Dimensionless numbers Bond number

Avogadro s constant The number of objects per mole of objects (Na = 6.022 14 X 102 mol ). Avogadro s number is the number of objects in one mole of objects (that is, the dimensionless number 6.022 14 XlO2 ). Avogadro s principle The volume of a sample of gas at a given temperature and pressure is proportional to the amount of gas molecules in the sample V n. axial bond A bond that is perpendicular to the molecular plane in a bipyramidal molecule, axial lone pair A lone pair lying on the axis of a bipyramidal molecule. 

In Eq. (48), y is the coefficient of surface tension, g is gravitational acceleration and Apm is the difference in mass densities between the aqueous and organic liquids. The interface position z = (r) and the deflection t(r) = — of the interface from its unperturbed position are shown schematically in Fig. 6. Nondimensionalization of Eq. (48) leads to two dimensionless groups that relate electrostatic and gravitational stresses to surface tension. These groups are called the electrostatic and gravitational bond numbers, and are given by [25]... 

Pharmaceutical compacts are complex structures that present difficult challenges when measuring their mechanical properties. Hiestand was a pioneer who quantified the compaction properties of pharmaceutical powders and (105-109) the result of his work are indices known as the Hiestand Tableting Indices. These indices are dimensionless numbers used to describe the mechanical properties and consolidation behavior of materials under compression and decompression. The three main Hiestand Tableting Indices are the bonding index, brittle fracture index BFl), and strain index. 

Dimensionless reduced bonding R(D) Cumulative number of pellets... 

Here the parameter pga /I. = Bo is the Bond number for the given capillary radius. The other dimensionless parameter follows from the form of the left-hand side of (17.16). Designate the characteristic velocity by U. Then it is possible to introduce the capillary number,... 

The control parameters are (a) cOq = 14.6 pm and T — Tc = 2Kand(b)(Uo = V.SpmandJ - Tc = 3K[3].(c) Experimental variation of the dimensionless height of the interface deformation versus the Bond number. The solid line represents the universal scaling behavior given by Eq. 8. The single black square represents the data for the water-air free surface [1]. Arrows in insets indicate the laser beam incidence... 

The capillary forces which cause trapping or resist mobilization can be overcome by viscous pressure gradient or buoyancy forces. The ratios of gravity to capillary forces and viscous to capillary forces are expressed as dimensionless groups, known respectively as the Bond number (Ng), and capillary number (N ). 

In flowing systems, the complex interplay between interfacial, gravitational, viscous and inertial forces is responsible for a variety of phase distributions and flow patterns. The dominant interfadal forces combined with the laminar nature of the flow result in very regularly shaped gas-liquid and liquid-liquid interfaces characteristic of multiphase microflows. Courbin et al. described dynamic wetting morphologies of a flat surface that is microstructured with a forest of posts upon droplet impact [44], Eijkel and co-workers [42, 48] provided a more general review of surface tension effects in the context of nanofluidic systems. The importance of interfadal forces with respect to gravity is described by the dimensionless Bond number. 

The dynamical response of two-phase flows can be commonly characterized successfully in terms of the dimensionless numbers [2]. Table 1 lists some force-related dimensionless numbers. These dimensionless numbers demonstrate competing phenomena of forces buoyancy, gravitational, inertial, viscous and interfacial forces. The Grashof number (buoyancy to viscous forces), the Bond number (gravitational to interfacial forces) and the... 

The flow in fluid-fluid microstructured channels is characterized using dimensionless numbers. The most important dimensionless number for characterization of all types of flows is the Re number that relates inertial force to viscous force. Due to low flow velocities and characteristic dimension in the micrometer range, Re is often less than 1 meaning that viscous force is dominant over inertial force. The capillary number Ca is the ratio of viscous to interfacial forces. The range of Ca in a typical microchannel is lO " to 10 . Multiplying both numbers. Re and Ca, results in the Weber number We, which represents the ratio between inertial and interfacial forces. The importance of gravity vhth respect to interfacial forces is characterized by the Bond number Bo. The definitions of the dimensionless numbers are summarized in Table 2.2. 

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