisperse particles. We aim to extend these considerations to sediment transport modelling by using a more realistic sediment composition. We investigate the rheological behaviour of sheared sediment beds composed of polydisperse spherical particles in a laminar Couette-type shear flow. The sediment beds consist of particles with a diameter size ratio of up to 10, which corresponds to grains ranging from fine to coarse sand. The data was generated using fully coupled, grain resolved direct numerical simulations using a combined lattice Boltzmann–discrete element method. These highly resolved data yield detailed depth-resolved profiles of the relevant physical quantities that determine the rheology, i.e. the local shear rate of the fluid, particle volume fraction, total shear and granular pressure. A comparison against experimental data shows excellent agreement for the monodisperse case. We improve upon the parameterization of the $\mu (J)$ -rheology by expressing its empirically derived parameters as a function of the maximum particle volume fraction. Furthermore, we extend these considerations by exploring the creeping regime for viscous numbers much lower than used by previous studies to calibrate these correlations. Considering the low viscous numbers of our data, we found that the friction coefficient governing the quasi-static state in the creeping regime tends to a finite value for vanishing shear, which decreases the critical friction coefficient by a factor of three for all cases investigated.

Electrically driven cylindrical free shear flows under an axial uniform magnetic field

We consider a mathematical model of two-dimensional electrically driven laminar axisymmetric circular free shear flows in a cylindrical vessel under the action of an applied axial uniform magnetic field. The mathematical approach is based on the studies by J.C.R. Hunt and W.E. Williams (J. Fluid. Mech., 31, 705, 1968). We solve a system of stationary partial differential equations with two unknown functions of velocity and induced magnetic field. The flows are generated as a result of the interaction of the electric current injected into the liquid and the applied field using one or two pairs of concentric annular electrodes located apart on the end walls. Two lateral free shear layers and two Hartmann layers on the end walls and a quasi-potential flow core between them emerge when the Hartmann number Ha >> 1. As a result, almost all injected current passes through these layers. Depending on the direction of the current injection, coinciding or two counter flows between the end walls are realized. The Hartmann number varies in a range from 2 to 300. When a moderate magnetic field (Ha = 50) is reached, the flow rate and the induced magnetic field flux cease to depend on the magnitude of the applied field but depend on the injected electric current value. Increasing magnetic field leads only to inner restructuring of the flows. Redistributions of velocities and induced magnetic fields, electric current density versus Hartmann number are analyzed. Figs 18, Refs 21.

Modeling of interfacial flows based on an explicit volume diffusion concept

A novel volume of fluid (VoF) model called explicit volume diffusion (EVD) is developed for the simulation of interfacial flows, including those with turbulence and primary spray atomization. It is derived by volume averaging the VoF equations over an explicit, physically-defined length scale. Fluctuations at the sub-volume scales, which can arise due to interface dynamics or turbulence, are attenuated by the volume averaging process and their effects appear in unclosed terms representing sub-volume flux, sub-volume stress, and volume averaged surface tension force. Models are proposed for each of these. The sub-volume flux is closed by a gradient diffusion model and involves an explicit volume diffusion coefficient, that is, linked to the explicit length scale. The sub-volume stress closure introduces an explicit volume viscosity that can be augmented by a turbulent viscosity in turbulent flows. The volume averaged surface tension force closure is based on a fractal representation of the wrinkled sub-volume interface. To test the closures individually and the EVD model overall, a series of two-dimensional laminar and three-dimensional turbulent interfacial shear flows and a laboratory-scale airblast spray jet are considered. Numerical convergence is demonstrated by keeping the explicit volume length scale constant while refining the numerical grid such that the numerical diffusion diminishes and becomes overwhelmed by the explicit volume diffusion. Sensitivity analyses are also conducted for variations in the explicit length scale which may be linked to the boundary layer thickness on the light fluid side of the interface.

Transient Permeabilization of Living Cells: Combining Shear Flow and Acoustofluidic Trapping for the Facilitated Uptake of Molecules

Here, we present a novel approach for the transient permeabilization of cells. We combined laminar shear flow in a microchannel with chaotic advection employing surface acoustic waves. First, as a fundamental result on the one hand, and as a kind of reference measurement for the more complex acoustofluidic approach on the other hand, we studied the permeabilization of cells in pure shear flow in a microchannel with Y-geometry. As a proof of principle, we used fluorescent dyes as model drugs and investigated their internalization into HeLa cells. We found that drug uptake scaled non-linearly with flow rate and thus shear stress. For calcein, we obtained a maximal enhancement factor of about 12 at an optimum flow rate of Q = 500 µL/h in the geometry used here compared to static incubation. This result is discussed in the light of structural phase transitions of lipid membranes accompanied by non-linear effects, as the plasma membrane is the main barrier to overcome. Second, we demonstrated the enhanced permeabilization of acoustically trapped cells in surface acoustic wave induced vortices in a microchannel, with an enhancement factor of about 18 compared to quasi-static incubation. Moreover, we optimized the trapping conditions regarding flow rate, the power level of the surface acoustic wave, and trapping time. Finally, we showed that our method is not limited to small molecules but can also be applied to compounds with higher molecular weight.

Bending and low‐frequency vortex shedding of flexible cylinders in laminar shear flow

AbstractSimulations of the interaction between flexible cylinders attached to a solid surface and a laminar shear flow have been performed. The flow simulations fully resolve the geometrical details and are based on the lattice‐Boltzmann method. An immersed boundary method is used to impose the no‐slip conditions at the cylinder surfaces and to determine the distribution of hydrodynamic forces over the cylinder. The latter are responsible for the bending deformation of the cylinders. We first study simple shear systems under steady conditions for which experimental data are available that we use for validation. We then study flexible cylinders in Poiseuille flow that exhibit vortex shedding and demonstrate that the flexibility of the cylinders has a pronounced effect on the temporal behavior of the flow system.

The SWELL1-LRRC8 complex regulates endothelial AKT-eNOS signaling and vascular function.

The endothelium responds to numerous chemical and mechanical factors in regulating vascular tone, blood pressure, and blood flow. The endothelial volume-regulated anion channel (VRAC) has been proposed to be mechanosensitive and thereby sense fluid flow and hydrostatic pressure to regulate vascular function. Here, we show that the leucine-rich repeat-containing protein 8a, LRRC8A (SWELL1), is required for VRAC in human umbilical vein endothelial cells (HUVECs). Endothelial LRRC8A regulates AKT-endothelial nitric oxide synthase (eNOS) signaling under basal, stretch, and shear-flow stimulation, forms a GRB2-Cav1-eNOS signaling complex, and is required for endothelial cell alignment to laminar shear flow. Endothelium-restricted Lrrc8a KO mice develop hypertension in response to chronic angiotensin-II infusion and exhibit impaired retinal blood flow with both diffuse and focal blood vessel narrowing in the setting of type 2 diabetes (T2D). These data demonstrate that LRRC8A regulates AKT-eNOS in endothelium and is required for maintaining vascular function, particularly in the setting of T2D.

Influence of Shear Flow on the Crystallization of Organic Melt Emulsions – A Rheo‐Nuclear Magnetic Resonance Investigation

AbstractThere is a need to better understand the influence of shear flow on the crystallization of a molten oil phase in an oil/water emulsion due to its high relevance for industrial processes. The present study focuses on the influence of laminar shear flow on the crystallization kinetics of polydisperse n‐hexadecane‐in‐water emulsions. The investigation was carried out by rheo‐nuclear magnetic resonance (NMR) spectroscopy in a Taylor‐Couette geometry. An accelerating impact of the shear rate on the overall crystallization kinetics was verified. This effect stems from an increase of the collision frequency of already crystallized droplets with not yet crystallized droplets. Nevertheless, the collision efficiency decreased with higher shear rate.