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## Abstract

Experiments showed that, when a brass cube coated with transparent bubble-free ice or opaque ice containing a high concentration of air bubbles was allowed to slide down an opaque or transparent ice incline, temperature differences were created between the ice specimens and charge was separated. In all cases the cube ice acquired negative charge if asymmetric rubbing caused it to become warmer than the ice incline, and positive charge if it became colder. These observations are consistent with the predictions of Hobbs and are explicable qualitatively in terms of the temperature-gradient theory. The magnitude of the charge transfer was in approximate agreement with the theory if both contacting ice specimens were transparent, but was appreciably greater than predicted if either or both of the specimens contained a high proportion of air bubbles.

## Abstract

Experiments showed that, when a brass cube coated with transparent bubble-free ice or opaque ice containing a high concentration of air bubbles was allowed to slide down an opaque or transparent ice incline, temperature differences were created between the ice specimens and charge was separated. In all cases the cube ice acquired negative charge if asymmetric rubbing caused it to become warmer than the ice incline, and positive charge if it became colder. These observations are consistent with the predictions of Hobbs and are explicable qualitatively in terms of the temperature-gradient theory. The magnitude of the charge transfer was in approximate agreement with the theory if both contacting ice specimens were transparent, but was appreciably greater than predicted if either or both of the specimens contained a high proportion of air bubbles.

## Abstract

A one-dimensional precipitative model of cloud electrification is outlined in which field growth results from the operation of either in inductive or non-inductive mechanism. The cloud is cylindrical, of finite dimensions, and charging is confined to a supercooled zone within which precipitation growth occurs. Account is taken of loss of negative charge arriving at the ground on precipitation and the storage of positive charge carried by the updraft to a level above the charging zone.

The most important conclusion is that previous models of cloud electrification, which have often been extremely elaborate, provide gross overestimates of the rate of field growth because they have assumed a cloud of infinite width. They also predict a “top-hat” distribution of field, which is shown to be quite unrealistic. The present calculations cast serious doubt on the capability of an inductive mechanism, *by itself*, to produce breakdown fields in the available time.

These calculations also indicate that 1) the retardation of field growth due to the effect of electrical forces on particle velocities is negligible; and that 2) the “lower positive charge” can be produced in the bases of clouds, in some circumstances, without having to invoke an additional charging mechanism.

## Abstract

A one-dimensional precipitative model of cloud electrification is outlined in which field growth results from the operation of either in inductive or non-inductive mechanism. The cloud is cylindrical, of finite dimensions, and charging is confined to a supercooled zone within which precipitation growth occurs. Account is taken of loss of negative charge arriving at the ground on precipitation and the storage of positive charge carried by the updraft to a level above the charging zone.

The most important conclusion is that previous models of cloud electrification, which have often been extremely elaborate, provide gross overestimates of the rate of field growth because they have assumed a cloud of infinite width. They also predict a “top-hat” distribution of field, which is shown to be quite unrealistic. The present calculations cast serious doubt on the capability of an inductive mechanism, *by itself*, to produce breakdown fields in the available time.

These calculations also indicate that 1) the retardation of field growth due to the effect of electrical forces on particle velocities is negligible; and that 2) the “lower positive charge” can be produced in the bases of clouds, in some circumstances, without having to invoke an additional charging mechanism.

## Abstract

When ice-coated spheres suspended from an insulating fiber were rotated rapidly through a stream of steadily falling natural snow crystals they acquired an electrical charge the magnitude of which increased markedly with an increase in impact velocity and degree of surface irregularity. A smooth sphere acquired a positive charge and the spheres of irregular surface structure acquired a much larger negative charge. The sign of the charging is in qualitative agreement with the temperature-gradient theory but the effects of impact velocity and surface geometry are not. Rough calculations indicate that the average charge transfer between a snow crystal and a sphere of irregular surface structure impacting at a velocity of several meters per second is several orders of magnitude greater than predicted by Mason's equations, but a comparison between these results and those emanating from the laboratory experiments of Latham and Stow indicates that the results of this field experiment are entirely explicable in terms of a temperature-gradient theory modified to accommodate these two enhancement processes. It is concluded that the experiments of Reynolds, Brook and Gourley yielded a more representative value for the average charge transfer per collision between an ice crystal and a soft-hail pellet inside a thundercloud than did the experiments of Latham and Mason, and that the Reynolds-Brook mechanism can easily generate charge inside a thunder-cloud at the minimum rate required by a tenable theory of thunderstorm electrification.

## Abstract

When ice-coated spheres suspended from an insulating fiber were rotated rapidly through a stream of steadily falling natural snow crystals they acquired an electrical charge the magnitude of which increased markedly with an increase in impact velocity and degree of surface irregularity. A smooth sphere acquired a positive charge and the spheres of irregular surface structure acquired a much larger negative charge. The sign of the charging is in qualitative agreement with the temperature-gradient theory but the effects of impact velocity and surface geometry are not. Rough calculations indicate that the average charge transfer between a snow crystal and a sphere of irregular surface structure impacting at a velocity of several meters per second is several orders of magnitude greater than predicted by Mason's equations, but a comparison between these results and those emanating from the laboratory experiments of Latham and Stow indicates that the results of this field experiment are entirely explicable in terms of a temperature-gradient theory modified to accommodate these two enhancement processes. It is concluded that the experiments of Reynolds, Brook and Gourley yielded a more representative value for the average charge transfer per collision between an ice crystal and a soft-hail pellet inside a thundercloud than did the experiments of Latham and Mason, and that the Reynolds-Brook mechanism can easily generate charge inside a thunder-cloud at the minimum rate required by a tenable theory of thunderstorm electrification.

## Abstract

The calculations of Gay *et al*. of the terminal velocities of charged hydrormeteors in the presence of electric fields have formed the basis of computations of the charging current density *J* flowing through a thunder-cloud as a result of the operation of a precipitative mechanism of cloud electrification. Values of *J* were calculated for a range of values of field strength *E*, precipitation rate *p*
_{O}, precipitation content *L*, cloud water content *C*, charge distribution, total separated charge, and the fraction of the small particles that have undergone a charging event.

It is found that the estimated field required for the initiation of a lightning stroke (σ3.5 kV cm^{−1} can be achieved only over a narrow range of conditions. The ease with which precipitative mechanisms can produce breakdown fields is considerably increased, however, if account is taken of spatial *inhomogenities* in the field.

## Abstract

The calculations of Gay *et al*. of the terminal velocities of charged hydrormeteors in the presence of electric fields have formed the basis of computations of the charging current density *J* flowing through a thunder-cloud as a result of the operation of a precipitative mechanism of cloud electrification. Values of *J* were calculated for a range of values of field strength *E*, precipitation rate *p*
_{O}, precipitation content *L*, cloud water content *C*, charge distribution, total separated charge, and the fraction of the small particles that have undergone a charging event.

It is found that the estimated field required for the initiation of a lightning stroke (σ3.5 kV cm^{−1} can be achieved only over a narrow range of conditions. The ease with which precipitative mechanisms can produce breakdown fields is considerably increased, however, if account is taken of spatial *inhomogenities* in the field.

## Abstract

A research airplane was used to study the microphysical characteristics of ice-free, nonprecipitating summertime cumulus clouds in Montana. Each cloud was penetrated at a multiplicity of levels encompassing, in general, a large fraction of the cloud depth. Similar studies covering a more limited altitude range were made in New Mexico.

The clouds were substantially diluted by entrainment of environmental air, which produced great variability—at all levels and on all scales of measurement—in the liquid water content, *L*, and droplet number concentration, *N*.

The effective radius, *r*
_{eff}, at any particular level was found to be essentially independent of *L* or *N*. Consideration of this result leads to the prediction that the parameter *A* = *r*
_{eff}/*r*
_{ad} ≈ 1 everywhere within these clouds, where *r*
_{ad} = (¾*πρ*
*w*)^{⅓} (*L*
_{ad}/*N*)^{⅓}, *N*
_{ad} and *L*
_{ad} are the “adiabatic” values of *N* and *L*, and *ρ*
*w* is the density of water.

Analysis of the airborne data (35 cloud penetrations) for the Montana cumuli reveals that *A* = 0.83 ± 0.07, while for the New Mexico study (25 penetrations) *A* = 0.93 ± 0.05. Thus, the foregoing prediction is confirmed to a reasonable degree of accuracy. Model calculations for both Montana and Hawaii cumulus consistently yield values of *A* close to 1.0.

It is considered that the parameter *A* should be useful in climate modeling.

## Abstract

A research airplane was used to study the microphysical characteristics of ice-free, nonprecipitating summertime cumulus clouds in Montana. Each cloud was penetrated at a multiplicity of levels encompassing, in general, a large fraction of the cloud depth. Similar studies covering a more limited altitude range were made in New Mexico.

The clouds were substantially diluted by entrainment of environmental air, which produced great variability—at all levels and on all scales of measurement—in the liquid water content, *L*, and droplet number concentration, *N*.

The effective radius, *r*
_{eff}, at any particular level was found to be essentially independent of *L* or *N*. Consideration of this result leads to the prediction that the parameter *A* = *r*
_{eff}/*r*
_{ad} ≈ 1 everywhere within these clouds, where *r*
_{ad} = (¾*πρ*
*w*)^{⅓} (*L*
_{ad}/*N*)^{⅓}, *N*
_{ad} and *L*
_{ad} are the “adiabatic” values of *N* and *L*, and *ρ*
*w* is the density of water.

Analysis of the airborne data (35 cloud penetrations) for the Montana cumuli reveals that *A* = 0.83 ± 0.07, while for the New Mexico study (25 penetrations) *A* = 0.93 ± 0.05. Thus, the foregoing prediction is confirmed to a reasonable degree of accuracy. Model calculations for both Montana and Hawaii cumulus consistently yield values of *A* close to 1.0.

It is considered that the parameter *A* should be useful in climate modeling.

## Abstract

A stochastic model of ice particle multiplication is outlined in which ice splinters are produced by riming and possibly also by the splintering of individual drops on freezing. The splinters may grow into rimers or be captured by supercooled drops, causing the drops to freeze and become rimers. The possibility of splinter-capture by supercooled drops reduces the average waiting time between the birth of a splinter and its subsequent development into a splinter-producing rimer. This reduction of the waiting time greatly enhances the growth rate of the ice particle population. In a particular calculation, with drops present, a multiplication factor of 10^{4} is achieved in about 50 min if *M*
_{p} (the number of ice splinters ejected per unit mass of rime) is 1 mg−1; this time is reduced to 10 min if we take the much higher values of *M*
_{p}≈140 found by Hallett and Mossop. The corresponding times in the absence of drops are about 74 and 37 min respectively.

## Abstract

A stochastic model of ice particle multiplication is outlined in which ice splinters are produced by riming and possibly also by the splintering of individual drops on freezing. The splinters may grow into rimers or be captured by supercooled drops, causing the drops to freeze and become rimers. The possibility of splinter-capture by supercooled drops reduces the average waiting time between the birth of a splinter and its subsequent development into a splinter-producing rimer. This reduction of the waiting time greatly enhances the growth rate of the ice particle population. In a particular calculation, with drops present, a multiplication factor of 10^{4} is achieved in about 50 min if *M*
_{p} (the number of ice splinters ejected per unit mass of rime) is 1 mg−1; this time is reduced to 10 min if we take the much higher values of *M*
_{p}≈140 found by Hallett and Mossop. The corresponding times in the absence of drops are about 74 and 37 min respectively.

## Abstract

In order to assess quantitatively the role of drop disintegrations in producing the electrification of warm clouds, it is necessary to establish the electrohydrodynamical equations governing the stability of drops subjected to electrical forces. In the present paper a theoretical and experimental study is presented of the disintegration of drops raised to equal and opposite potentials.

In his theoretical treatment of the deformation and disintegration of individual water drops of undistorted radius *R*
_{0} raised to a potential *V*, Taylor assumed that the drop retained a spheroidal shape until the instability point was reached and that the equations of equilibrium between the stresses due to surface tension *T*, the potential *V*, and the difference between the external and internal pressures was satisfied at the poles and the equator. He showed that since there is no stationary value for *V* as the elongation *a*/*b* increases, the only stable condition is when the drop is stable and *V*(*π*
*R*
_{0}
*T*)^{−½} < 4. Taylor's spheroidal assumption has been applied to the problem of the deformation and disintegration of pairs of drops raised to equal and opposite potentials. In this case directionality is imposed upon the problem by the attractive forces between the drops which provide a contribution, increasing with decreasing separation, to the outwardly-directed stresses in their surfaces. Stationary values of *V* were found to exist at values of *a*/*b* > 1, and the corresponding values of *V*(*π*
*R*
_{0}
*T*)^{−½} were less than 4.0 by a factor which increased rapidly as the initial separation was decreased. These critical values of *V*(*π*
*R*
_{0}
*T*)^{−½} at the disintegration point ranged from Rayleigh's value of 4.0 at infinite separations to 3.117, 6.842 × 10^{−1}, 2.880 × 10^{−2} and 8.654 × 10^{−4} for initial separations of 10, 1, 0.1 and 0.01 radii, respectively. These values of *V*(*π*
*R*
_{0}
*T*)^{−½} are slightly reduced for larger drops owing to the influence of the hydrostatic pressure difference between their vertical extremities.

These calculations were tested experimentally on suspended drops of water, aniline and benzene, and good agreement was obtained in all cases. High speed photographs indicated that the process of disintegration was similar to that observed by Taylor, with an extremely rapid transformation (<10^{−8} sec) from an approximately spheroidal shape to a conical profile. Measurements taken from the photographs demonstrated that the radius of curvature and the elongation of a drop at the moment of disintegration agreed quite closely with the predicted values.

## Abstract

In order to assess quantitatively the role of drop disintegrations in producing the electrification of warm clouds, it is necessary to establish the electrohydrodynamical equations governing the stability of drops subjected to electrical forces. In the present paper a theoretical and experimental study is presented of the disintegration of drops raised to equal and opposite potentials.

In his theoretical treatment of the deformation and disintegration of individual water drops of undistorted radius *R*
_{0} raised to a potential *V*, Taylor assumed that the drop retained a spheroidal shape until the instability point was reached and that the equations of equilibrium between the stresses due to surface tension *T*, the potential *V*, and the difference between the external and internal pressures was satisfied at the poles and the equator. He showed that since there is no stationary value for *V* as the elongation *a*/*b* increases, the only stable condition is when the drop is stable and *V*(*π*
*R*
_{0}
*T*)^{−½} < 4. Taylor's spheroidal assumption has been applied to the problem of the deformation and disintegration of pairs of drops raised to equal and opposite potentials. In this case directionality is imposed upon the problem by the attractive forces between the drops which provide a contribution, increasing with decreasing separation, to the outwardly-directed stresses in their surfaces. Stationary values of *V* were found to exist at values of *a*/*b* > 1, and the corresponding values of *V*(*π*
*R*
_{0}
*T*)^{−½} were less than 4.0 by a factor which increased rapidly as the initial separation was decreased. These critical values of *V*(*π*
*R*
_{0}
*T*)^{−½} at the disintegration point ranged from Rayleigh's value of 4.0 at infinite separations to 3.117, 6.842 × 10^{−1}, 2.880 × 10^{−2} and 8.654 × 10^{−4} for initial separations of 10, 1, 0.1 and 0.01 radii, respectively. These values of *V*(*π*
*R*
_{0}
*T*)^{−½} are slightly reduced for larger drops owing to the influence of the hydrostatic pressure difference between their vertical extremities.

These calculations were tested experimentally on suspended drops of water, aniline and benzene, and good agreement was obtained in all cases. High speed photographs indicated that the process of disintegration was similar to that observed by Taylor, with an extremely rapid transformation (<10^{−8} sec) from an approximately spheroidal shape to a conical profile. Measurements taken from the photographs demonstrated that the radius of curvature and the elongation of a drop at the moment of disintegration agreed quite closely with the predicted values.

## Abstract

Experiments showed that, as an ice specimen evaporated by exposure to a stream of dry nitrogen, a temperature gradient was created in the surface of the specimen, which became electrically charged. The charge was positive if the surface of the specimen was warmer than its interior, and negative if it was colder. A typical result was that a specimen of surface area 37 cm^{2} and internal temperature −20C exposed to a nitrogen stream of temperature −30C and velocity 15 cm sec^{−1} acquired a temperature gradient of magnitude 90C cm^{−1} in its surface and became negatively charged at a rate *i*=3.3 × l0^{−4} esu of current. These observations are explicable qualitatively in terms of the Latham-Mason theory of charge transfer associated with temperature gradients in ice. Calculations indicate that it cannot be determined whether quantitative agreement exists until measurements have been made of the distribution of temperature and charge within the volume of ice specimens along which temperature gradients exist. An estimate is also made of the importance of this evaporation process in generating electric charge in the atmosphere.

## Abstract

Experiments showed that, as an ice specimen evaporated by exposure to a stream of dry nitrogen, a temperature gradient was created in the surface of the specimen, which became electrically charged. The charge was positive if the surface of the specimen was warmer than its interior, and negative if it was colder. A typical result was that a specimen of surface area 37 cm^{2} and internal temperature −20C exposed to a nitrogen stream of temperature −30C and velocity 15 cm sec^{−1} acquired a temperature gradient of magnitude 90C cm^{−1} in its surface and became negatively charged at a rate *i*=3.3 × l0^{−4} esu of current. These observations are explicable qualitatively in terms of the Latham-Mason theory of charge transfer associated with temperature gradients in ice. Calculations indicate that it cannot be determined whether quantitative agreement exists until measurements have been made of the distribution of temperature and charge within the volume of ice specimens along which temperature gradients exist. An estimate is also made of the importance of this evaporation process in generating electric charge in the atmosphere.