Patent Publication Number: US-2021169142-A1

Title: Shisha cartridge

Description:
This invention relates to shisha devices and to cartridges containing an aerosol-forming substrate for use in shisha devices; and more particularly, to cartridges for use in shisha devices that heat the aerosol-forming substrate without combusting the substrate. 
     Traditional shisha devices are used to smoke tobacco and are configured such that vapor and smoke pass through a water basin before inhalation by a consumer. Shisha devices may include one outlet, or more than one outlet so that the device can be used by more than one consumer at a time. Use of shisha devices is considered by many to be a leisure activity and a social experience. 
     The tobacco used in shisha devices may be mixed with other ingredients to, for example, increase the volume of the vapour and smoke produced, to alter flavour, or both. Charcoal pellets are typically used to heat the tobacco in a traditional shisha device, which may cause full or partial combustion of the tobacco or other ingredients. Additionally, charcoal pellets may generate harmful, or potentially harmful products, such as carbon monoxide, which may mix with the shisha vapor and pass through the water basin. 
     Some shisha devices have been proposed that use electric heat sources to combust the tobacco to, for example, avoid by-products of burning charcoal or to improve the consistency with which the tobacco is combusted. Other shisha devices have been proposed that employ e-liquids rather than tobacco. Shisha devices that employ e-liquids eliminate combustion by-products but deprive shisha consumers of the tobacco-based experience. 
     Various shisha devices have been proposed that use electric heaters to heat an aerosol-forming substrate, such as tobacco, without burning the substrate. Such shisha devices provide for a tobacco-based experience without combustion by-products. However, substituting an electric heater for charcoal may reduce the total aerosol mass produced from the substrate. 
     Charcoal-operated shisha devices rely on conduction and convection for thermal transfer and aerosol production. Through conduction, the charcoal heats the aerosol-forming substrate to temperatures up to about 200° C., which remains fairly constant throughout the experience. Through convection, the aerosol-forming substrate may be heated up to about 230° C., with air temperatures reaching up to about 700° C. during puffing. 
     Electric heaters, for example resistive heaters, may provide similar levels of thermal transfer through conduction. However, reaching air temperatures of about 700° C. with electric heaters, particularly if the shisha device is battery powered, presents challenges. As such, the substrate may not be sufficiently heated to cause substantial aerosol generation for a sustained period of time, which may result in generation of less total aerosol mass when compared to shisha devices employing charcoal. 
     It would be desirable to provide a shisha cartridge containing an aerosol-forming substrate that may be heated by an electric heater in a manner that provides aerosol production that is similar to the aerosol production experienced with charcoal-heated shisha devices. More particularly, it would be desirable to provide a cartridge for use in a heat-not-burn shisha device that produces desirable levels of aerosol mass. 
     Various aspects of the invention relate to a shisha cartridge comprising a body defining a cavity. The cartridge comprises an aerosol-forming substrate disposed in the cavity. The cartridge comprises a heatable surface area. The heatable surface area may be defined by the body. A ratio of the heatable surface area of the cartridge to a volume of the cavity is in a range from about 1 cm −1  to about 4 cm −1 . For example, the ratio of the heatable surface area to the volume of the cavity may be in a range from about 1 cm −1  to about 2 cm −1 , such as from about 1.2 cm −1  to about 1.6 cm −1  or from about 1.3 cm −1  to about 1.5 cm −1 . In some embodiments, the heatable surface area is from about 25 cm 2  to about 100 cm 2 , such as from about 25 cm 2  to about 55 cm 2 . 
     Various aspects of the invention relate to a shisha cartridge comprising a body defining a cavity. The cartridge comprises an aerosol-forming substrate disposed in the cavity. The cavity comprises a cavity surface area. The cavity surface area may be defined by the body. A ratio of the cavity surface area of the cartridge to a volume of the cavity is in a range from about 1 cm −1  to about 4 cm −1 . 
     Various aspects of the invention relate to a shisha cartridge comprising a body defining a cavity. The cartridge comprises an aerosol-forming substrate disposed in the cavity. The cavity comprises a cavity surface area comprising a lateral cavity surface area. The cavity surface area may be defined by the body. The lateral cavity surface area may be defined by a sidewall of the body, such as a cylindrical or frustoconical sidewall of the body. A ratio of the lateral cavity surface area of the cartridge to a volume of the cavity is in a range from about 1 cm −1  to about 4 cm −1 . 
     Various aspects of the invention relate to a shisha cartridge comprising a body defining a cavity having a maximum inner width of 4 cm. In some embodiments, the shisha cartridge comprises a body defining a cavity having a maximum inner width of 3.5 cm. In some embodiments, the shisha cartridge comprises a body defining a cavity having a maximum inner width of 3 cm. The cartridge comprises an aerosol-forming substrate disposed in the cavity. The body comprises a sidewall having and inner surface that defines at least a part of the cavity. The cartridge has a longitudinal axis, a height along the longitudinal axis, and an inner width. For purposes of the present disclosure, the inner width of the cartridge is determined along an axis orthogonal to the longitudinal axis from the inner surface of the sidewall at one side of the sidewall to an inner surface of the sidewall at an opposing side of the side wall when measured through the geometric center of the cavity. If a section of the sidewall in a plane orthogonal to the longitudinal axis is circular, the width may be a diameter. Preferably, the maximum width is the width of a section at or near the top of the container. 
     Various aspects of the invention relate to a shisha cartridge comprising a body defining a cavity having a height of 3 cm or greater. The cartridge comprises an aerosol-forming substrate disposed in the cavity. 
     Various aspects of the invention relate to a shisha cartridge comprising a body defining a cavity having a height of 3.5 cm or greater. The cartridge comprises an aerosol-forming substrate disposed in the cavity. 
     The body may define a cavity having a height of 3 cm or greater and a width of 4 cm or less. The body may define a cavity having a height of 3 cm or greater and a width of 4 cm or less, and the cartridge may have a ratio of heatable surface area to a volume of the cavity in a range from about 1 cm −1  to about 4 cm −1 . The body may define a cavity having a height of 3 cm or greater, and the cartridge may have a ratio of heatable surface area to a volume of the cavity in a range from about 1 cm −1  to about 4 cm −1 . The body may define a cavity having a width of 4 cm or less, and the cartridge may have a ratio of heatable surface area of the cartridge to a volume of the cavity in a range from about 1 cm −1  to about 4 cm −1 . 
     The body may define a cavity having a height of 3.5 cm or greater and a width of 4 cm or less. The body may define a cavity having a height of 3.5 cm or greater and a width of 4 cm or less, and the cartridge may have a ratio of heatable surface area to a volume of the cavity in a range from about 1 cm −1  to about 4 cm −1 . The body may define a cavity having a height of 3.5 cm or greater, and the cartridge may have a ratio of heatable surface area to a volume of the cavity in a range from about 1 cm −1  to about 4 cm −1 . The body may define a cavity having a width of 4 cm or less, and the cartridge may have a ratio of heatable surface area of the cartridge to a volume of the cavity in a range from about 1 cm −1  to about 4 cm −1 . 
     The body may define a cavity having a height of 3 cm or greater and a width of 3.5 cm or less. The body may define a cavity having a height of 3 cm or greater and a width of 3.5 cm or less, and the cartridge may have a ratio of heatable surface area to a volume of the cavity in a range from about 1 cm −1  to about 4 cm −1 . The body may define a cavity having a height of 3 cm or greater, and the cartridge may have a ratio of heatable surface area to a volume of the cavity in a range from about 1 cm −1  to about 4 cm −1 . The body may define a cavity having a width of 3.5 cm or less, and the cartridge may have a ratio of heatable surface area of the cartridge to a volume of the cavity in a range from about 1 cm −1  to about 4 cm −1 . 
     The body may define a cavity having a height of 3.5 cm or greater and a width of 3.5 cm or less. The body may define a cavity having a height of 3.5 cm or greater and a width of 3.5 cm or less, and the cartridge may have a ratio of heatable surface area to a volume of the cavity in a range from about 1 cm −1  to about 4 cm −1 . The body may define a cavity having a height of 3.5 cm or greater, and the cartridge may have a ratio of heatable surface area to a volume of the cavity in a range from about 1 cm −1  to about 4 cm −1 . The body may define a cavity having a width of 3.5 cm or less, and the cartridge may have a ratio of heatable surface area of the cartridge to a volume of the cavity in a range from about 1 cm −1  to about 4 cm −1 . 
     The body may define a cavity having a height of 3.5 cm or greater and a width of 3 cm or less. The body may define a cavity having a height of 3.5 cm or greater and a width of 3 cm or less, and the cartridge may have a ratio of heatable surface area to a volume of the cavity in a range from about 1 cm −1  to about 4 cm −1 . The body may define a cavity having a height of 3.5 cm or greater, and the cartridge may have a ratio of heatable surface area to a volume of the cavity in a range from about 1 cm −1  to about 4 cm −1 . The body may define a cavity having a width of 3 cm or less, and the cartridge may have a ratio of heatable surface area of the cartridge to a volume of the cavity in a range from about 1 cm −1  to about 4 cm −1 . 
     The body may define a cavity having a height of 3 cm or greater and a width of 3 cm or less. The body may define a cavity having a height of 3 cm or greater and a width of 3 cm or less, and the cartridge may have a ratio of heatable surface area to a volume of the cavity in a range from about 1 cm −1  to about 4 cm −1 . The body may define a cavity having a height of 3 cm or greater, and the cartridge may have a ratio of heatable surface area to a volume of the cavity in a range from about 1 cm −1  to about 4 cm −1 . The body may define a cavity having a width of 3 cm or less, and the cartridge may have a ratio of heatable surface area of the cartridge to a volume of the cavity in a range from about 1 cm −1  to about 4 cm −1 . 
     In some preferred embodiments, the body defines a cavity having a height of 3.5 cm or greater and a width of 3 cm or less and may have a ratio of heatable surface area of the cartridge to a volume of the cavity in a range from about 1 cm −1  to about 4 cm −1 . 
     A ratio of heatable surface area, such as a surface area of the cavity defined by the body, to volume of the cavity of about 1 cm −1  or greater increases heat transfer by conduction, relative to conventional charcoal-operated shisha devices. This increases aerosol production. The increase in heat transfer by conduction may overcome, or at least partially compensate for absent thermal transfer by convection in electrically heated shisha devices, relative to conventional charcoal-operated shisha devices. A ratio of heatable surface area to volume of the cavity of about 1 cm −1  or greater maybe particularly useful in increasing aerosol production during initial puffs. This helps to reduce a time between initiating heating of the aerosol-forming substrate and a time at which the device is ready for a user to take a first puff. 
     A ratio of heatable surface area, such as a surface area of the cavity defined by the body, to volume of the cavity of about 4 cm −1  or less prevents premature depletion of the substrate. In some embodiments, the ratio of the heatable surface area of the body of the cavity to the volume of the cavity is from about 1.2 cm −1  to about 3 cm −1 , such as from about 1.5 cm −1  to about 3 cm −1 , or such as from about 2.5 cm −1  to about 3 cm −1 . 
     The heatable surface area to volume ratio of the cavity may be readily varied by altering one or more dimensional constraints of the cartridge, such as the length, inner diameter, or shape of the body of the cartridge. As used herein, “inner diameter” of the cartridge means an average transverse sectional distance across the cavity when measured through the geometric center of the section. If the transverse cross-section is circular, each measured transverse distance should be the same as the average transverse sectional distance. However, the transverse cross-section may have any suitable shape, including shapes other than circular. The cartridge may have different inner diameters along the length of the cartridge or the inner diameter may be uniform along the length of the capsule. 
     The heatable surface area may be readily varied by employing one or more thermal bridges inside the cavity to increase the heatable surface area. The one or more thermal bridges may be provided inside the cavity of the cartridge. 
     The cartridge may be of any suitable shape configured to be received by a shisha device. The shisha device is preferably configured to heat the aerosol-forming substrate in the cartridge by conduction. The cartridge is preferably shaped and sized to allow contact, or minimize distance, between a heating element of shisha device to provide efficient heat transfer from a heater of the shisha to the aerosol-generating substrate in the cartridge. 
     The cartridge may have a substantially cubioidal shape, cylindrical shape, a frustoconical shape, or any other suitable shape. Preferably, the cartridge has a generally cylindrical shape or a frustoconical shape. 
     Where the cartridge has a frustoconical shape, in some embodiments, sidewalls of the cartridge body deviate from the longitudinal axis at an angle of between about 2° and about 45°, preferably at an angle between about 3° and about 5°. In some embodiments, sidewalls of the cartridge body deviate from the longitudinal axis at an angle of between about 4.5°. 
     The cartridge may comprise any suitable body defining a cavity in which the aerosol-forming substrate is disposed. The body is preferably formed from one or more heat resistant materials, such as a heat resistant polymer or metal. Preferably, the body comprises a thermally conductive material. For example, the body may comprise any of: aluminium, copper, zinc, nickel, silver, any alloys thereof and combinations thereof. Preferably, the body comprises aluminium. 
     The body may comprise a top, bottom and sidewall. 
     In some embodiments, the bottom may be a flat bottom. In some embodiments, the bottom may be a substantially planar bottom. In some embodiments, the bottom may transition to the sidewalls in a single transition, such as by way of a vertex or a curved edge. 
     In some embodiments, the bottom is not entirely planar or flat. In some embodiments, the bottom deviates from a flat bottom at an angle. The angle may be about 5° to about 40°, such as from about 10° to about 30°, preferably from about 15° to about 25° or from about 15° to about 20°, such as 18°. In some embodiments, the bottom deviates from a flat portion by means of an intermediate transition medium, providing a first transition between the sidewall and the intermediate transition medium and a second transition between the intermediate transition region and the bottom. In some embodiments, the intermediate transition medium may be at an angle to the remainder of the bottom. The angle may be about 5° to about 40°, such as from about 10° to about 30°, preferably from about 15° to about 25° or from about 15° to about 20°, such as 18°. The remainder of the bottom may be substantially flat. The remainder of the bottom may be substantially planar. The intermediate transition may lie in a plane intersecting both a plane of the remainder of the bottom region and a plant of the sidewall. The angle at which the plane of the intermediate transition and the remainder of the bottom region may be about 5° to about 40°, such as from about 10° to about 30°, preferably from about 15° to about 25° or from about 15° to about 20°, such as 18°. The intermediate transition may be a bevelled edge in some embodiments. 
     The body may comprise one or more part. For example, the sidewall and the bottom may be a single part or two parts configured to engage one another in any suitable manner, such as threaded engagement or interference fit. The top and sidewall may be a single part or two parts configured to engage one another in any suitable manner, such as threaded engagement or interference fit. 
     The body defines a cavity in which the aerosol-forming substrate may be disposed. The portion of the body defining the cavity has a heatable surface area. As used herein, “heatable surface area” means an area of a surface through which heat applied at a location other than the area of the surface may be transferred to the area of the surface. For example, the heatable surface area of the portion of the body defining the cavity is a surface area through which heat may be transferred from outside of the cavity through the body to the surface of the body defining the cavity. For example, the heatable surface area of the portion of the body defining the cavity is a surface area of the cavity interior through which heat may be transferred from the outside of the cavity, such as an external surface area of the body, through the body to the surface of the body defining the cavity. For example, heat may be applied to the external surface area of the body, which heat may be transferred to the heatable surface area, the surface area of the cavity defined by the body, to the cavity. The heatable surface area may be a laterally heatable surface area. The heatable surface area may be a radially heatable surface area. Preferably, a heatable surface area has a thermal conductivity of at least about 100 W·m −1 ·K −1 . More preferably, the heatable surface area has a thermal conductivity of at least about 150 W·m −1 ·K −1 , such as at least about 200 W·m −1 ·K −1 . 
     The heatable surface area, may have any suitable total surface area, provided that the ratio of the heatable surface area to the cavity is in a range from about 1 cm −1  to about 4 cm −1 . In some embodiments, the ratio of the heatable surface area to the volume of the cavity is in a range from about 1.2 cm −1  to about 3 cm −1 . Preferably, the ratio of the heatable surface area to the volume of the cavity is in a range from about 1.5 cm −1  to about 3 cm −1 , such as from about 2.5 cm −1  to about 3 cm −1 . In some preferred embodiments, the ratio of the heatable surface area to the volume of the cavity is in a range from about 1 cm −1  to about 2 cm −1 , such as from about 1.2 cm −1  to about 1.6 cm −1  or from about 1.3 cm −1  to about 1.5 cm −1 . 
     To achieve such heatable surface area to volume ratios, the body may be long and narrow, or short and wide. The cartridge may comprise one or more elements or features within the cavity for increasing the heatable surface area within the cavity. For example, the sidewall may comprise one or more fins that extend into the cavity. The cartridge may comprise a thermal bridge within the cavity. Preferably, the thermal bridges are positioned in the cavity such that the aerosol-forming substrate is disposed in the cavity is in contact with the thermal bridge on opposing major surfaces. In some embodiments, the thermal bridge may comprise the same material as the body. In some embodiments, the thermal bridge may comprise a different material to that of the body. The thermal bridge may be in thermal connection with another portion of the body. For example, the thermal bridge may be in thermal contact with one or more of the top, bottom, and sidewall. In some embodiments, the thermal bridge extends from one portion of the sidewall to another portion of the sidewall. In some embodiments, the thermal bridge may not be in contact with the sidewall. Where a thermal bridge is provided in the cavity, the thermal bridge forms part of the heatable surface area of the cartridge. In some embodiments, more than one thermal bridge may be provided. 
     The thermal bridge may have any suitable shape. For example, the thermal bridge may form a cylinder. The cylinder may be within the cavity. The cylinder may be concentric with the cavity, such as with the sidewall of the body. The thermal bridge may be in thermal contact with the top or bottom of the body. The thermal bridge may include one or more additional thermal bridges that extend from the sidewall to the cylindrical thermal bridge or may be in contact with one or more of the top, bottom, and sidewall. 
     In some examples, the thermal bridge is substantially rectangular and extends from one portion the sidewall to another portion of the sidewall. In some examples, the thermal bridge comprises an S-shaped cross section and extends from one portion the sidewall to another portion of the sidewall. The thermal bridge preferably has a thermal conductivity at least as high as the portion of the body, such as the sidewall, bottom, or top, with which thermal bridge is in contact. Preferably, the thermal bridge has a conductivity greater than the portion of the body with which thermal bridge is in contact. The thermal bridge may divide the cavity into more than one compartment. Preferably, the compartments are of sufficiently large dimensions to allow the aerosol-forming substrate to readily occupy at least a portion of each compartment to allow contact between opposing major surfaces of the thermal bridge and the aerosol-forming substrate. 
     In some embodiments, heatable surface area has a total surface area from about 20 cm 2  to about 105 cm 2 , such as from about 25 cm 2  to about 100 cm 2 . In some embodiments, the heatable surface area has a total surface area from about 30 cm 2  to about 100 cm 2 , such as from about such as from about 70 cm 2  to about 100 cm 2 . 
     The body may have any suitable dimensions, such as length and inner diameter, and shape. It will be understood that the length may refer to a height of the body. In some embodiments, the body has a length of about 10 cm or less, such as about 6.5 cm or less. The length of the body is preferably greater than about 2.5 cm. In some preferred embodiments, the body has a length from about 3.5 cm to about 7 cm. 
     The body may have an inner diameter of about 1 cm or greater, such as about 1.5 cm or greater, about 1.75 cm or greater, or about 2 cm or greater. The body preferably has an inner diameter of about 5 cm or less. In some preferred embodiments, the body has an inner diameter in a range from about 1.5 cm to about 4 cm. 
     Preferably, the body has a length of about 15 cm or less and has an inner diameter of about 1 cm or more. More preferably, the body has a length of about 10 cm or less and an inner diameter of about 1.75 cm or more. Even more preferably, the body has a length in a range from about 3.5 cm to about 7 cm and has an inner diameter in a range from about 1.5 cm to about 4 cm. Preferably, the body is cylindrical or frustroconical. If the body has a frustroconical shape, the body preferably has a length from about 3 cm to about 5 cm and has a maximum inner diameter from about 2.5 cm to about 3 cm, such as about 2.7 cm, and has a minimum inner diameter from about 1.5 cm to about 2.5 cm, such as from about 1.8 cm to about 2.3 cm. 
     In some embodiments, the body has a length of about 15 cm or less, has an inner diameter of about 1 cm or more, and has a heatable surface area inside the cavity from about 30 cm 2  to about 100 cm 2 ; preferably from about 70 cm 2  to about 100 cm 2 . In some embodiments, the body has a length of about 10 cm or less, an inner diameter of about 1.75 cm or more, and has a heatable surface inside the cavity from about 30 cm 2  to about 100 cm 2 ; for example, from about 70 cm 2  to about 100 cm 2 . In some embodiments, the body has a length in a range from about 3.5 cm to about 7 cm, has an inner diameter in a range from about 1.5 cm to about 4 cm, and has a heatable surface inside the cavity from about 30 cm 2  to about 100 cm 2 ; preferably from about 70 cm 2  to about 100 cm 2 . In some embodiments, the body is cylindrical or frustroconical. If the body has a frustroconical shape, the body preferably has a length from about 3 cm to about 5 cm and has a maximum inner diameter from about 2.5 cm to about 3 cm, such as about 2.7 cm, and has a minimum inner diameter from about 1.5 cm to about 2.5 cm, such as from about 1.8 cm to about 2.3 cm. 
     The body may define a cavity having a maximum inner width of 4 cm. For example, the body may define a cavity having a maximum inner width of about 2 cm to about 4 cm. Preferably, the body defines a cavity having a maximum inner width from about 2.5 cm to about 3.5 cm, such as from about 2.7 cm to about 3.3 cm or from about 2.9 cm to about 3.1 cm. 
     The body may define a cavity having a height of height of 3 cm or greater. For example, the body may define a cavity having a height from about 3 cm to about 5 cm. Preferably, the body defines a cavity having a height from about 3.5 cm to about 4.5 cm, such as from about 3.6 cm to about 3.9 cm or about 3.8 cm to about 3.9 cm. Preferably, the height of the cavity is greater than the maximum inner width of the cavity. 
     Preferably, the body defines a cavity having a maximum inner width of 4 cm and a height of 3 cm or greater. Preferably, the height of the cavity is greater than the maximum inner width of the cavity. For example, the body may define a cavity having a maximum inner width of about 2 cm to about 4 cm and a height from about 3 cm to about 5 cm. Preferably, the body defines a cavity having a maximum inner width from about 2.5 cm to about 3.5 cm and height from about 3.5 cm to about 4.5 cm. More preferably, the body defines a cavity having a maximum inner width from about 2.7 cm to about 3.3 cm and a height from about 3.7 cm to about 3.9 cm. Even more preferably, the body defines a cavity having a maximum inner width from about 2.9 cm to about 3.1 cm and a height from about 3.8 cm to about 3.9 cm. 
     Preferably, the body defines a cavity having a maximum inner width of 4 cm, and the cartridge has a ratio of heatable surface area to a volume of the cavity in a range from about 1 cm −1  to about 2 cm −1 . More preferably, the body defines a cavity having a maximum inner width from about 2 cm to about 4 cm, and the cartridge has a ratio of heatable surface area to a volume of the cavity in a range from about 1 cm −1  to about 2 cm −1 . Even more preferably, the body defines a cavity having a maximum inner width from about 2.5 cm to about 3.5 cm, and the cartridge has a ratio of heatable surface area to a volume of the cavity in a range from about 1.2 cm −1  to about 1.6 cm −1 . Still more preferably, the body defines a cavity having a maximum inner width from about 2.7 cm to about 3.3 cm, and the cartridge has a ratio of heatable surface area to a volume of the cavity in a range from about 1.2 cm −1  to about 1.6 cm −1 . More preferably, the body defines a cavity having a maximum inner width from about 2.9 cm to about 3.1 cm, and the cartridge has a ratio of heatable surface area to a volume of the cavity in a range from about 1.3 cm −1  to about 1.5 cm −1 . 
     Preferably, the body defines a cavity having a height of 3 cm or greater, and the cartridge has a ratio of heatable surface area to a volume of the cavity in a range from about 1 cm −1  to about 2 cm −1 . More preferably, the body defines a cavity having a height from about 3 cm to a about 5 cm, and the cartridge has a ratio of heatable surface area to a volume of the cavity in a range from about 1 cm −1  to about 2 cm −1 . Even more preferably, the body defines a cavity having a height about 3.5 cm to about 4.5 cm, and the cartridge has a ratio of heatable surface area to a volume of the cavity in a range from about 1.2 cm −1  to about 1.6 cm −1 . Still more preferably, the body defines a cavity having a height from about 3.7 cm to about 3.9 cm, and the cartridge has a ratio of heatable surface area to a volume of the cavity in a range from about 1.2 cm −1  to about 1.6 cm −1 . More preferably, the body defines a cavity having a height from about 3.8 cm to about 3.9 cm, and the cartridge has a ratio of heatable surface area to a volume of the cavity in a range from about 1.3 cm −1  to about 1.5 cm −1 . 
     Preferably, the body defines a cavity having a maximum inner width of 4 cm and a height of 3 cm or greater, and the cartridge has a ratio of heatable surface area to a volume of the cavity in a range from about 1 cm −1  to about 2 cm −1 . More preferably, the body defines a cavity having a maximum inner width from about 2 cm to about 4 cm and a height from about 3 cm to a about 5 cm, and the cartridge has a ratio of heatable surface area to a volume of the cavity in a range from about 1 cm −1  to about 2 cm −1 . Even more preferably, the body defines a cavity having a maximum inner width from about 2.5 cm to about 3.5 cm and a height about 3.5 cm to about 4.5 cm, and the cartridge has a ratio of heatable surface area to a volume of the cavity in a range from about 1.2 cm −1  to about 1.6 cm −1 . Still more preferably, the body defines a cavity having a maximum inner width from about 2.7 cm to about 3.3 cm, a height from about 3.7 cm to about 3.9 cm and the cartridge has a ratio of heatable surface area to a volume of the cavity in a range from about 1.2 cm −1  to about 1.6 cm −1 . More preferably, the body defines a cavity having a maximum inner width from about 2.9 cm to about 3.1 cm and a height from about 3.8 cm to about 3.9 cm, and the cartridge has a ratio of heatable surface area to a volume of the cavity in a range from about 1.3 cm −1  to about 1.5 cm −1 . 
     The cavity may have any suitable volume. Preferably, the cavity has a volume from about 10 cm 3  to about 50 cm 3 ; such as from about 15 cm 3  to about 40 cm 3  or from about 15 cm 3  to about 30 cm 3 . In some preferred embodiments, the cavity has a volume from about 15 cm 3  to about 25 cm 3  or from about 18 cm 3  to about 22 cm 3 . 
     Preferably, the body has a cylindrical or frustoconical shape, and defines a cylindrical cavity or a frustoconical cavity, respectively. In some such embodiments, the angle at which the sidewall deviates from the longitudinal axis of the cartridge is preferably from about 2° to about 10°, such as about 3° to about 8°. More preferably, the angle at which the sidewall deviates from the longitudinal axis is preferably from about 3° to about 6°, such as about 4° to about 5°. Such frustoconical cartridges with such angles may advantageously provide improved thermal transfer to an aerosol-forming substrate disposed in the cavity, when the cartridge is heated aerosol-forming substrate. Such frustoconical cartridges with such angles may advantageously provide more efficient heating of an aerosol-forming substrate disposed in the cavity, when the cartridge is heated aerosol-forming substrate. Such frustoconical cartridges with such angles may advantageously be more easily manufactured. Such frustoconical cartridges with such angles may advantageously be more easily manufactured using deep drawing techniques. Such frustoconical cartridges with such angles may advantageously be more easily inserted into or removed from a heating chamber of an aerosol-generating device, such as a shisha aerosol-generating device. 
     In some embodiments, the cartridge comprises a flange at the top. The flange may be arranged to rest on a shoulder of a receptacle of a shisha device so that cartridge may be readily removed from the receptacle after use by grasping the flange. The flange may also help to prevent over-insertion of the cartridge into the receptacle. 
     The aerosol-forming substrate may occupy any suitable volume of the cavity. The volume of the aerosol-forming substrate in the cartridge may be varied by altering the mass of the aerosol-forming substrate placed in the cartridge. The volume of the aerosol-forming substrate in the cartridge may be varied by altering the composition of the substrate placed in the cartridge. The volume of the aerosol-forming substrate in the cartridge may be varied by altering the shape or format of the aerosol-forming substrate placed in the cartridge. Preferably, the ratio of the heatable surface area to the volume of aerosol-forming substrate in the cavity is in a range from about 1 cm −1  to about 4 cm −1 , such as from about 1.2 cm −1  to about 3 cm −1 , from about 1 cm −1  to about 2 cm −1 , from about 1.2 cm −1  to about 1.6 cm −1 , or from about 1.3 cm −1  to about 1.5 cm −1 . In some embodiments, the volume of substrate in the cavity is from about 10 cm 3  to about 50 cm 3 ; preferably from about 20 cm 3  to about 40 cm 3 , such as from about 20 cm 3  to about 25 cm 3 . 
     Any suitable aerosol-forming substrate may be provided in the cavity defined by the body of the cartridge. The aerosol-forming substrate is preferably a substrate capable of releasing volatile compounds that may form an aerosol. The volatile compounds may be released by heating the aerosol-forming substrate. The aerosol-forming substrate may be solid or liquid or comprise both solid and liquid components. Preferably, the aerosol-forming substrate comprises a solid. 
     The aerosol-forming substrate may comprise nicotine. The nicotine containing aerosol-forming substrate may comprise a nicotine salt matrix. The aerosol-forming substrate may comprise plant-based material. The aerosol-forming substrate preferably comprises tobacco, and preferably the tobacco containing material contains volatile tobacco flavor compounds, which are released from the aerosol-forming substrate upon heating. The aerosol-forming substrate may comprise homogenized tobacco material. Homogenized tobacco material may be formed by agglomerating particulate tobacco. The aerosol-forming substrate may alternatively or additionally comprise a non-tobacco-containing material. The aerosol-generating substrate may comprise homogenized plant-based material. 
     The aerosol-forming substrate may comprise, for example, one or more of: powder, granules, pellets, shreds, spaghettis, strips or sheets containing one or more of: herb leaf, tobacco leaf, fragments of tobacco ribs, reconstituted tobacco, homogenized tobacco, extruded tobacco and expanded tobacco. 
     The aerosol-forming substrate may comprise at least one aerosol-former. The aerosol-former may be any suitable known compound or mixture of compounds that, in use, facilitates formation of a dense and stable aerosol and that is substantially resistant to thermal degradation at the operating temperature of the shisha device. Suitable aerosol-formers are well known in the art and include, but are not limited to: polyhydric alcohols, such as triethylene glycol, 1,3-butanediol and glycerine; esters of polyhydric alcohols, such as glycerol mono-, di- or triacetate; and aliphatic esters of mono-, di- or polycarboxylic acids, such as dimethyl dodecanedioate and dimethyl tetradecanedioate. Particularly preferred aerosol formers are polyhydric alcohols or mixtures thereof, such as triethylene glycol, 1,3-butanediol and, most preferred, glycerine. The aerosol-forming substrate may comprise other additives and ingredients, such as flavorants. The aerosol-forming substrate preferably comprises nicotine and at least one aerosol-former. In a particularly preferred embodiment, the aerosol-former is glycerine. 
     The aerosol-forming substrate may comprise any suitable amount of an aerosol-former. For example, the aerosol-former content may be equal to or greater than 5% on a dry weight basis, and preferably between greater than 30% by weight on a dry weight basis. The aerosol-former content may be less than about 95% on a dry weight basis. Preferably, the aerosol-former content is up to about 55%. 
     The aerosol-forming substrate may be provided on or embedded in a thermally stable carrier. The carrier may comprise a thin layer on which the substrate deposited on a first major surface, on second major outer surface, or on both the first and second major surfaces. The carrier may be formed of, for example, a paper, or paper like material, a non-woven carbon fiber mat, a low mass open mesh metallic screen, or a perforated metallic foil or any other thermally stable polymer matrix. Alternatively, the carrier may take the form of powder, granules, pellets, shreds, spaghettis, strips or sheets. The carrier may be a non-woven fabric or fiber bundle into which tobacco components have been incorporated. The non-woven fabric or fiber bundle may comprise, for example, carbon fibers, natural cellulose fibers, or cellulose derivative fibers. 
     In some examples, the aerosol-forming substrate comprises one or more sugars in any suitable amount. Preferably, the aerosol-forming substrate comprises invert sugar, which is a mixture of glucose and fructose obtained by splitting sucrose. Preferably, the aerosol-forming substrate comprises from about 1% to about 40% sugar, such as invert sugar, by weight. In some example, one or more sugars may be mixed with a suitable carrier such as cornstarch or maltodextrin. 
     In some examples, the aerosol-forming substrate comprises one or more sensory-enhancing agent. Suitable sensory-enhancing agents include flavorants and sensation agents, such as cooling agents. Suitable flavorants include natural or synthetic menthol, peppermint, spearmint, coffee, tea, spices (such as cinnamon, clove and/or ginger), cocoa, vanilla, fruit flavors, chocolate,  eucalyptus , geranium, eugenol, agave, juniper, anethole, linalool, and any combination thereof. 
     In some examples, the aerosol-forming substrate is in the form of a suspension. For example, the aerosol generating substrate may comprise molasses. As used herein, “molasses” means an aerosol-forming substrate composition comprising about 20% or more sugar. For example, the molasses may comprise at least about 25% by weight sugar, such as at least about 35% by weight sugar. Typically, the molasses will contain less than about 60% by weight sugar, such as less than about 50% by weight sugar. 
     Aerosol-forming substrates for use with traditional shisha devices are in the form of a molasses, which may be inhomogeneous and may contain lumps and cavities. Such cavities prevent direct thermal contact between the substrate and a heated surface making thermal conduction particularly inefficient. As a consequence, electronic heated shisha devices tend to depart from traditional molasses by using, for example, e-liquids or dry stones. Due to the ratio of heated surface area to volume of the cavity of the cartridge described in the present application, more traditional aerosol-forming substrate molasses may be used to preserve the typical ritual and shisha experience while using electric heating. 
     Any suitable amount of the molasses may be disposed in the cavity. In some preferred embodiments, about 3 g to about 25 g of the molasses is disposed in the cavity. Preferably, from about 7 g to about 13 g of the molasses is disposed in the cavity. More preferably, about 10 g of the molasses is disposed in the cavity. 
     In some embodiments, the body has a length of about 15 cm or less, has an inner diameter of about 1 cm or more, and has a heatable surface area in the cavity from about 30 cm 2  to about 100 cm 2 , such as from about 70 cm 2  to about 100 cm 2 , and the volume of the cavity is from about 10 cm 3  to about 50 cm 3 ; for example, from about 25 cm 3  to about 40 cm 3 . In some embodiments, the body has a length of about 10 cm or less, an inner diameter of about 1.75 cm or more, and has a heatable surface area in the cavity from about 30 cm 2  to about 100 cm 2 , such as from about 70 cm 2  to about 100 cm 2 , and the volume of the cavity is from about 10 cm 3  to about 50 cm 3 ; such as from about 25 cm 3  to about 40 cm 3 . In some embodiments, the body has a length in a range from about 3.5 cm to about 7 cm, has an inner diameter in a range from about 1.5 cm to about 4 cm, and has a heatable surface area in the cavity from about 30 cm 2  to about 100 cm 2 , such as from about 70 cm 2  to about 100 cm 2 , and the volume of the cavity is from about 10 cm 3  to about 50 cm 3 ; preferably from about 25 cm 3  to about 40 cm 3 . Preferably, the body is cylindrical or frustroconical. 
     In some embodiments, the body has a length of about 15 cm or less, has an inner diameter of about 1 cm or more, and has a heatable surface area in the cavity from about 30 cm 2  to about 100 cm 2 , such as from about 70 cm 2  to about 100 cm 2 , and the aerosol-forming substrate in the cavity is a molasses having a mass of about 3 g to about 25 g, such as from about 1 g to about 13 g. In some embodiments, the body has a length of about 10 cm or less, an inner diameter of about 1.75 cm or more, and has a heatable surface area in the cavity from about 30 cm 2  to about 100 cm 2 , such as from about 70 cm 2  to about 100 cm 2 , and the aerosol-forming substrate in the cavity is a molasses having a mass of about 3 g to about 25 g, such as from about 1 g to about 13 g. In some embodiments, the body has a length in a range from about 3.5 cm to about 7 cm, has an inner diameter in a range from about 1.5 cm to about 4 cm, and has a heatable surface area in the cavity from about 30 cm 2  to about 100 cm 2 , such as from about 70 cm 2  to about 100 cm 2 , and the aerosol-forming substrate in the cavity is a molasses having a mass of about 3 g to about 25 g, such as from about 7 g to about 13 g. Preferably, the body is cylindrical or frustroconical. 
     In some embodiments, the body has a length of about 15 cm or less, has an inner diameter of about 1 cm or more, and has a heatable surface area in the cavity from about 30 cm 2  to about 100 cm 2 , such as from about 70 cm 2  to about 100 cm 2 , and the volume of the cavity is from about 10 cm 3  to about 50 cm 3 , such as from about 25 cm 3  to about 40 cm 3 , and the aerosol-forming substrate in the cavity is a molasses having a mass of about 3 g to about 25 g, such as from about 7 g to about 13 g. In some embodiments, the body has a length of about 10 cm or less, an inner diameter of about 1.75 cm or more, and has a heatable surface area in the cavity from about 30 cm 2  to about 100 cm 2 , such as from about 70 cm 2  to about 100 cm 2 , and the volume of the cavity is from about 10 cm 3  to about 50 cm 3 , such as from about 25 cm 3  to about 40 cm 3 , and the aerosol-forming substrate in the cavity is a molasses having a mass of about 3 g to about 25 g, such as from about 7 g to about 13 g. In some embodiments, the body has a length in a range from about 3.5 cm to about 6.7 cm, has an inner diameter in a range from about 1.5 cm to about 4 cm, and has a heatable surface area in the cavity from about 30 cm 2  to about 100 cm 2 , such as from about 70 cm 2  to about 100 cm 2 , and the volume of the cavity is from about 10 cm 3  to about 50 cm 3 , such as from about 25 cm 3  to about 40 cm 3 , and the aerosol-forming substrate in the cavity is a molasses having a mass of about 3 g to about 25 g, such as from about 7 g to about 13 g. Preferably, the body is cylindrical or frustroconical. 
     Preferably, the cartridge comprises an amount of aerosol-forming substrate that will provide a sufficient amount of aerosol for a shisha experience lasting from about 10 minutes to about 60 minutes; preferably from about 20 minutes to about 50 minutes; and more preferably from about 30 minutes to about 40 minutes. 
     In some embodiments, the cartridge comprises one or more inlets and one or more outlets to allow air to flow through the aerosol-forming substrate when the cartridge is used with a shisha device. In some embodiments, the top of the cartridge may define one or more apertures to form the one or more inlets of the cartridge. In some embodiments, the bottom of the cartridge may define one or more apertures to form the one or more outlets of the cartridge. Preferably, the one or more inlets and outlets are sized and shaped to provide a suitable resistance to draw (RTD) through the cartridge. In some examples, the RTD through the cartridge, from the inlet or inlets to the outlet or outlets, may be from about 10 mm H 2 O to about 50 mm H 2 O, preferably from about 20 mm H 2 O to about 40 mm H 2 O. The RTD of a specimen refers to the static pressure difference between the two ends of the specimen when it is traversed by an air flow under steady conditions in which the volumetric flow is 17.5 millilitres per second at the output end. The RTD of a specimen can be measured using the method set out in ISO Standard 6565:2002 with any ventilation blocked. 
     The cartridge may include a first removable seal covering the one or more inlets and a second removable seal covering the one or more outlets. The first and second seals are preferably sufficient to prevent air flow through the inlets and outlets to prevent leakage of the contents of the cartridge and to extend shelf life. The seal may comprise a peelable label of sticker, foil, or the like. The label, sticker, or foil may be affixed to the cartridge in any suitable manner, such as with an adhesive, crimping, welding, or otherwise being joined to the container. The seal may comprise a tab that may be grasped to peel or remove the label, sticker, or foil from the cartridge. 
     In some embodiments, the cartridge does not comprise one or more inlets and one or more outlets. 
     A shisha cartridge according to the present invention may be used with any suitable shisha device. Preferably, the shisha device is configured to sufficiently heat the aerosol-generating substrate in the cartridge to cause formation of aerosol from the aerosol-forming substrate but not to combust the aerosol-forming substrate. For example, the shisha device may be configured to heat the aerosol-forming substrate to a temperature in a range from about 150° C. to about 300° C.; more preferably from about 180° C. to about 250° C. or from about 200° C. to about 230° C. 
     The shisha device is preferably configured to heat the cartridge. The shisha device may comprise a receptacle for receiving the cartridge. The shisha device comprises a heating element configured to contact or to be in proximity to the body of the cartridge when the cartridge is received in the receptacle. The heating element may form at least part of the receptacle. The heating element may form at least a portion of the surface of the receptacle. The shisha cartridge may be configured to transfer from the heating element to the aerosol-forming substrate in the cavity by conduction. In some embodiments, the heating element comprises an electric heating element. In some embodiments, the heating element comprises a resistive heating component. For example, the heating element may comprise one or more resistive wires or other resistive elements. The resistive wires may be in contact with a thermally conductive material to distribute heat produced over a broader area. Examples of suitable conductive materials include aluminium, copper, zinc, nickel, silver, and combinations thereof. For purposes of this disclosure, if resistive wires are in contact with a thermally conductive material, both the resistive wires and the thermally conductive material are part of the heating element. The heating element may form at least a portion of the surface of the receptacle. 
     The shisha device may comprise control electronics operably coupled to the heating element to control heating of the heating element and thus control the temperature at which the aerosol-forming substrate in the cartridge is heated. The control electronics may be provided in any suitable form and may, for example, include a controller or a memory and a controller. The controller may include one or more of an Application Specific Integrated Circuit (ASIC) state machine, a digital signal processor, a gate array, a microprocessor, or equivalent discrete or integrated logic circuitry. Control electronics may include memory that contains instructions that cause one or more components of the circuitry to carry out a function or aspect of the control electronics. Functions attributable to control electronics in this disclosure may be embodied as one or more of software, firmware, and hardware. 
     The electronic circuitry may comprise a microprocessor, which may be a programmable microprocessor. The electronic circuitry may be configured to regulate a supply of power. The power may be supplied to the heater element in the form of pulses of electrical current. 
     In some examples, the control electronics may be configured to monitor the electrical resistance of the heating element and to control the supply of power to the heating element depending on the electrical resistance of the heating element. In this manner, the control electronics may regulate the temperature of the resistive element. 
     The shisha device may comprise a temperature sensor, such as a thermocouple, operably coupled to the control electronics to control the temperature of the heating element. The temperature sensor may be positioned in any suitable location. For example, the temperature sensor may be configured to insert into the cartridge when received within the receptacle to monitor the temperature of the aerosol-forming substrate being heated. In addition or alternatively, the temperature sensor may be in contact with the heating element. In addition or alternatively, the temperature sensor may be positioned to detect temperature at an aerosol outlet of the shisha device or a portion thereof. The sensor may transmit signals regarding the sensed temperature to the control electronics, which may adjust heating of the heating elements to achieve a suitable temperature at the sensor. 
     The control electronics may be operably coupled to a power supply. The shisha device may comprise any suitable power supply. For example, a power supply of a shisha device may be a battery or set of batteries. The batteries of the power supply may be rechargeable, removable and replaceable, or rechargeable and removable and replaceable. Any suitable battery may be used. For example, heavy duty type or standard batteries existing in the market, such as used for industrial heavy duty electrical power-tools. Alternatively, the power supply may be any type of electric power supply including a super or hyper-capacitor. Alternatively, the assembly can be connected to an external electrical power source, and electrically and electronically designed for such purpose. Regardless of the type of power supply employed, the power supply preferably provides sufficient energy for the normal functioning of the assembly for at least one shisha session until aerosol is depleted from the aerosol-forming substrate in the cartridge before being recharged or needing to connect to an external electrical power source. Preferably, the power supply provides sufficient energy for the normal functioning of the assembly for at least about 70 minutes of continuous operation of the device, before being recharged or needing to connect to an external electrical power source. 
     In one example, a shisha device includes an aerosol-generating element that comprises a cartridge receptacle, a heating element, an aerosol outlet, and a fresh air inlet. The cartridge receptacle is configured to receive a cartridge containing the aerosol-forming substrate. The cartridge may be as above described. The heating element may define at least part of a surface of the receptacle. 
     The shisha device comprises a fresh air inlet channel in fluid connection with the receptacle. In use, fresh air flows through the fresh air inlet channel to the receptacle and through the cartridge disposed in the receptacle. Fresh air flowing through the cartridge becomes entrained with aerosol generated from the aerosol-forming substrate in the cartridge. The fresh air entrained with aerosol flows to the aerosol. 
     The fresh air inlet channel may comprise one or more apertures through the cartridge receptacle such that fresh air from outside the shisha device may flow through the channel and into the cartridge receptacle through the one or more apertures. If a channel comprises more than one aperture, the channel may comprise a manifold to direct air flowing through the channel to each aperture. Preferably, the shisha device comprises two or more fresh air inlet channels. 
     As described above, the cartridge comprises one or more inlets formed in the housing to allow air flow through the chambers of the cartridge when in use. If the receptacle comprises one or more inlet apertures, at least some of the inlets in the cartridge may align with the apertures in the top of the receptacle. The cartridge may comprise an alignment feature configured to mate with a complementary alignment feature of the receptacle to align the inlets of the cartridge with the apertures of the receptacle when the cartridge is inserted into the receptacle. 
     Air that enters the cartridge flows across the aerosol-forming substrate, entrains aerosol, and exits the cartridge and receptacle via an aerosol outlet. From the aerosol outlet, the air carrying the aerosol enters a vessel of the shisha device. 
     The shisha device may comprise any suitable vessel defining an interior volume configured to contain a liquid and defining an outlet in head-space above a liquid fill level. The vessel may comprise an optically transparent or opaque housing to allow a consumer to observe contents contained in the vessel. The vessel may comprise a liquid fill demarcation, such as a liquid fill line. The vessel housing may be formed of any suitable material. For example, the vessel housing may comprise glass or suitable rigid plastic material. Preferably, the vessel is removable from a portion of the shisha assembly comprising the aerosol-generation element to allow a consumer to fill, empty or clean the vessel. 
     The vessel may be filled to a liquid fill level by a consumer. The liquid preferably comprises water, which may optionally be infused with one or more colorants, flavorants, or colorant and flavorants. For example, the water may be infused with one or both of botanical or herbal infusions. 
     Aerosol entrained in air exiting the aerosol outlet of the receptacle may travel through a conduit positioned in the vessel. The conduit may be coupled to the aerosol outlet of the aerosol generating element of the shisha assembly and may have an opening below the liquid fill level of the vessel, such that aerosol flowing through the vessel flows through the opening of the conduit, then through the liquid, into headspace of the vessel and exits through a headspace outlet, for delivery to a consumer. 
     The headspace outlet may be coupled to a hose comprising a mouthpiece for delivering the aerosol to a consumer. The mouthpiece may comprise a switch activatable by a user or a puff sensor operably coupled to the control electronics of the shisha device. Preferably, the switch or puff sensor is wirelessly coupled to the control electronics. Activation of a switch or puff sensor may cause the control electronics to activate the heating element, rather than constantly supplying energy to the heating element. Accordingly, the use of a switch or puff sensor may serve to save energy relative to devices not employing such elements to provide on-demand heating rather than constant heating. 
     For purposes of example, one method for using a shisha device as described herein is provided below in chronological order. The vessel may be detached from other components of the shisha device and filled with water. One or more of natural fruit juices, botanicals, and herbal infusions may be added to the water for flavoring. The amount of liquid added should cover a portion of the conduit but should not exceed a fill level mark that may optionally exist on the vessel. The vessel is then reassembled to the shisha device. A portion of the aerosol generating element may be removed or opened to allow the cartridge to be inserted into the receptacle. The aerosol generating element is then reassembled or closed. The device may then be turned on. Turning on the device may initiate a heating profile of a heating element, to heat the aerosol-forming substrate to a temperature at or above a vaporisation temperature of the aerosol-forming substrate, but below a combustion temperature of the aerosol-forming substrate. The user may puff on the mouth piece as desired. The user may continue using the device until no more aerosol is visible or being delivered. In some embodiments, the device will automatically shut off when the cartridge is depleted of usable aerosol-generating substrate. In some embodiments, the consumer may refill the device with a fresh cartridge after, for example, receiving the cue from the device that the aerosol-forming substrate in the cartridge is depleted or nearly depleted. If refilled with a fresh cartridge, the device may continue to be used. Preferably, the shisha device may be turned off at any time by a consumer by, for example, switching off the device. 
     The shisha device may have any suitable air management. In one example, puffing action from the user will create a suction effect causing a low pressure inside the device which will cause external air to flow through air inlet of the device, into the fresh air inlet channel, and into the receptacle. The air may then flow through the cartridge in the receptacle to carry aerosol produced from the aerosol-forming substrate. The air with entrained aerosol then exits the aerosol outlet of the receptacle, flows through the conduit to the liquid inside the vessel. The aerosol will then bubble out of the liquid and into head space in the vessel above the level of the liquid, out the headspace outlet, and through the hose and mouthpiece for delivery to the consumer. The flow of external air and the flow of the aerosol inside the shisha device may be driven by the action of puffing from the user. 
    
    
     
       Reference will now be made to the drawings, which depict one or more aspects described in this disclosure. However, it will be understood that other aspects not depicted in the drawings fall within the scope and spirit of this disclosure. Like numbers used in the figures refer to like components. However, it will be understood that the use of a number to refer to a component in a given figure is not intended to limit the component in another figure labeled with the same number. In addition, the use of different numbers to refer to components in different figures is not intended to indicate that the different numbered components cannot be the same or similar to other numbered components. The figures are presented for purposes of illustration and not limitation. Schematic drawings presented in the figures are not necessarily to scale. 
         FIG. 1  is a schematic sectional view of a cartridge without aerosol-forming substrate. 
         FIG. 2  is a schematic sectional view of a cartridge with aerosol-forming substrate. 
         FIG. 3  is a top-down plan view of a top of a cartridge. 
         FIG. 4  is a bottom-up plan view of a bottom of a cartridge. 
         FIG. 5  is schematic perspective view of a cartridge. 
         FIG. 6  is a schematic top-down plan view of a cartridge with a top removed showing a thermal bridge disposed in a cavity. 
         FIG. 7  is a schematic top-down plan view of a cartridge with a top removed showing a thermal bridge disposed in a cavity. 
         FIGS. 8-9  are schematic drawings of sectional views of cartridges. 
         FIG. 10  is a schematic sectional view of a shisha device. 
         FIG. 11A  is an image of a thermal bridge used in a cartridge. 
         FIG. 11B  is a top-down image of a cartridge with its top removed. The thermal bridge of  FIG. 11A  is disposed in the cavity of the cartridge. 
         FIG. 11C  is a side image of a cartridge having a sidewall slit for accommodating a portion of the thermal bridge, such as the thermal bridge depicted in  FIG. 11A . 
         FIG. 11D  is a side image of the cartridge depicted in  FIG. 11C  in which the thermal bridge of  FIG. 11A  is inserted. 
         FIG. 12  is a top-down image of a cartridge with its top removed, revealing a thermal bridge disposed in the cavity. 
         FIG. 13  is a graph showing the total aerosol mass per puff generated using a variety of cartridge designs. 
         FIG. 14  is a graph of heatable surface area (S H ) obtainable by cartridges having various dimensions, with and without thermal bridges. 
         FIG. 15  is a plot of absolute and relative evaporated molasses for various cartridge designs. 
         FIG. 16  is a plot of total aerosol mass produced for various cartridge designs. 
         FIG. 17  is a plot of absolute and relative evaporated molasses for cartridges containing different amounts of molasses. 
         FIG. 18  is a plot of total aerosol mass produced for cartridges containing different amounts of molasses. 
     
    
    
     Referring to  FIGS. 1-2 , a cartridge  200  has body  210  defining a cavity  218  in which an aerosol-forming substrate  300  may be disposed. The body  210  includes a top  215 , bottom  213 , and a sidewall  212 . The body  210  may be formed from one or more parts. For example, the top  215  or bottom  213  may be removably attached from the sidewall  212  to allow the aerosol-forming substrate  300  to be disposed in the cavity  218 . The cartridge  200  has a length (I) and width (w) referred to herein as the inner diameter. The cartridge  200  has a heatable surface area (S H ) inside the cavity  215 , which is a surface area capable of transferring heat applied to the exterior of the body, for example, by a heating element of a shisha device, to aerosol-forming substrate  300  in the cavity  218 . The cavity  218  has a volume such that the ratio of the ratio of the heatable surface area (S H ) of the body  210  to the volume of the cavity  218  is in range from about 1 cm −1  to about 4 cm −1 . The aerosol-forming substrate  300  occupies a volume within the cavity  218 . Preferably, the ratio of heatable surface area of the body  210  in the cavity  218  (S H ) to the volume of the aerosol-forming substrate  300  in the cavity  218  is in range from about 1 cm −1  to about 4 cm −1 . Such ratios allow for the aerosol-forming substrate  300  to produce desired amount of aerosol mass without prematurely depleting the aerosol-forming substrate  300 . 
     Referring now to  FIGS. 3-4 , the top  215  and bottom  213  of the body may have a plurality of apertures  217 ,  216  to allow air flow through the cartridge, when the cartridge is in use. The apertures  216 ,  217  of the top  215  and bottom  213  may be aligned. The apertures  217 ,  216  may be blocked when the cartridge is stored prior to use. For example, the apertures  216 ,  217  may be blocked by a releasable liner (not shown). 
       FIG. 5  is a schematic perspective view of a cartridge  200 . The sidewall  212  defines a frustroconical shape. The bottom  213  defines a plurality of apertures to allow air flow through the cartridge  200 . The top comprises a flange  219  that extends from the sidewall  212 . The flange  219  may rest on shoulder of a receptacle of a shisha device so that cartridge  200  may be readily removed from the receptacle after use by grasping the flange. 
       FIG. 6  is a schematic top-down view into a cavity  218  of a cartridge  200 . A thermal bridge having two arms  221 ,  223  that span the cavity  218  and contact the sidewall  212  is shown. The arms  221 ,  223  may also contact the bottom  213 . The thermal bridge increases the heatable surface area in the cavity  218  (S H ) relative to a cartridge of the same dimensions that does not include a thermal bridge. 
       FIG. 7  is a schematic top-down view into a cavity  218  of a cartridge  200 . A cylindrical thermal bridge  220  is disposed in the cavity  218 . The thermal bridge  220  contacts the bottom  213  of the cartridge  200 . The thermal bridge  220  increases the heatable surface area in the cavity  218  (S H ) relative to a cartridge of the same dimensions that does not include the thermal bridge. 
       FIGS. 8-9  are schematic sectional views of cartridges  200 . The cartridges  200  have a sidewall  212  a top  215  and a bottom  213  that together define a cavity  218  into which an aerosol generating substrate (not shown) may be disposed. The cartridge  200  in  FIG. 8  includes a generally flat bottom  213  with slightly rounded edges, and the cartridge  200  in  FIG. 9  includes a generally frustoconical bottom  213 . Otherwise, the cartridges  200  in  FIGS. 8-9  are substantially the same. 
     The cartridges  200  have a flange  219  at the top  215 . The flange  219  may rest on a shoulder of a receptacle of a shisha device so that cartridge  200  may be readily removed from the receptacle after use by grasping the flange. The flange may also help to prevent over-insertion of the cartridge  200  into the receptacle. 
     The cavity  218  has a maximum inner width (Wt) and a height (h). In the case of a frustoconical shaped cartridge  200 , the maximum inner width (Wt) may be substantially at the top of the cartridge  200 . The maximum inner width (Wt) in the example illustrated in  FIG. 8  may be about 2.98 cm, and the height (h) may be about 3.63 cm. The bottom of the cavity  218  has a width (Wb). The width of the bottom of the cavity (Wb) may be about 2.43 cm. 
     The bottom  213  of the container  200  in  FIG. 9  is generally frustoconical. As can be seen in  FIG. 9 , width Wb is generally measured at a position where the angle of the sidewall  212  changes plane. In some embodiments, such as the example of  FIG. 9 , the sidewall of the bottom portion  213  deviates from a flat bottom at an angle β. Angle β may be about 18°. The width (Wc) of the smaller bottom portion may be about 0.84 cm. We may be measured at a longitudinal position at which the width of the cavity is at a minimum. In the example of  FIG. 9 , the maximum inner width (Wt) may be about 2.98 cm, the height (h) may be about 3.83 cm, the bottom width (Wb) may be about 2.43 cm and the width of the smaller bottom portion (Wc) may be about 0.84 cm. 
     The body of the cartridges  200  in  FIGS. 8-9  are generally frustoconical. The sidewalls  212  deviate from the longitudinal axis at an angle α. Angle α may be about 4.5°. 
     The cartridge  200  in  FIG. 8  has in internal surface area defined by the sidewalls  212 , the top  215 , and the bottom  213  of about 41.5 cm 2 . The internal surface area of the cavity  218  defined by the sidewalls  212  only is about 29.6 cm 2 . The volume defined by the cavity  218  is about 20.6 cm 3 . The ratio of the internal surface area of the cavity  218  defined by the sidewalls  212  to the volume defined by the cavity  218  is about 1.4 cm −1 . The ratio of the internal surface area of the cavity  218  defined by the sidewalls  212 , the top  215 , and the bottom  213  to the volume defined by the cavity  218  is about 2 cm −1 . 
     The cartridge  200  in  FIG. 9  has in internal surface area defined by the sidewalls  212 , the top  215 , and the bottom  213  of about 42 cm 2 . The internal surface area of the cavity  218  defined by the sidewalls  212  only is about 29.9 cm 2 . The volume defined by the cavity  218  is about 21.4 cm 3 . The ratio of the internal surface area of the cavity  218  defined by the sidewalls  212  to the volume defined by the cavity  218  is about 1.4 cm −1 . The ratio of the internal surface area of the cavity  218  defined by the sidewalls  212 , the top  215 , and the bottom  213  to the volume defined by the cavity  218  is about 2 cm −1 . 
       FIG. 10  is a schematic sectional view of an example of a shisha device  100 . The device  100  includes a vessel  17  defining an interior volume configured to contain liquid  19  and defining a headspace outlet  15  above a fill level for the liquid  19 . The liquid  19  preferably comprises water, which may optionally be infused with one or more colorants, one or more flavorants, or one or more colorants and one or more flavorants. For example, the water may be infused with one or both of botanical infusions or herbal infusions. 
     The device  100  also includes an aerosol-generating element  130 . The aerosol-generating element  130  includes a receptacle  140  configured to receive a cartridge  200  containing an aerosol-generating substrate. The aerosol-generating element  130  also includes a heating element  160  that forms at least one surface of the receptacle  140 . In the depicted embodiment, the heating element  160  defines the top and side surfaces of the receptacle  140 . The aerosol-generating element  130  also includes a fresh air inlet channel  170  that draws fresh air into the device  100 . A portion of the fresh air inlet channel  170  is formed by the heating element  160  to heat the air before the air enters the receptacle  140 . The pre-heated air then enters the cartridge  150  (or substrate that is not a cartridge), which is also heated by heating element  160 , to carry aerosol generated by aerosol generating substrate. The air exits an outlet of the aerosol-generating element  130  and enters a conduit  190 . 
     The conduit  190  carries the air and aerosol into the vessel  17  below the level of the liquid  19 . The air and aerosol may bubble through the liquid  19  and exit the headspace outlet  15  of the vessel  17 . A hose  20  may be attached to the headspace outlet  15  to carry the aerosol to the mouth of a user. A mouthpiece  25  may be attached to, or form a part of, the hose  20 . 
     The air flow path of the device, in use, is depicted by thick arrows in  FIG. 10 . 
     The mouthpiece  25  may include an activation element  27 . The activation element  27  may be a switch, button or the like, or may be a puff sensor or the like. The activation element  27  may be placed at any other suitable location of the device  100 . The activation element  27  may be in wireless communication with the control electronics  30  to place the device  100  in condition for use or to cause control electronics to activate the heating element  160 ; for example, by causing power supply  35  to energize the heating element  140 . 
     The control electronics  30  and power supply  35  may be located in any suitable position of the aerosol generating element  130  other than the bottom portion of the element  130  as depicted in  FIG. 1 . 
       FIGS. 11-18  are discussed below in the Examples.  FIG. 11A  is an image of an embodiment of a thermal bridge used in a cartridge.  FIG. 11B  is a top-down image of an embodiment of a cartridge with its top removed. The thermal bridge of  FIG. 9A  is disposed in the cavity of the cartridge in  FIG. 11B .  FIG. 11C  is a side image of an embodiment of a cartridge having a sidewall slit for accommodating a portion of the thermal bridge, such as the thermal bridge depicted in  FIG. 11A .  FIG. 11D  is a side image of the cartridge depicted in  FIG. 11C  in which the thermal bridge of  FIG. 11A  is inserted.  FIG. 12  is a top-down image of an embodiment of a cartridge with its top removed, revealing a thermal bridge disposed in the cavity.  FIG. 13  is a graph showing the total aerosol mass per puff generated using a variety of cartridge designs.  FIG. 14  is a graph of heatable surface area (S H ) obtainable by cartridges having various dimensions, with and without thermal bridges.  FIG. 15  is a plot of absolute and relative evaporated molasses for various cartridge designs.  FIG. 16  is a plot of total aerosol mass produced for various cartridge designs.  FIG. 17  is a plot of absolute and relative evaporated molasses for cartridges containing different amounts of molasses.  FIG. 18  is a plot of total aerosol mass produced for cartridges containing different amounts of molasses. 
     The specific embodiments described above are intended to illustrate the invention. However, other embodiments may be made without departing from the scope of the invention as defined in the claims, and it is to be understood that the specific embodiments described above are not intended to be limiting. 
     As used herein, the singular forms “a,” “an,” and “the” encompass embodiments having plural referents, unless the content clearly dictates otherwise. 
     As used herein, “or” is generally employed in its sense including “and/or” unless the content clearly dictates otherwise. The term “and/or” means one or all the listed elements or a combination of any two or more of the listed elements. 
     As used herein, “have,” “having,” “include,” “including,” “comprise,” “comprising” or the like are used in their open-ended sense, and generally mean “including, but not limited to”. It will be understood that “consisting essentially of,” “consisting of,” and the like are subsumed in “comprising,” and the like. 
     The words “preferred” and “preferably” refer to embodiments of the invention that may afford certain benefits, under certain circumstances. However, other embodiments may also be preferred, under the same or other circumstances. Furthermore, the recitation of one or more preferred embodiments does not imply that other embodiments are not useful, and is not intended to exclude other embodiments from the scope of the disclosure, including the claims. 
     Any direction referred to herein, such as “top,” “bottom,” “left,” “right,” “upper,” “lower,” and other directions or orientations are described herein for clarity and brevity are not intended to be limiting of an actual device or system. Devices and systems described herein may be used in a number of directions and orientations. 
     EXAMPLES 
     Example 1: Cylindrical Cartridges 
     Presented below are non-limiting examples illustrating the effect of various cartridge designs on production of aerosol from aerosol-forming substrate disposed in shisha cartridges. Each cartridge contained 10 g of commercially available tobacco molasses (Al-Fakher) having a calculated volume of about 31.5 cm 3 . 
     Three cartridge designs were tested. Each cartridge was cylindrical and made from aluminium. The cartridges had a length of 55 mm and an inner diameter of 27 mm. One cartridge contained no thermal bridge and had a heatable surface area in the cavity (S H ) of about 52 cm 2 . Another cartridge included a 0.2 mm thick copper plate (see  FIGS. 11A-D ) in the shape of a T, which spanned the cavity to provide a total S H  of about 69 cm 2 . Another cartridge further included a 0.2 mm thick copper plate having an S shaped cross section that spanned the cavity (see  FIG. 12 ) to provide a S H  of about 90 cm 2 . 
     The cartridges were placed in communication with a conduit. A frustroconical nozzle made of high temperature epoxy resin having an exit orifice of 3 mm was incorporated into the conduit. The exit orifice of the nozzle was about 55 mm from cartridge outlet. The conduit extended below a liquid level in a vessel. Aerosol exiting an outlet in communication with a headspace above the liquid level of the vessel was collected. 
     The cartridges were heated using a wire wound heating element set at a constant temperature of 200 degree Celsius. 
     The generated aerosol was collected using a total of 10 Cambridge pads whose weight was recorded before and after the shisha experience. The total duration of the experience corresponds to 105 puffs. To achieve the desired puffing experience, four Programmable Dual Syringe Pumps (PDSP) manufactured by Pomac BV (Tolbert, Groninen, Netherlands) were used simultaneously to create the following puffing regime:
         Puff volume: 530 mL   Puff duration: 2600 ms   Duration between puffs: 17 s       

     The experimental setup was arranged such that only two of the ten Cambridge pads collect the generated aerosol at a given moment. Every 21 puffs, a check valve ensured that the aerosol was diverted to the correct pair of Cambridge pads. As a consequence, the production of aerosol could be monitored as a function of time. 
     The evaporated mass of the molasses was determined by comparing the weight of the molasses before and after the shisha experience. 
     In addition, the total aerosol mass and evaporated mass was determined for a charcoal operated shisha using similar conditions. 
     The results from the various cartridge designs are shown in  FIG. 13  and Table 1. In  FIG. 13  the TAM per puff is shown after the initial 20 puffs. In  FIG. 13 , the curve labeled ( 1 ) represents the results from the charcoal operated shisha device, the curve labeled ( 2 ) represents the cartridge having the S H  of about 52 cm 2 , the curve labeled ( 3 ) represents the cartridge having the S H  of about 69 cm 2 , and the curve labeled ( 4 ) represents the cartridge having the S H  of about 90 cm 2 . 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 TAM and mass evaporated 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 Cartridge 
                 Cartridge 
                 Cartridge 
               
               
                   
                   
                 (S H  = 52 cm 2 ) 
                 (S H  = 69 cm 2 ) 
                 (S H  = 90 cm 2 ) 
               
               
                 Puff 
                 Charcoal 
                 (mg/puff) 
                 (mg/puff) 
                 (mg/puff) 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 20 
                 12.7 
                 8.7 
                 9.5 
                 12.0 
               
               
                 40 
                 17.8 
                 12.7 
                 14.5 
                 17.0 
               
               
                 60 
                 18.3 
                 15.9 
                 18.0 
                 19.7 
               
               
                 80 
                 16.6 
                 16.9 
                 18.9 
                 20.3 
               
               
                 106 
                 14.6 
                 17.3 
                 19.2 
                 19.2 
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 Total 
                 1696 
                 mg 
                 1370 
                 mg 
                 1684 
                 mg 
                 1853 
                 mg 
               
               
                 Evapo- 
                 3.5 
                 g 
                 2.8 
                 g 
                 3.41 
                 g 
                 3.97 
                 g 
               
               
                 rated 
               
               
                   
               
            
           
         
       
     
     The cartridges tested had a ratio of S H  to volume of aerosol-forming substrate (tobacco molasses) of between 1.5 cm −1  (for the S H =52 cm 2  cartridge) and 3 cm −1  (for the S H =90 cm 2 ). 
     The charcoal operated shisha used for these experiments consumed 3.5 g having a S H  of 25 cm 2 . Since the thermal transfer through convection is much smaller in the electric shisha, only 2.8 g are consumed for S H =52 cm 2 . As a consequence, the total TAM collected for the electrically heated shisha is only ˜80% of the charcoal operated shisha for this cartridge (1700 mg vs. 1370 mg). Notably, the aerosol mass production was substantially less during the first 21 puffs where a TAM of 8.7 mg/puff was collected for the S H =52 cm 2  cartridge relative to the 12.7 mg/puff obtained with the charcoal operated shisha. However, increasing S H  to 90 cm 2  brought the results obtained with the electric shisha to values similar to the charcoal operated shisha. In this case, the consumption of molasses increased to 3.9 g and the total TAM collected to 1850 mg, and the TAM collected during the first puffs increases to 12.0 mg/puff. 
     To illustrate design considerations to achieve a desired ratio of S H  to volume of aerosol-forming substrate, reference is made to  FIG. 14 . In  FIG. 14 , the bottom trace indicates the S H  calculated for a cylinder with a volume of 31.5 cm 3  of different diameters. The corresponding length is shown on the upper x-axis. The calculated results show that cartridges with a length of almost 18 cm are needed to achieve a S H  of 90 cm 2  if not thermal bridge is employed. However, such lengths are not practical for most shisha devices. 
     The trace labelled D/3 indicates the S H  calculated for a cylinder having the same dimensions as the bottom trace, but with a cylindrical thermal bridge having a diameter equivalent to a third of the cartridge&#39;s diameter. The trace labelled D/2 indicates the S H  calculated for a cylinder having the same dimensions as the bottom trace, but with a cylindrical thermal bridge having a diameter equivalent to half the cartridges diameter. As shown, the thermal bridges quickly increase the S H  to provide a cartridge having more desirable dimensions. For example, the cartridges may have a length of less than 10 cm and have a S H  of 90 cm 2 . 
     Example 2: Frustroconical Cartridges 
     The effect of cartridge shape on various performance aspects were tested. The performance of cartridges having various frustroconical designs were compared to a cylindrical cartridge. 
     The cartridges were cylindrical and made from aluminium. The cylindrical cartridge had a length of 41.25 mm and an inner diameter of 27 mm (C 27). The frustroconical cartridges each had a length of 41.25 mm and an upper inner diameter of 27 mm. The lower inner diameters of the frustroconical cartridges were 22 mm (LD 22), 18 mm (LD 18) and 14 mm (LD 14). The tops and bottoms of each cartridge contained 19 holes, each hole having a 2 mm diameter. 
     Substrate temperature and total aerosol mass produced from each cartridge was tested as indicated in Example 1 above. 
     In one experiment, each cartridge contained 10 g of commercially available tobacco molasses (Al-Fakher), and the temperature of the substrate was monitored as the cartridge was heated, and the time for the substrate to reach 80° C. was determined. The results are presented below in Table 2. 
     
       
         
           
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                 Amount of time for substrate to reach 80° C. 
               
            
           
           
               
               
               
            
               
                   
                 Cartridge 
                 Time (min) 
               
               
                   
                   
               
            
           
           
               
               
               
            
               
                   
                 C 27 
                 4 
               
               
                   
                 LD 22 
                 4.5 
               
               
                   
                 LD 18 
                 5 
               
               
                   
                 LD 14 
                 5.5 
               
               
                   
                   
               
            
           
         
       
     
     The time to reach 80° C. may be directly related to time to first puff. Accordingly, a cylindrical cartridge (C 27) may allow for more rapid initial heating and allow for the first puff to be taken more quickly. However, the longer times associated with the frustroconical cartridges (LD 22, LD 18, and LD 14) may more closely mimic time to first puff associated with conventional charcoal-based shisha devices and thus may maintain certain ritual aspects of such conventional devices. 
     In another experiment, C 27, LD 22, and LD 18 cartridges containing 10 g of molasses were heated and total aerosol mass and mass of evaporated molasses were measured. 
     Relative to the C 27 cartridge, the LD 22 cartridge was heated for an additional 30 seconds prior to testing and the LD 18 cartridge was heated for an additional 60 seconds based on the results presented in Table 2 above. 
     The mass of evaporated molasses is shown in  FIG. 15 , and the total aerosol mass produced is shown in  FIG. 16 . As shown in  FIG. 16 , the most total aerosol mass was observed with the LD 22 cartridge. As indicted in  FIG. 15 , the amount of evaporated molasses increased with decreasing lower diameters of the cartridges. 
     In another experiment, the total aerosol mass and evaporated molasses was measured for a C 27 cartridge containing 10 g of molasses and for LD 22 cartridges containing 10 g, 8 g, and 6 g of molasses. Relative to the C 27 cartridge, the LD 22 cartridges were heated for an additional 30 seconds prior to testing based on the results presented in Table 2 above. 
     The mass of evaporated molasses is shown in  FIG. 17 , and the total aerosol mass produced is shown in  FIG. 18 . As shown in  FIG. 18 , the total aerosol mass was similar between LD 22 cartridges containing 10 g and 8 g of molasses, suggesting that less molasses may be employed. In addition, the LD 22 cartridges containing 6 g of molasses exhibited increased total aerosol mass for the first sixty puffs relative to the C 27 cartridge containing 10 g of molasses, suggesting that shape of cartridge may have a substantial impact on total aerosol production and amount of molasses that may be employed. 
     Thus, cartridges for shisha devices are described. Various modifications and variations of the invention will be apparent to those skilled in the art without departing from the scope and spirit of the invention. Although the invention has been described in connection with specific preferred embodiments, it should be understood that the invention as claimed should not be unduly limited to such specific embodiments. Indeed, various modifications of the described modes for carrying out the invention which are apparent to those skilled in the mechanical arts, chemical arts, and aerosol generating article manufacturing or related fields are intended to be within the scope of the following claims.