Droplet Spreading on Heterogeneous Surfaces Using a Three-Dimensional Lattice Boltzmann Model

Abstract

Abstract. We use a three-dimensional lattice Boltzmann model to investigate the spreading of mesoscale droplets on homogeneous and heterogeneous surfaces. On a homogeneous substrate the base radius of the droplet grows with time as t 0.28 for a range of viscosities and surface tensions. The time evolutions collapse onto a single curve as a function of a dimensionless time. On a surface comprising of alternate hydrophobic and hydrophilic stripes the wetting velocity is anisotropic and the equilibrium shape of the droplet reflects the wetting properties of the underlying substrate.

Application to natural convection enclosed flows of a lattice Boltzmann BGK model coupled with a general purpose thermal boundary condition

“…However, whereas LBE techniques shine for the simulation of isothermal, quasi-incompressible flows in complex geometries, and LBM has been shown to be useful in applications involving interfacial dynamics and complex boundaries (see, for example, the recent works of Nie et al [6], Lim et al [7], Nguyen et al [8], Hoekstra et al [9], Facin et al [10], Inamuro et al [11] and Dupuis et al [12]), the application to fluid flow coupled with non negligible heat Nomenclature c i = (c ix , c iy ) discrete particle speeds c = dx/dt minimum speed on the lattice c s lattice sound speed dt time increment dx = dy lattice spacing T = T h − T c temperature difference between hot and cold wall e internal energy density e counter-slip internal energy density used in the thermal boundary conditions f , g continuous single-particle distribution functions for density-momentum and internal energy-heat flux fields f ,g modified continuous single-particle distribution functions for density-momentum and internal energy-heat flux fields f i , g i discrete distribution functions f i ,g i modified discrete distribution functions f e i , g e i equilibrium discrete distribution functions G 1 = βg(T − T ) buoyancy force per unit mass transfer turned out to be much more difficult (see, for example, Chen et al [13] and [14], Mc Namara et al [15], Chen [16], Vahala et al [17], Karlin et al [18], Luo [19], Succi et al [20] and Lallemand and Luo [21]). …”

Spreading Dynamics of Nanodrops: A Lattice Boltzmann Study

“…This relation can be derived from lubrication theory [1,4] and is known as Tanner's law [5].The experimentally observed value of the exponent n often deviates from the theoretical predictions and is found to depend on several physical parameters, such as substrate roughness, liquid viscosity or vapor density. This is reflected in the range of values that have been reported by experiments [6] and simulations [7][8][9].Most experiments deal with the spreading of droplets that are at least of micrometer size and thus are unaffected by thermal fluctuations. It is, however, interesting to ask what happens to droplets at the nanoscale, where thermal fluctuations become important.…”

Diffusion Problems of Crystal Growth

“…[21] may be applied to such particles: Therefore, Boltzmann's kinetic equation in the form proposed in Ref.…”

“…Equation (3.49) is reduced to the NavierÀStokes equation for nonideal gas, if we apply the function f eq i of a certain type [22]. [21]. In particular, the free surface energy and wetting according to a model of Caen [23] were taken into account in Ref.…”

“…Dupuis et al [21] have studied the spreading of the microscopic drop (of mesoscale size, such as drops in jet printers have) on the substrate by the lattice Boltzmann method. They considered a lattice 80 3 80 3 40, in which the spherical drop with the radius 16 was set so that it touched the flat substrate with coordinate…”