An experimental study of binary collisions of miscible droplets with non-identical viscosities

The dynamics of binary collisions of equi-diameter droplets with non-identical viscosities have been investigated experimentally and compared to previously generated data from identical droplet collisions (Al-Dirawi and Bayly in Phys Fluids 31(2):027105, 2019). Three hydroxypropyl methylcellulose (HPMC) aqueous solutions, 2%, 4%, and 8% HPMC, were used to generate the droplets of different viscosities, 2.8, 8.2, and 28.4 mPa s, respectively. High-speed imaging techniques were applied to observe and capture the collision outcomes. Collision outcomes were characterised and regime maps were generated. The non-identical viscosity droplet collisions produced regime maps with well-defined boundaries which are comparable in shape to the conventional regime maps of identical droplet collisions. The boundaries of the bouncing and reflexive separation regimes of the non-identical collisions show intermediate position between the identical cases of the low and the high viscosity droplets. However, the boundary of the stretching separation regimes of the non-identical collisions showed good agreement with the boundary of the identical case of the lower viscosity droplet. Moreover, the ability of models developed for predicting the regimes boundaries of collisions of identical viscosity droplets was assessed for the non-identical collisions. They proved capable in the non-identical cases, and the changes in adjustable parameters were consistent with the underlying physical basis of the models

A new model for the bouncing regime boundary in binary droplet collisions

This work experimentally investigates binary collisions of identical droplets over a range of liquid viscosities, using 2%, 4%, and 8% of hydroxypropyl methylcellulose solutions in water. The collisions were captured by using a high-speed camera, and regime maps of collision outcomes were derived. The performance of existing models of the boundary of the bouncing regime was assessed and found to give poor predictions. This was attributed to assumptions and errors in the treatment of kinetic energy and the droplet shape factors used in these models. A new model was derived which addresses these issues: the definition of the kinetic energy that contributes to deformation was corrected; a new shape factor that accurately reflects the geometry of the droplet at maximum deformation was proposed, and, importantly, an empirical approach was implemented to account for the effect of the impact parameter on this shape factor. Moreover, the model includes an estimate of the viscous dissipation, which is calculated directly from the experimentally observed difference between the impact and the rebound kinetic energies and measurements of the post-collision droplet oscillations. The proposed model shows a striking improvement versus the existing models, reducing the mean absolute error by an order of magnitude

Inertial stretching separation in binary droplet collisions

Binary droplet collisions exhibit a wide range of outcomes, including coalescence and stretching separation, with a transition between these two outcomes arising for high Weber numbers and impact parameters. Our experimental study elucidates the effect of viscosity on this transition, which we show exhibits inertial (viscosity-independent) behaviour over an order-of-magnitude-wide range of Ohnesorge numbers. That is, the transition is not always shifted towards higher impact parameters by increasing droplet viscosity, as it might be thought from the existing literature. Moreover, we provide compelling experimental evidence that stretching separation only arises if the length of the coalesced droplet exceeds a critical multiple of the original droplet diameters (3.35). Using this as a criterion, we provide a simple but robust model (without any arbitrarily chosen free parameters) to predict the coalescence/stretching-separation transition

A non-adiabatic model for jacketed agitated batch reactors experiencing thermal losses

Accurate modeling of process temperatures within jacketed batch reactors has the potential to mitigate the risk of thermal runaways and enhance process control. A non-adiabatic heat-transfer model is derived for the investigation of heat transfer in laboratory to pilot-scale reactors of 0.5–40 L. By accounting for heat removed from the process by a total condenser and losses through the process lid, the model is able to predict process temperature profiles within the uncertainty limits of the experimental measurements. Heat losses from the outer jacket wall had a negligible impact on the evolution of process temperature but may contribute significantly to utility costs. Jacket duty measurements implied greater heat accumulation within the reactor vessel than anticipated, equivalent to ∼60% of that in the process fluid at 40 L scale. This raises the potential for heat-transfer coefficients to be systematically under-estimated by adiabatic models, particularly at the laboratory to pilot scale

Correlations between powder wettability and part colour in the High Speed Sintering process

High Speed Sintering (HSS) is a powder bed fusion additive manufacturing technology that relies on inkjet printing of an infrared (IR) radiation absorbing material (RAM) onto a polymer powder bed in order to produce cross-sections which can be selectively sintered using an IR lamp. The RAM used in HSS is carbon black, which is suspended in a petroleum-based carrier fluid to form an ink. The use of carbon black in this way means that any parts currently produced by HSS are inevitably some shade of black or grey depending on the amount and distribution of RAM on the part surface. As well as affecting aesthetics, the effect of printing different densities of RAM has previously been shown to influence part sintering and subsequently mechanical properties, which demonstrates the importance of RAM distribution in determining the final properties of parts made using HSS. Anecdotally, it has also been observed that parts produced with the same type, amount and printed density of ink, but using different polymer powders, can be significantly different colours. This suggests that the wetting interaction between the ink and the polymer powder is also significant factor in determining the distribution of RAM on a part surface. However, to date there has been no investigation into the nature of this relationship. By measuring part colour, in this work we quantify differences in RAM distribution when different polymers are processed via HSS using the same printed density of ink, with parts made from commercially available powders of poly(propylene) (PP), pol(ether-b-amide) (PEBA), poly(styrene) (PS), poly(amide)-11 (PA11), and poly(amide)-12 (PA12) having Relative Luminance (i.e. brightness) of (5.3 0.2)%, (5.5 0.5)%, (12 1)%, (15 2)%, and (18 1)%, respectively. The contact angles of the ink on the powder beds were measured in a simple model system, and these were found to be (46.1 0.8)°, (80 3)°, 82°, (90 2)°, and (93 2)° for PP, PEBA, PS, PA11, and PA12, respectively. With the exception of one anomalous data point for PEBA, it is demonstrated that part Relative Luminance can be correlated to contact angle, and that we can describe that relationship to good precision using a semi-empirical model. Knowledge about the effect of ink wettability on RAM distribution should prove useful for continuing the optimisation of the parts obtained by HSS