Gradient Force

"Gradient" refers to how rapidly a quantity (such as pressure or temperature) changes in a given distance. It can be thought of as measure of "steepness", like the topography on a contour plot.

The pressure gradient force is the force which results when there is a difference in pressure across a surface. In general, a pressure is a force per unit area, across a surface. A difference in pressure across a surface then implies a difference in force, which can result in an acceleration according to Newton's second law, if there is no additional force to balance it. The resulting force is always directed from the region of higher-pressure to the region of lower-pressure. When a fluid is in an equilibrium state (i.e. there are no net forces, and no acceleration), the system is referred to as being in hydrostatic equilibrium. In the case of atmospheres, the pressure gradient force is balanced by the gravitational force, maintaining hydrostatic equilibrium. In the Earth's atmosphere, for example, air pressure decreases at increasing altitudes above the Earth's surface, thus providing a pressure gradient force which counteracts the force of gravity on the atmosphere

In optical tweezer Gradient force is used to compensate Scattering force.

In cases where the diameter of a trapped particle is significantly greater than the wavelength of light, the trapping phenomenon can be explained using ray optics. As shown in the figure, individual rays of light emitted from the laser will be refracted as it enters and exits the dielectric bead. As a result, the ray will exit in a direction different from which it originated. Since light has a momentum associated with it, this change in direction indicates that its momentum has changed. Due to Newton's third law, there should be an equal and opposite momentum change on the particle.

Most optical traps operate with a Gaussian beam (TEM₀₀ mode) profile intensity. In this case, if the particle is displaced from the center of the beam, as in the right part of the figure, the particle has a net force returning it to the center of the trap because more intense beams impart a larger momentum change towards the center of the trap than less intense beams, which impart a smaller momentum change away from the trap center. The net momentum change, or force, returns the particle to the trap center.

If the particle is located at the center of the beam, then individual rays of light are refracting through the particle symmetrically, resulting in no net lateral force. The net force in this case is along the axial direction of the trap, which cancels out the scattering force of the laser light. The cancellation of this axial gradient force with the scattering force is what causes the bead to be stably trapped slightly downstream of the beam waist.

This is the output when beam is linear.

If the particle is located at the center of the beam, then individual rays of light are refracting through the particle symmetrically, resulting in no net lateral force. The net force in this case is along the axial direction of the trap, which cancels out the scattering force of the laser light. The cancellation of this axial gradient force with the scattering force is what causes the bead to be stably trapped slightly downstream of the beam waist.

This is the output, when beam is focused.

The standard tweezers works with the trapping laser propagated in the direction of gravity and the inverted tweezers works against gravity.

Wind is simply air in motion relative to the earth's surface. We normally think of the wind as the horizontal motion of the air, although air actually moves in three dimensions. The vertical component of the wind is generally quite small, except in thunderstorm updrafts. The vertical motion of air, however, is very important in determining our weather. Air that is rising cools, which may cause it to reach saturation and form clouds and precipitation. Conversely, air that is sinking warms, which causes clouds to evaporate and produce clear weather.

Surface maps usually have H's and L's at various locations. The H's and L's represent high and low pressure systems. On weather maps highs and lows are surrounded by lines called isobars. Isobars are lines of constant pressure; they connect every location that has the same value of pressure. When isobars are packed close together, the pressure is changing rapidly over a small distance. The closer the isobars are packed together, the stronger thepressure gradient (the rate of pressure change over a given distance.) Also, notice that (in the Northern Hemisphere) the wind blows clockwise around a high pressure system and also slightly outward from its center. Around a low pressure system, the wind blows counterclockwise and slightly in towards its center.