Impaction of spray droplets on leaves: Influence of formulation and leaf character on shatter, bounce and adhesion

This paper combines experimental data with simple mathematical models to investigate the influence of spray formulation type and leaf character (wettability) on shatter, bounce and adhesion of droplets impacting with cotton, rice and wheat leaves. Impaction criteria that allow for different angles of the leaf surface and the droplet impact trajectory are presented; their predictions are based on whether combinations of droplet size and velocity lie above or below bounce and shatter boundaries. In the experimental component, real leaves are used, with all their inherent natural variability. Further, commercial agricultural spray nozzles are employed, resulting in a range of droplet characteristics. Given this natural variability, there is broad agreement between the data and predictions. As predicted, the shatter of droplets was found to increase as droplet size and velocity increased, and the surface became harder to wet. Bouncing of droplets occurred most frequently on hard to wet surfaces with high surface tension mixtures. On the other hand, a number of small droplets with low impact velocity were observed to bounce when predicted to lie well within the adhering regime. We believe this discrepancy between the predictions and experimental data could be due to air layer effects that were not taken into account in the current bounce equations. Other discrepancies between experiment and theory are thought to be due to the current assumption of a dry impact surface, whereas, in practice, the leaf surfaces became increasingly covered with fluid throughout the spray test runs.

Mathematical modelling of the impaction and spreading of spray droplets on leaves

This thesis concerns the development of mathematical models to describe the interactions that occur between spray droplets and leaves. Models are presented that not only provide a contribution to mathematical knowledge in the field of fluid dynamics, but are also of utility within the agrichemical industry. The thesis is presented in two parts. First, thin film models are implemented with efficient numerical schemes in order to simulate droplets on virtual leaf surfaces. Then the interception event is considered, whereby energy balance techniques are employed to instantaneously predict whether an impacting droplet will bounce, splash, or adhere to a leaf.

Towards a model of spray-canopy interactions : interception, shatter, bounce and retention of droplets on horizontal leaves

Pesticides used in agricultural systems must be applied in economically viable and environmentally sensitive ways, and this often requires expensive field trials on spray deposition and retention by plant foliage. Computational models to describe whether a spray droplet sticks (adheres), bounces or shatters on impact, and if any rebounding parent or shatter daughter droplets are recaptured, would provide an estimate of spray retention and thereby act as a useful guide prior to any field trials. Parameter-driven interactive software has been implemented to enable the end-user to study and visualise droplet interception and impaction on a single, horizontal leaf. Living chenopodium, wheat and cotton leaves have been scanned to capture the surface topography and realistic virtual leaf surface models have been generated. Individual leaf models have then been subjected to virtual spray droplets and predictions made of droplet interception with the virtual plant leaf. Thereafter, the impaction behaviour of the droplets and the subsequent behaviour of any daughter droplets, up until re-capture, are simulated to give the predicted total spray retention by the leaf. A series of critical thresholds for the stick, bounce, and shatter elements in the impaction process have been developed for different combinations of formulation, droplet size and velocity, and leaf surface characteristics to provide this output. The results show that droplet properties, spray formulations and leaf surface characteristics all influence the predicted amount of spray retained on a horizontal leaf surface. Overall the predicted spray retention increases as formulation surface tension, static contact angle, droplet size and velocity decreases. Predicted retention on cotton is much higher than on chenopodium. The average predicted retention on a single horizontal leaf across all droplet size, velocity and formulations scenarios tested, is 18, 30 and 85% for chenopodium, wheat and cotton, respectively.

Characterization of expiration air jets and droplet size distributions immediately at the mouth opening

Size distributions of expiratory droplets expelled during coughing and speaking and the velocities of the expiration air jets of healthy volunteers were measured. Droplet size was measured using the Interferometric Mie imaging (IMI) technique while the Particle Image Velocimetry (PIV) technique was used for measuring air velocity. These techniques allowed measurements in close proximity to the mouth and avoided air sampling losses. The average expiration air velocity was 11.7 m/s for coughing and 3.9 m/s for speaking. Under the experimental setting, evaporation and condensation effects had negligible impact on the measured droplet size. The geometric mean diameter of droplets from coughing was 13.5m and it was 16.0m for speaking (counting 1 to 100). The estimated total number of droplets expelled ranged from 947 – 2085 per cough and 112 – 6720 for speaking. The estimated droplet concentrations for coughing ranged from 2.4 - 5.2cm-3 per cough and 0.004 – 0.223 cm-3 for speaking.

Modelling water droplet movement on a leaf surface

The central aim for the research undertaken in this PhD thesis is the development of a model for simulating water droplet movement on a leaf surface and to compare the model behavior with experimental observations. A series of five papers has been presented to explain systematically the way in which this droplet modelling work has been realised. Knowing the path of the droplet on the leaf surface is important for understanding how a droplet of water, pesticide, or nutrient will be absorbed through the leaf surface. An important aspect of the research is the generation of a leaf surface representation that acts as the foundation of the droplet model. Initially a laser scanner is used to capture the surface characteristics for two types of leaves in the form of a large scattered data set. After the identification of the leaf surface boundary, a set of internal points is chosen over which a triangulation of the surface is constructed. We present a novel hybrid approach for leaf surface fitting on this triangulation that combines Clough-Tocher (CT) and radial basis function (RBF) methods to achieve a surface with a continuously turning normal. The accuracy of the hybrid technique is assessed using numerical experimentation. The hybrid CT-RBF method is shown to give good representations of Frangipani and Anthurium leaves. Such leaf models facilitate an understanding of plant development and permit the modelling of the interaction of plants with their environment. The motion of a droplet traversing this virtual leaf surface is affected by various forces including gravity, friction and resistance between the surface and the droplet. The innovation of our model is the use of thin-film theory in the context of droplet movement to determine the thickness of the droplet as it moves on the surface. Experimental verification shows that the droplet model captures reality quite well and produces realistic droplet motion on the leaf surface. Most importantly, we observed that the simulated droplet motion follows the contours of the surface and spreads as a thin film. In the future, the model may be applied to determine the path of a droplet of pesticide along a leaf surface before it falls from or comes to a standstill on the surface. It will also be used to study the paths of many droplets of water or pesticide moving and colliding on the surface.

Clinical results : Acetabular impaction grafting

Written by the surgeons of the Exeter Hip Team and their colleagues from around the world, this book describes 40 years of innovation and development with cemented hip replacement. Topics covered include the basic science behind successful cemented hip replacement, modern surgical techniques and recent advances. There is also extensive coverage of the revision techniques developed at Exeter and elsewhere, focussing on femoral and acetabular impaction grafting. Each chapter is a self-contained article with an emphasis, where appropriate, on practical techniques and surgical tips, supported by line drawings and intra-operative photographs.

Modelling water droplet movement on a leaf surface

Modelling droplet movement on leaf surfaces is an important component in understanding how water, pesticide or nutrient is absorbed through the leaf surface. A simple mathematical model is proposed in this paper for generating a realistic, or natural looking trajectory of a water droplet traversing a virtual leaf surface. The virtual surface is comprised of a triangular mesh structure over which a hybrid Clough-Tocher seamed element interpolant is constructed from real-life scattered data captured by a laser scanner. The motion of the droplet is assumed to be affected by gravitational, frictional and surface resistance forces and the innovation of our approach is the use of thin-film theory to develop a stopping criterion for the droplet as it moves on the surface. The droplet model is verified and calibrated using experimental measurement; the results are promising and appear to capture reality quite well.

Femoral impaction grafting in revision total hip arthroplasty

Between 1987 and 1999, 540 revision total hip replacements in 487 patients were performed at our institution with the femoral impaction grafting technique with a cemented femoral stem. All patients were prospectively followed for 2-15years post-operatively with no loss to follow-up. 494 hips remained successfully in situ at an average 6.7years. The ten year survival rate was 98.0% (95% CI 96.2 to 99.8) with aseptic loosening as the endpoint and 84.2% (95% CI 78.5 to 89.9) for re-operation for any reason. Indication for surgery and the use of any kind of reinforcement significantly influenced outcome (p<0.001). This is the largest known series of revision THR with femoral impaction grafting and the results support continued use of this technique.

Acetabular impaction grafting in total hip replacement

Background and purpose: Acetabular impaction grafting has been shown to have excellent results, but concerns regarding its suitability for larger defects have been highlighted. We report the use of this technique in a large cohort of patients with the aim of better understanding the limitations of the technique. Methods: We investigated a consecutive group of 339 cases of impaction grafting of the cup with morcellised impacted allograft bone for survivorship and mechanisms for early failure. Results: Kaplan Meier survival was 89.1% (95% CI 83.2 to 95.0%) at 5.8 years for revision for any reason, and 91.6% (95% CI 85.9 to 97.3%) for revision for aseptic loosening of the cup. Of the 15 cases revised for aseptic cup loosening, nine were large rim mesh reconstructions, two were fractured Kerboull-Postel plates, two were migrating cages, one medial wall mesh failure and one impaction alone failed. Interpretation: In our series, results were disappointing where a large rim mesh or significant reconstruction was required. In light of these results, our technique has changed in that we now use predominantly larger chips of purely cancellous bone, 8-10 mm3 in size, to fill the cavity and larger diameter cups to better fill the mouth of the reconstructed acetabulum. In addition we now make greater use of i) implants made of a highly porous in-growth surface to constrain allograft chips and ii) bulk allografts combined with cages and morcellised chips in cases with very large segmental and cavitary defects.

The results of acetabular impaction grafting in 129 primary cemented total hip arthroplasties

Between 1995 and 2003, 129 cemented primary THRs were performed using full acetabular impaction grafting to reconstruct acetabular deficiencies. These were classified as cavitary in 74 and segmental in 55 hips. Eighty-one patients were reviewed at mean 9.1 (6.2-14.3) years post-operatively. There were seven acetabular component revisions due to aseptic loosening, and a further 11 cases that had migrated >5mm or tilted >5° on radiological review - ten of which reported no symptoms. Kaplan-Meier analysis of revisions for aseptic loosening demonstrates 100% survival at nine years for cavitary defects compared to 82.6% for segmental defects. Our results suggest that the medium-term survival of this technique is excellent when used for purely cavitary defects but less predictable when used with large rim meshes in segmental defects.

Clinical and radiographic outcomes of acetabular impaction grafting without cage reinforcement for revision hip replacement : a minimum ten-year follow-up study

Impaction bone grafting for reconstitution of bone stock in revision hip surgery has been used for nearly 30 years. We used this technique, in combination with a cemented acetabular component, in the acetabula of 304 hips in 292 patients revised for aseptic loosening between 1995 and 2001. The only additional supports used were stainless steel meshes placed against the medial wall or laterally around the acetabular rim to contain the graft. All Paprosky grades of defect were included. Clinical and radiographic outcomes were collected in surviving patients at a minimum of 10 years following the index operation. Mean follow-up was 12.4 years (SD 1.5; range 10.0-16.0). Kaplan-Meier survivorship with revision for aseptic loosening as the endpoint was 85.9% (95% CI 81.0 to 90.8%) at 13.5 years. Clinical scores for pain relief remained satisfactory, and there was no difference in clinical scores between cups that appeared stable and those that appeared loose radiographically.

Results using Trabecular Metal™ augments in combination with acetabular impaction bone grafting in deficient acetabula

We examined whether the use of trabecular metal wedges to fill segmental defects is an effective method of socket reconstruction when used in combination with impaction grafting and implantation of a cemented socket. Fifteen hips in 14 patients underwent impaction grafting in combination with a TM wedge with a minimum of 2 years follow-up. All patients had their defects assessed using the Paprosky classification. Patients were reviewed with x-rays and migration of the implant was measured. Outcome scores were also collected. Mean follow-up was 39 months (25-83). The mean age at surgery was 67.8 (49-85) years. Seven of the patients had previously undergone impaction grafting with the use of a stainless steel rim mesh to constrain the graft. None of the patients had failed either clinically or radiologically.

DroplIT, an improved image analysis method for droplet identification in high-throughput crystallization trials

The application of robotics to protein crystallization trials has resulted in the production of millions of images. Manual inspection of these images to find crystals and other interesting outcomes is a major rate-limiting step. As a result there has been intense activity in developing automated algorithms to analyse these images. The very first step for most systems that have been described in the literature is to delineate each droplet. Here, a novel approach that reaches over 97% success rate and subsecond processing times is presented. This will form the seed of a new high-throughput system to scrutinize massive crystallization campaigns automatically. © 2010 International Union of Crystallography Printed in Singapore-all rights reserved.

Simulating droplet motion on virtual leaf surfaces

A curvilinear thin film model is used to simulate the motion of droplets on a virtual leaf surface, with a view to better understand the retention of agricultural sprays on plants. The governing model, adapted from Roy et al. (2002 J. Fluid Mech. 454, 235–261) with the addition of a disjoining pressure term, describes the gravity- and curvature driven flow of a small droplet on a complex substrate: a cotton leaf reconstructed from digitized scan data. Coalescence is the key mechanism behind spray coating of foliage, and our simulations demonstrate that various experimentally observed coalescence behaviours can be reproduced qualitatively. By varying the contact angle over the domain, we also demonstrate that the presence of a chemical defect can act as an obstacle to the droplet’s path, causing break-up. In simulations on the virtual leaf, it is found that the movement of a typical spray size droplet is driven almost exclusively by substrate curvature gradients. It is not until droplet mass is sufficiently increased via coalescence that gravity becomes the dominating force.