Other Forces

There are several other mechanisms that may lead to forces between particles. In very dry air static charge may result in Columbic interactions between particles. Columbic interactions are usually of little significance in ambient air which is usually humid enough that the static charge dissipates rapidly. In solution, nonadsorbing polymers can result in another type of weak attraction called depletion attraction. Layers of solvent molecules on particles surfaces, such as water on 

---

Redlich [3] has criticized the so-called zeroth law on the grounds that the argument applies equally well for the introduction of any generalized force, mechanical (pressure), electrical (voltage), or otherwise. The difference seems to be that the physical nature of these other forces has already been clearly defined or postulated (at least in the conventional development of physics) while in classical thennodynamics, especially in the Bom-Caratheodory approach, the existence of temperature has to be inferred from experiment. 

These numbers are not negligible. At present such effects are on the average compensated by other force field terms through empirical parametrization. 

YETI is a force held designed for the accurate representation of nonbonded interactions. It is most often used for modeling interactions between biomolecules and small substrate molecules. It is not designed for molecular geometry optimization so researchers often optimize the molecular geometry with some other force held, such as AMBER, then use YETI to model the docking process. Recent additions to YETI are support for metals and solvent effects. 

An atom that has sp hybridization tends to be coplanar with its attached atoms. This effect is accounted for by improper torsions in other force fields and by out-of-plane-bending interactions in... 

In computational chemistry it can be very useful to have a generic model that you can apply to any situation. Even if less accurate, such a computational tool is very useful for comparing results between molecules and certainly lowers the level of pain in using a model from one that almost always fails. The MM+ force field is meant to apply to general organic chemistry more than the other force fields of HyperChem, which really focus on proteins and nucleic acids. HyperChem includes a default scheme such that when MM+ fails to find a force constant (more generally, force field parameter), HyperChem substitutes a default value. This occurs universally with the periodic table so all conceivable molecules will allow computations. Whether or not the results of such a calculation are realistic can only be determined by close examination of the default parameters and the particular molecular situation. ... 

Static holdup depends upon the balance between surface-tension forces tending to hold hquiciin the bed and gravity or other forces that tend to displace the liquid out of the bed. Estimates of static holdup (for gravity drainage) may be made from the following relationship of Shulman et al. [Am. Jn.st. Chem. Eng. J., 1, 259 (1955)] ... 

This has also commonly heen termed direct interception and in conventional analysis would constitute a physical boundary condition path induced hy action of other forces. By itself it reflects deposition that might result with a hyj)othetical particle having finite size hut no fThis parameter is an alternative to N f, N i, or and is useful as a measure of the interactive effect of one of these on the other two. Schmidt numher. 

Belt Presses Belt presses were fiiUy described in the section on filtration. The description here is intended to cover only the parts and designs that apply expression pressure by a mechanism in adchtion to the normal compression obtained from tensioning the belts and pulling them over rollers of smaller and smaller diameters. The tension on the belt produces a squeezing pressure on the filter cake proportional to the diameter of the rollers. Normally, that static pressure is calculated as P = 2T/D, where P is the pressure (psi), T is the tension on the belts (Ib/hnear in), and D is the roller diameter. This calculation results in values about one-half as great as the measured values because it ignores pressure created by drive torque and some other forces [Laros, Advances in Filtration and Separation Technology, 7 (System Approach to Separation and Filtration Process Equipment), pp. 505-510 (1993)]. 

Significant progress in the optimization of VDW parameters was associated with the development of the OPLS force field [53]. In those efforts the approach of using Monte Carlo calculations on pure solvents to compute heats of vaporization and molecular volumes and then using that information to refine the VDW parameters was first developed and applied. Subsequently, developers of other force fields have used this same approach for optimization of biomolecular force fields [20,21]. Van der Waals parameters may also be optimized based on calculated heats of sublimation of crystals [68], as has been done for the optimization of some of the VDW parameters in the nucleic acid bases [18]. Alternative approaches to optimizing VDW parameters have been based primarily on the use of QM data. Quantum mechanical data contains detailed information on the electron distribution around a molecule, which, in principle, should be useful for the optimization of VDW... 

The continuum model, in which solvent is regarded as a continuum dielectric, has been used to study solvent effects for a long time [2,3]. Because the electrostatic interaction in a polar system dominates over other forces such as van der Waals interactions, solvation energies can be approximated by a reaction field due to polarization of the dielectric continuum as solvent. Other contributions such as dispersion interactions, which must be explicitly considered for nonpolar solvent systems, have usually been treated with empirical quantity such as macroscopic surface tension of solvent. 

Molecular interactions are the result of intermolecular forces which are all electrical in nature. It is possible that other forces may be present, such as gravitational and magnetic forces, but these are many orders of magnitude weaker than the electrical forces and play little or no part in solute retention. It must be emphasized that there are three, and only three, different basic types of intermolecular forces, dispersion forces, polar forces and ionic forces. All molecular interactions must be composites of these three basic molecular forces although, individually, they can vary widely in strength. In some instances, different terms have been introduced to describe one particular force which is based not on the type of force but on the strength of the force. Fundamentally, however, there are only three basic types of molecular force. 

The other forces affecting the particle are the gravitational force and friction hence the force balance is... 

In the models discussed thus far in this section, emphasis has been placed on electrostatic effects and solvent polarity. An alternative view that to some extent takes other forces into account begins with the idea that, in order to dissolve a solute molecule in a solvent, energy is required to create a cavity in the solvent the solute is then inserted into this cavity. In Section 8.2 we saw that the energy to create a cavity can be expressed as a product of the surface area of the cavity and the surface tension of the solvent. An equivalent expression is obtained as the product of the volume of the cavity and the pressure exerted by the solvent, and we now explore this concept. 

Against the backdrop of an Earth warmed by its own greenhouse effect, other forces operate that can increase or decrease the retention of heat by the atmosphere. Some of these forces are of human origin, some are produced by nature, and some are produced by mutual feedback reactions. 

After 1986, the CAFE and appliance standards in place resulted in stock turnovers to more efficient automobiles and appliances. However, the decline in energy consumption per dollar of GDP slowed appreciably and, between 1986 and 1997, the energy intensity trend remained rather flat. Other forces in the U.S. economy were pushing energy consumption higher, resulting in increases in the energy-intensity measure. 

Gravity acts downwards The denser constituents in a mixture often tend to move to the bottom of a space, unless other forces acting on them oppose such motion. 

Gravity, which acts at all times on all bodies, regardless of other forces. 

Other forces, such as the side-load created by V-belt drives, also generate unique frequencies or modify existing component frequencies. For example, excessive belt tension increases the side-load on the machine-train s shafts. This increase in side-load changes the load zone in the machine s bearings. The result of this change is a marked increase in the amplitude at the outer-race rotational frequency of the bearings. 

A condition that can result from a mechanical and/or a force imbalance. Mechanical imbalance is when there is more weight on one side of a center line of a rotor than on the other. Force imbalance can result when there is an imbalance of the centripetal forces generated by rotation and/or when there is an imbalance between the lift generated by the rotor and gravity. 

It should be noted that this and some of the other proposed explanations would yield similar barrier contributions in other molecules where steric or electrostatic interactions are expected. In any calculations, the basic ethane-like contribution has to be subtracted before the other forces can be considered. This has not been customary. 

The most important driving forces for the motion of ionic defects and electrons in solids are the migration in an electric field and the diffusion under the influence of a chemical potential gradient. Other forces, such as magnetic fields and temperature gradients, are commonly much less important in battery-type applications. It is assumed that the fluxes under the influence of an electric field and a concentration gradient are linearly superimposed, which... 

In the above we have assumed that no other forces than the electrical are acting at the surface of separation. In general, there will be the capillary forces as well, and we have to take account of the influence of the electrical double layer in considering the adsorption of an electrolyte. If w is the area of the surface, o the interfacial tension, e the charge per unit area, and E the difference of potential, we shall have ... 

---