Malcolm's Archive

Davidson, M.R. (2025).  Editorial Addendum for ``Influences of longitudinal magnetic field on wave propagation in carbon nanotubes embedded in elastic matrix'' [Appl. Math. Model. 34 (2010) 878--889] and ``Wave propagation in single-walled carbon nanotube under longitudinal magnetic field using nonlocal Euler–Bernoulli beam theory'' [Appl. Math. Model. 36 (2012) 4529--4538].  Applied Mathematical Modelling 145, 116113

Haribabu, M., Dunstan, D.E., Martin, G.J.O., Davidson, M.R., and Harvie, D.J.E. (2020). Simulating the ultrafiltration of whey proteins isolate using a mixture model. Journal of Membrane Science 613, 118388.

Hsu, W-L., Harvie, D.J.E., Davidson, M.R., Dunstan, D., Hwang, J. and Daiguji, H. (2017). Viscoelectric effects in nanochannel electrokinetics. The Journal of Physical Chemistry, Part C 121(37), 20517-20523.

Pillai, R., Berry, J.D., Harvie, D.J.E. and Davidson, M.R. (2017). Electrophoretically mediated partial coalescence of a charged microdrop. Chemical Engineering Science 169, 273-283.

Hsu, W-L., Daiguji, H., Dunstan, D.E., Davidson, M.R. and Harvie, D.J.E. (2016). Electrokinetics of the silica and aqueous electrolyte solution interface: Viscoelectric effects. Advances in Colloid and Interface Science 234, 108-131.

Pillai, R., Berry, J.D., Harvie, D.J.E. and Davidson, M.R. (2016). Electrohydrodynamic deformation and interaction of microscale drop pairs. Int. J. Comp. Meth. and Exp. Meas. 4(1), 33-41.

Pillai, R., Berry, J.D., Harvie, D.J.E. and Davidson, M.R. (2016). Electrokinetics of isolated electrified drops. Soft Matter 12, 3310-3325.

Davidson, M.R., Berry, J.D., Pillai, R. and Harvie, D.J.E. (2016). Numerical simulation of two-fluid flow of electrolyte solution with charged deforming interfaces. Applied Mathematical Modelling 40, 1989-2001.

Pillai, R., Berry, J.D., Harvie, D.J.E. and Davidson, M.R. (2015). Electrolytic drops in an electric field: A numerical study of drop deformation and breakup. Physical Review E 92, 013007.

Biscombe, C., Davidson, M.R. and Harvie D. (2015). Corrections to `Microfluidic circuit analysis I: Ion current relationships for thin slits and pipes', J. Colloid Interface Sci. 365 (2012) 1-15 and `Microfluidic circuit analysis II: Implications of ion conservation for microchannels connected in series', J. Colloid Interface Sci. 365 (2012) 16-27. J. Colloid Interface Sci. 442, 162.

Hsu, W-L, Inglis, D.W., Startsev, M.A., Goldys, E.M., Davidson, M.R. and Harvie, D.J.E. (2014). Isoelectric focusing in a silica nanofluidic channel: Effects of electromigration and electroosmosis. Analytical Chemistry 86, 8711-8718.

Hsu, W-L., Harvie, D. J.E., Davidson, M.R., Jeong, H., Goldys, E.M. and Inglis, D. W. (2014). Concentration gradient focusing and separation in a silica nanofluidic channel with a non-uniform electroosmotic flow. Lab on a Chip 14, 3539-3549.

Berry, J.D., Foong, A.E., Lade C.E., Biscombe, C.J.C., Davidson. M.R. and Harvie, D.J.E. (2014). Electroviscous resistance of nanofluidic bends. Physical Review E 90, 043008.

Berry, J.D., Davidson, M.R. and Harvie, D.J.E. (2014). Electroviscous flow through nanofluidic junctions. Applied Mathematical Modelling 38, 4215-4225.

Hsu, W-L., Inglis, D., Jeong, H., Dunstan, D., Davidson, M., Goldys, E. and Harvie, D. J. E. (2014). Stationary chemical gradients for concentration gradient-based separation and focusing in nanofluidic channels. Langmuir 30(18), 5337-5348.

Biscombe, C.J.C., Davidson, M.R. and Harvie, D.J.E. (2014). Electrokinetic flow in parallel channels: circuit modelling for microfluidics and membranes. Colloids and Surfaces A: Physicochemical and Engineering Aspects 440, 63-73.

Berry, J.D., Davidson, M.R. and Harvie, D.J.E. (2013). A multiphase electrokinetic flow model for electrolytes with liquid/liquid interfaces. J. Computational Physics 251, 209-222.

Biscombe, C.J.C., Davidson, M.R. and Harvie, D.J.E. (2012). Electrokinetic flow in connected channels: a comparison of two circuit models. Microfluidics and Nanofluidics 13, 481-490.

Harvie, D.J.E. Biscombe, C.J.C.  and Davidson, M.R. (2012). Microfluidic circuit analysis I: Ion current relationships for thin slits and pipes. Journal of Colloid and Interface Science 365, 1-15 (Editor's Choice).

Biscombe, C.J.C., Davidson, M.R. and Harvie, D.J.E. (2012). Microfluidic circuit analysis II: Implications of ion conservation for microchannels connected in series. Journal of Colloid and Interface Science 365, 16-27 (Editor's Choice & Front Cover).

Mynard, J.P., Davidson, M.R., Penny, D.J. and Smolich, J.J. (2012). A simple, versatile valve model for use in lumped parameter and one-dimensional cardiovascular models. Int. J. Numer. Meth. Biomed. Engng. 28(6-7), 626-641.

Mynard, J.P., Penny, D.J., Davidson, M.R. and Smolich, J.J. (2012). Non-linear separation of pressure, velocity and wave intensity into forward and backward components. Medical and Biological Engineering and Computing 50(6), 641-648.

Mynard, J.P., Penny, D.J., Davidson, M.R. and Smolich, J.J. (2012). The reservoir-wave paradigm introduces error into arterial wave analysis: a computer modelling and in-vivo study. J. Hypertension 30(4), 734-743.

Mynard, J.P., Penny, D.J., Davidson, M.R. and Smolich, J.J. (2012). The reservoir-wave paradigm introduces error into arterial wave analysis: a computer modelling and in-vivo study: Erratum. J. Hypertension 30(12), 2446-2446.

Mynard, J.P., Penny, D.J., Davidson, M.R. and Smolich, J.J. (2012). The reservoir-wave paradigm Reply. J. Hypertension 30(9), 1881-1883.

Biscombe, C.J.C., Davidson, M.R. and Harvie, D.J.E. (2011). Comparative evaluation of microfluidic circuit model performance for electroviscous flow. ANZIAM J. 52 (CTAC2010), C447-C462.

Berry, J.D., Davidson, M.R. and Harvie, D.J.E. (2011). Electrokinetic development length of electroviscous flow through a contraction. ANZIAM J. 52 (CTAC2010), C837-C852.

Berry, J.D., Davidson, M.R., Bharti, R.P. and Harvie, D.J.E. (2011). Effect of wall permittivity on electroviscous flow through a contraction. Biomicrofluidics J. 5, 044102.

Davidson, M.R. and Harvie, D.J.E. (2011). Viscoelastic drop deformation in a micro-contraction. Fluid Dynamics and Materials Processing 7(3), 317-328.

Schwartz, L.W. and Davidson, M.R. (2011). Mathematical modelling and numerical simulation of wave-front flow on a vertical wall with surfactant effects. J. Eng. Math. 70, 307-320.

Davidson, M.R., Bharti, R.P. and Harvie, D.J.E. (2010). Electroviscous effects in a Carreau liquid flowing through a cylindrical microfluidic contraction. Chemical Engineering Science 65, 6259-6269.

Sands, S.A., Edwards, B.A., Kelly, V.J., Skuza, E.M., Davidson, M.R., Wilkinson, M.H. and Berger, P.J. (2010). Mechanism underlying accelerated arterial oxygen desaturation during recurrent apnea. American Journal of Respiratory and Critical Care Medicine 182, 961-969.

Sands, S.A., Kelly, V.J., Edwards, B.A., Davidson, M.R., Wilkinson, M.H. and Berger, P.J. (2010). A dynamic model for assessing the impact of diffusing capacity on arterial oxygenation during apnea. Respiratory Physiology and Neurobiology 171(3), 193-200.

Sands, S.A., Edwards, B.A., Kelly, V.J., Davidson, M.R., Wilkinson, M.H. and Berger, P.J. (2010). A model investigation of the impact of ventilation-perfusion mismatch on oxygenation during apnea in preterm infants. Journal of Theoretical Biology 264(3), 657-662.

Mynard, J.P., Davidson, M.R., Penny, D.J. and Smolich, J.J. (2010). A numerical model of neonatal pulmonary atresia with intact ventricular septum and RV-dependent coronary flow. Int. J. for Numerical Methods in Biomedical Engineering 26(7), 843-861.

Sands, S.A., Edwards, B.A., Kelly, V.J., Davidson, M.R., Wilkinson, M.H. and Berger, P.J. (2009). A model analysis of arterial oxygen desaturation during apnea in preterm infants. PLoS Computational Biology 5(12), 1-14.

van Embden, J., Sader, J.E., Davidson, M. and Mulvaney, P. (2009). Evolution of colloidal nanocrystals: Theory and modelling of their nucleation and growth. J. Phys. Chem. C  113, 16342-16355.

Higgins, D.R., Gray, N.B. and Davidson, M.R. (2009). Simulating particle agglomeration in the flash smelting reaction shaft. Minerals Engineering 22, 1251-1265.

Bharti, R.P., Harvie, D.J.E. and Davidson, M.R. (2009). Electroviscous effects in steady fully developed flow of a power-law liquid through a cylindrical microchannel.Int. J. of Heat and Fluid Flow 30, 804-811.

Holbeach, J.W. and Davidson, M.R. (2009). An Eulerian-Eulerian model for the dispersion of a suspension of microscopic particles injected into a quiescent liquid.Engineering Applications of Computational Fluid Dynamics 3(1), 84-97.

Harvie, D.J.E., Cooper-White, J.J. and Davidson, M.R. (2008). Deformation of a viscoelastic droplet passing through a microfluidic contraction. J. Non-Newtonian Fluid. Mech. 155, 67-79.

Bharti, R.P., Harvie, D.J.E. and Davidson, M.R. (2008). Steady flow of ionic liquid through a cylindrical microfluidic contraction-expansion pipe: Electroviscous Effects and Pressure Drop. Chemical Engineering Science 63, 3593-3604.

Harvie, D.J.E., Rudman, M. and Davidson, M.R. (2008). Parasitic current generation in combined level set and volume of fluid immiscible fluid simulations. ANZIAM J. 48, C868-C884.

Davidson, M.R. and Harvie, D.J.E. (2007). Electroviscous effects in low Reynolds number liquid flow through a slit-like microfluidic contraction. Chemical Engineering Science 62, 4229-4240.

Davidson, M.R. and Harvie, D.J.E. (2007). Predicting the effect of interfacial flow of insoluble surfactant on the deformation of drops rising in a liquid. ANZIAM J. 48, C661–C676.

Davidson, M.R., Nguyen, Q.D. and Rønningsen, H.P. (2007). Restart model for a multi-plug gelled waxy oil pipeline. Journal of Petroleum Science and Engineering 59, 1-16.

Harvie, D.J.E., Davidson, M.R., Cooper-White, J.J. and Rudman, M. (2007). A parametric study of droplet deformation through a microfluidic contraction: Shear thinning liquids. International Journal of Multiphase Flow 33, 545-556.

Leahy, M.J., Davidson, M.R. and Schwarz, M.P. (2007). A model for heap bioleaching of chalcocite with heat balance: mesophiles and moderate thermophiles.Hydrometallurgy 85, 24-41.

Kentish, S.E., Lee, J., Davidson, M. and Ashokkumar, M. (2006). The Dissolution of a Stationary Spherical Bubble Beneath a Flat Plate. Chemical Engineering Science 61, 7697-7705.

Arruda M.P., Lawson N.J. and Davidson M.R. (2006). Control of an Oscillatory Rectangular Cavity Jet Flow by Secondary Injection. JSME International Journal B 49(4), 1105-1110.

Harvie, D.J.E., Davidson, M.R., Cooper-White, J.J. and Rudman, M (2006). A parametric study of droplet deformation through a microfluidic contraction: Low viscosity Newtonian droplets. Chemical Engineering Science 61, 5149-5158.

Davidson, M.R., Harvie, D.J.E. and Cooper-White, J.J. (2006). Simulations of pendant drop formation of a viscoelastic liquid. Korea-Australia Rheology Journal 18(2), 41-49.

Davidson, M.R. and Cooper-White, J.J. (2006). Pendant drop formation of shear-thinning and yield stress fluids. Applied Mathematical Modelling 30, 1392-1405.

Leahy, M.J., Schwarz, M.P. and Davidson, M.R. (2006). An air sparging CFD model for heap bioleaching of chalcocite. Applied Mathematical Modelling 30, 1428-1444.

Harvie, D.J.E., Davidson, M.R. and Rudman, M.J. (2006). An analysis of parasitic current generation in Volume of Fluid simulations. Applied Mathematical Modelling 30, 1056-1066.

Leahy, M.J., Davidson, M.R. and Schwarz, M.P. (2005). A model for heap bioleaching of chalcocite with heat balance: Bacterial temperature dependence. Minerals Engineering 19, 1239-1252.

Leahy, M.J., Davidson, M.R. and Schwarz, M.P. (2005). A two-dimensional CFD model for heap bioleaching of chalcocite. ANZIAM J. 46(E), C439-C457.

Lawson, N.J., Arruda, M.P. and Davidson, M.R. (2005). Control of a submerged jet in a thin rectangular cavity. J. Fluids and Structures 20, 1025-1042.

Croll, T.I., Gentz, S., Mueller, K., Davidson, M., O'Connor, A.J., Stevens, G.W. and Cooper-White, J.J.(2005). Modelling oxygen diffusion and cell growth in a porous, vascularising scaffold for soft tissue engineering applications. Chemical Engineering Science 60, 4924-4934.

Harvie, D.J.E., Davidson, M.R., Cooper-White, J.J. and Rudman, M. (2005). A parametric study of droplet deformation through a microfluidic contraction. ANZIAM J. 46(E), C150-C166.

Davidson, M.R., Harvie, D.J.E. and Cooper-White, J.J. (2005). Flow focusing in microchannels. ANZIAM J. 46(E), C47-C58.

Sader, J.E. and Davidson, M.R. (2005). Scaling behavior for gravity induced flow of a yield stress material. J. Rheology 49(1), 105-112.

Kentish, S., Davidson, M., Hassan, H. and Bloore, C. (2005). Milk skin formation during drying. Chemical Engineering Science 60(3), 635-646.

Davidson, M.R., Nguyen, Q.D., Chang, C. and Ronningsen, H.P. (2004). A model for restart of a pipeline with compressible gelled waxy crude oil. J. Non-Newtonian Fluid Mech. 123, 269-280.

Cao, Y., Davidson, M.R., O'Connor, A.J., Stevens, G.W. and Cooper-White, J.J. (2004). Architecture control of three-dimensional polymeric scaffolds for soft tissue engineering. I. Establishment and validation of numerical models. J. Biomed. Mater. Res. 71A, 81-89.

Holbeach, J.W. and Davidson, M.R. (2004). Predicting the extent of dissolution of a cloud of particles entering a liquid. ANZIAM J. 45(E), C604-C617.

Davidson, M.R., Cooper-White, J.J. and Tirtaatmadja, V. (2004). Shear-thinning drop formation. ANZIAM J. 45(E), C405-C418.

Holbeach, J.W. and Davidson, M.R. (2004). Modelling the dispersion of dissolving spherical particles. Progress in Computational Fluid Dynamics 4(2), 78-91.

Davidson, M.R. (2002). Spreading of an inviscid drop impacting on a liquid film. Chemical Engineering Science 57(17), 3639-3647.

Lawson, N.J. and Davidson, M.R. (2002). Oscillatory flow in a physical model of a thin slab casting mould with a bifurcated submerged entry nozzle. J. Fluids Eng. 124, 535-543.

Davidson, M.R. and Rudman, M. (2002). Volume-of-Fluid calculation of heat or mass transfer across deforming interfaces in two-fluid flow. Numerical Heat Transfer Part B 41(3), 291-308.

Lawson, N.J. and Davidson, M.R. (2001). Self-sustained oscillation of a submerged jet in a thin rectangular cavity. J. Fluids and Structures 15(1), 59-81.

Whyte, D.S., Davidson, M.R., Carnie, S. and Rudman, M. (2000). Calculation of droplet deformation at intermediate Reynolds number using a Volume of Fluid technique.ANZIAM J. 42(E), C1520-C1535.

Davidson, M.R., Khan, N.H. and Yeow, Y.L.(2000). Collapse of a cylinder of Bingham fluid. ANZIAM J. 42(E), C499-C512.

Smith, K.M., Davidson, M.R. and Lawson, N.J. (2000). Dispersion of Neutrally Buoyant Solids Falling Vertically into Stationary Liquid and Horizontal Channel Flow. Computers and Fluids 29, 369-384.

Davidson, M.R. (2000). Boundary integral prediction of the spreading of an inviscid drop impacting on a solid surface. Chemical Engineering Science 55(6), 1159-1170.

Lawson, N.J. and Davidson, M.R. (1999). Cross-flow characteristics of an oscillating jet in a thin slab casting mould. J. Fluids Eng. 121, 588-595.

Gebert, B.M., Davidson, M.R. and Rudman, M.J. (1998). Computed oscillations of a confined submerged liquid jet. Applied Mathematical Modelling 22, 843-850.

Davidson, M.R. (1998). Comparison of two-way coupling models for confined turbulent gas-particle jets in flash smelting. Applied Mathematical Modelling 22, 39-55.

Davidson, M.R. (1995). An adaptive method of predicting the air core diameter for numerical models of hydrocyclone flow. Int. J. Mineral Processing 43, 167-177.

Davidson, M.R. (1990). Numerical calculations of two-phase flow in a liquid bath with bottom gas injection: The central plume. Applied Mathematical Modelling 14, 67-76.

Davidson, M.R. (1990). Flow in the stagnation zone during submerged injection of a swirling gas jet. Chemical Engineering Science 45(3), 687-694.

Townley, L.R. and Davidson, M.R. (1988). Definition of a capture zone for shallow water table lakes. J. Hydrology 104, 53-76.

Davidson, M.R. (1988). Similarity solutions for flow in hydrocyclones. Chemical Engineering Science 43, 1499-1505.

Davidson, M.R. (1988). Numerical calculations of flow in a hydrocyclone operating without an air core. Applied Mathematical Modelling 12, 119-128.

Davidson, M.R. (1987). Asymptotic infiltration into soil which contains cracks or holes but whose surface is otherwise impermeable. Transport in Porous Media 2, 165-176.

Davidson, M.R. (1986). Natural convection of gas/vapour mixtures in a porous medium. Int. J. Heat Mass Transfer 29, 1371-1381.

Davidson, M.R. and Dickson, B.L. (1986). A porous flow model for steady state transport of radium in groundwater. Water Resources Research 22, 34-44.

Dickson, B.L. and Davidson, M.R. (1985). Interpretation of 234U/238U activity ratios in groundwaters. Chem. Geol. (Isot. Geosci. Sect.) 58, 83-88.

Davidson, M.R. (1985). Asymptotic behavior of infiltration in soils containing cracks or holes. Water Resources Research 21, 1345-1353.

Davidson, M.R. (1985). Numerical calculation of saturated-unsaturated infiltration in a cracked soil. Water Resources Research 21, 709-714.

Davidson, M.R. (1985). Numerical calculation of unstable immiscible fluid displacement in a two-dimensional porous medium or Hele-Shaw cell. J. Austral. Math. Soc. Ser. B 26, 452-469.

Davidson, M.R. (1984). A Green-Ampt model of infiltration in a cracked soil. Water Resources Research 20, 1685-1690.

Davidson, M.R. (1984). An integral equation for immiscible fluid displacement in a two dimensional porous medium or Hele-Shaw cell. J. Austral. Math. Soc. Ser. B. 26, 14-30.

Davidson, M.R. and Schroter, R.C. (1983). A theoretical model of absorption of gases by the bronchial wall. J. Fluid Mech. 129, 313-335.

Davidson, M.R. and Engel, L.A. (1982). Gas transport in an asymetrical acinus. Bull. Europ. Physiopath. Resp. 18, 203-214.

Davidson, M.R. and Airey, P.L. (1982). The effect of dispersion on the establishment of a paleoclimatic record from groundwater. J. Hydrology 58, 131-147.

Davidson, M.R. (1981). Further considerations in a theoretical description of gas transport in lung airways. Bull. Math. Biol. 43, 517-548.

Sylva, R.N. and Davidson, M.R. (1979). The hydrolysis of metal ions. Part 2. Dioxouranium (VI). J. Chem. Soc. Dalton Trans. 465-471.

Sylva, R.N. and Davidson, M.R. (1979). The hydrolysis of metal ions. Part 1. Copper (II). J. Chem Soc. Dalton Trans. 232-235.

Davidson, M.R. (1977). The influence of gas exchange on lung gas concentrations during air breathing. Bull. Math. Biol. 39, 73-86.

Davidson, M.R. (1975). Lung gas mixing during expiration following an inspiration of air. Bull. Math. Biol. 37, 113-126.

Davidson, M.R. and Fitz-Gerald, J.M. (1974). Transport of O2 along a model pathway through the respiratory region of the lung. Bull. Math. Biol. 36, 275-303.

Davidson, M.R. and Fitz-Gerald, J.M. (1972). Flow patterns in models of small airway units of the lung. J. Fluid Mech. 52, 161-177.