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.

Role of Basement Membrane and Extracellular Matrix Proteins in the Adhesion and Spreading of Immortalized Human Corneal Epithelial Cells

The repair of corneal wounds requires both epithelial cell adhesion and migration. Basement membrane (BM) and extracellular matrix (ECM) proteins function in these processes via integrin and non-integrin receptors. We have studied the adhesion, spreading and migration of immortalized human corneal epithelial (HCE) cells and their interactions with the laminins (Lms), fibronectins and tenascins produced. Human corneal BM expresses Lms-332 and -511, while Lm-111 was not found in these experiments. HCE cells produced both processed and unprocessed Lm-332, whereas neither Lm-111 nor Lm-511 was produced. Because HCE cells did not produce Lm-511, although it was present in corneal BM, we suggest that Lm-511 is produced by stromal keratocytes. The adhesion of HCE cells to Lms-111, -332 and -511 was studied first by determining the receptor composition of HCE cells and then by using quantitative cell adhesion assays. Immunofluorescence studies revealed the presence of integrin α2, α3, α6, β1 and β4 subunits. Among the non-integrin receptors, Lutheran (Lu) was found on adhering HCE cells. The cells adhered via integrin α3β1 to both purified human Lms-332 and -511 as well as to endogenous Lm-332. However, only integrin β1 subunit functioned in HCE cell adhesion to mouse Lm-111. The adhesion of HCE cells to Lm-511 was also mediated by Lu. Since Lm-511 did not induce Lu into focal adhesions in HCE cells, we suggest that Lm-511 serves as an ECM ligand enabling cell motility. HCE cells produced extradomain-A fibronectin, oncofetal fibronectin and tenascin-C (Tn-C), which are also found during corneal wound healing. Monoclonal antibodies (MAbs) against integrins α5β1 and αvβ6 as well as the arginine-glycine-aspartic acid (RGD) peptide inhibited the adhesion of HCE cells to fibronectin. Although the cells did not adhere to Tn-C, they adhered to the fibronectin/Tn-C coat and were then more efficiently inhibited by the function-blocking MAbs and RGD peptide. During the early adhesion, HCE cells codeposited Lm-332 and the large subunit of tenascin-C (Tn-CL) beneath the cells via the Golgi apparatus and microtubules. Integrin β4 subunit, which is a hemidesmosomal component, did not mediate the early adhesion of HCE cells to Lm-332 or Lm-332/Tn-C. Based on these results, we suggest that the adhesion of HCE cells is initiated by Lm-332 and modulated by Tn-CL, as it has been reported to prevent the assembly of hemidesmosomes. Thereby, Tn-CL functions in the motility of HCE cells during wound healing. The different distribution of processed and unprocessed Lm-332 in adhering, spreading and migrating HCE cells suggests a distinct role for these isoforms. We conclude that the processed Lm-332 functions in cell adhesion, whereas the unprocessed Lm-332 participates in cell spreading and migration.

Influences of Allee effects in the spreading of malignant tumours

A recent study by Korolev et al. [Nat. Rev. Cancer, 14:371–379, 2014] evidences that the Allee effect—in its strong form, the requirement of a minimum density for cell growth—is important in the spreading of cancerous tumours. We present one of the first mathematical models of tumour invasion that incorporates the Allee effect. Based on analysis of the existence of travelling wave solutions to this model, we argue that it is an improvement on previous models of its kind. We show that, with the strong Allee effect, the model admits biologically relevant travelling wave solutions, with well-defined edges. Furthermore, we uncover an experimentally observed biphasic relationship between the invasion speed of the tumour and the background extracellular matrix density.

Spreading Sequences for Asynchronous Spectrally Phase Encoded Optical CDMA

In phase encoding optical CDMA (OCDMA) the spreading is achieved by encoding the phase of signal spectrum. In this paper we first derive a mathematical model for the output of phase encoding OCDMA systems. Based on this model we introduce a metric to design spreading sequences for asynchronous transmission. Then we connect the phase encoding sequence design problem to OFDM PMEPR (peak to mean envelope power ratio) problem. Using this connection we conclude that designing sequences with good properties for samples of timing delay guarantees that the same sequence to be good for all timing delays. Finally using generalized bent function we manage to construct a family of sequences which are good for asynchronous phase encoding OCDMA systems and using these sequences we introduce an M-ary modulation scheme for phase encoding OCDMA

Spreading and atomization of droplets on a vibrating surface in a standing pressure field

We report the first observation and analytical model of deformation and spreading of droplets on a vibrating surface under the influence of an ultrasonic standing pressure field. The standing wave allows the droplet to spread, and the spreading rate varies inversely with viscosity. In low viscosity droplets, the synergistic effect of radial acoustic force and the transducer surface acceleration also leads to capillary waves. These unstable capillary modes grow to cause ultimate disintegration into daughter droplets. We find that using nanosuspensions, spreading and disintegration can be prevented by suppressing the development of capillary modes and subsequent break-up. (C) 2012 American Institute of Physics. http://dx.doi.org/10.1063/1.4757567]

Maximum Spreading of Liquid Drops Impacting on Groove-Textured Surfaces: Effect of Surface Texture

Maximum, spreading of liquid drops impacting on solid surfaces textured with unidirectional parallel grooves is studied for drop Weber number in the range 1-100 focusing on the role of texture geometry and wettability. The maximum spread factor of impacting drops measured perpendicular to grooves; beta(m,perpendicular to) is seen to be less than, that:measured parallel to grooves, beta(m,perpendicular to).The difference between beta(m,perpendicular to), and beta(m,parallel to) increases with drop impact velocity. This deviation of beta(m,perpendicular to) from beta(m,parallel to) is analyzed by considering the possible mechanisms, correspond, ing to experimental observations (1) impregnation of drop into the grooves, (2) convex shape of liquid vapor interface near contact line at maximum spreading, and (3) contact line pinning of spreading drop at the pillar edges by incorporating them into an energy conservation-based model. The analysis reveals that contact line pinning offers a physically meaningful justification of the observed: deviation of beta(m,perpendicular to) from beta(m,parallel to) compared to other possible candidates. A unified model, incorporating all the above-mentioned mechanisms, is formulated, which predicts beta(m,perpendicular to) on several groove-textured surfaces made of intrinsically hydrophilic and hydrophobic materials with an average error of 8.3%. The effect of groove-texture geometrical parameters,on maximum drop spreading is explained using this unified model. A special case of the unified model, with contact line pinning, absent, predicts beta(m,parallel to) with an average error of 6.3%.

Effect of ambient pressure and radiation reabsorption of atmosphere on the flame spreading over thermally thin combustibles in microgravity

For the flame spread over thermally thin combustibles in an atmosphere, if the atmosphere cannot emit and absorb the thermal radiation (e.g. for atmosphere Of O-2-N-2), the conductive heat transfer from the flame to the fuel surface dominates the flame spread at lower ambient atmosphere. As the ambient pressure increases, the flame spread rate increases, and the radiant heat transfer from the flame to the fuel surface gradually becomes the dominant driving force for the flame spread. In contrast, if the atmosphere is able to emit and absorb the thermal radiation (e.g. for atmosphere Of O-2-CO2), at lower pressure, the heat transfer from flame to the fuel surface is enhanced by the radiation reabsorption of the atmosphere at the leading edge of the flame, and both conduction and thermal radiation play important roles in the mechanism of flame spread. With the increase in ambient pressure, the oxygen diffuses more quickly from ambient atmosphere into the flame, the chemical reaction in the flame is enhanced, and the flame spread rate increases. When the ambient pressure is greater than a critical value, the thermal radiation from the flame to the solid surface is hampered by the radiation reabsorption of ambient atmosphere with the further increase in ambient pressure. As a result, with the increase in ambient pressure, the flame spread rate decreases and the heat conduction gradually dominates the flame spread over the fuel surface.

The statistics of the second order response of an FPSO in spreading seas

An expression for the probability density function of the second order response of a general FPSO in spreading seas is derived by using the Kac-Siegert approach. Various approximations of the second order force transfer functions are investigated for a ship-shaped FPSO. It is found that, when expressed in non-dimensional form, the probability density function of the response is not particularly sensitive to wave spreading, although the mean squared response and the resulting dimensional extreme values can be sensitive. The analysis is then applied to a Sevan FPSO, which is a large cylindrical buoy-like structure. The second order force transfer functions are derived by using an efficient semi-analytical hydrodynamic approach, and these are then employed to yield the extreme response. However, a significant effect of wave spreading on the statistics for a Sevan FPSO is found even in non-dimensional form. It implies that the exact statistics of a general ship-shaped FPSO may be sensitive to the wave direction, which needs to be verified in future work. It is also pointed out that the Newman's approximation regarding the frequency dependency of force transfer function is acceptable even for the spreading seas. An improvement on the results may be attained when considering the angular dependency exactly. Copyright © 2009 by ASME.