对于大多数应用场景，在不带挡板的容器中，液位高度(h)与容器内径(d)之比为1.5:1是理想的；建议h:d比值在1:1到2:1之间。参阅图 2。

超出此范围可能会出现不同的工况。如果比值小于1，且搅拌桨尺寸相对于容器内径选择得当，通常能获得良好的混合效果，但这种配置会抑制涡流的形成。如果比值大于2，对于底部安装的磁力耦合搅拌器而言，流体可能无法获得足够的动量以到达液面，从而可能在顶部靠近器壁处形成浓度不均匀的区域。在使用无轴搅拌器设计时，应避免出现这种情况。图2详细展示了不同比值对混合流模式的影响。在处理水状物料时，图中所示的死区（流动受限的区域）通常会消失，且流态多为湍流。随着粘度增加（通常超过1,000 cP，具体取决于流体的流变特性），这些死区便开始出现；当粘度进一步升高且流态转变为层流时，死区现象会变得更加明显。搅拌器在底部封头上的安装位置也会影响最终的混合效果。参阅图3。

将搅拌器安装在半径的二分之一处（即半径中点）通常能获得最佳的混合性能。然而，选择安装位置时也可能需要考虑其他因素，例如低液位下的混合需求。在这种情况下，若要优化低液位混合效果，搅拌桨应尽可能靠近出口阀安装，但这会导致一定的混合效率损失。

For most applications, a ratio of liquid height (h) to vessel internal diameter (d) of 1.5:1 is ideal for unbaffled vessels. A range of h:d from 1:1 to 2:1 is recommended. Refer to figure 2.

Outside of this range, different conditions may occur. If the ratio is below one and the impeller is properly sized considering the vessel internal diameter, a good degree of mixing can be expected, but this configuration inhibits a vortex formation. If the ratio is above 2, for bottom mount magnetic coupled mixers this would mean that it is not possible to create enough momentum in the flow to reach the surface, thus potentially creating zones of different concentration at the top, against the walls. When working with mixer designs without a shaft, this condition should be avoided. Figure 2 shows more details of the results of the different ratios in terms of the mixing flow pattern. In water-like applications, the dead zones depicted (zones with limited movement) are eliminated and the flow is typically turbulent. As viscosity increases (often beyond 1,000 cP, depending on the specific fluid rheology), these dead zones would start to appear and would be more prominent as the viscosity increases and the flow regime turns into laminar. The location of the mixer in the bottom dish also affects the resulting mixing pattern. Refer to figure 3.

A placement in the half radius would give the best location for mixing performance. However, other considerations may be relevant when choosing placement, such as low level mixing. In this case, if trying to optimize low level mixing the impeller would be placed as close as possible to the outlet valve and some loss on mixing efficiency would occur.

是否需要产生涡流取决于具体的应用需求。涡流并不代表“混合效果更好”。在许多情况下，应避免产生涡流，因为它可能会滞留空气。对于容易起泡的工艺流体而言，这一点尤为关键。但处理轻质粉末时是个例外。如果固体物质容易漂浮、具有疏水性或容易结块，则需要利用涡流将其吸入并带向搅拌桨。若应用场景有此需求，务必确保选用的高径比（h:d）不低于 1:1，因为较低的比值会抑制搅拌器形成涡流的能力。这是生物制药行业在设计搅拌容器时的常见错误。鉴于多种因素都可能影响容器的几何形状，必须优先考虑那些对混合结果影响显著的因素。毕竟，如果流型无法实现预期的混合效果（例如将轻质固体充分溶解），那么即使是昂贵的生物制药级搅拌压力容器也将失去其价值。设计高径比低于1:1的容器，主要原因之一通常是为了节省顶部空间（headroom），因为较矮的容器也能达到相同的有效容积。然而，必须仔细权衡这对工艺过程可能带来的后果。涡流的形状和深度取决于搅拌器的吸入速率、液体粘度以及容器的几何形状。无量纲的弗劳德数（Froude number）常用于描述液面状态，并与表面涡流的形成密切相关；它代表了流动惯性力与重力的比值。对于搅拌容器，弗劳德数可表示为（符号定义见本白皮书末尾）：

较高的弗劳德数（Froude number）更有利于表面涡旋的形成。然而，这是一个复杂的现象，需要考量各种其他参数。搅拌容器内的任何附属构件都可能改变流动动力学特性，从而促进或抑制涡旋的形成。在生物制药容器中，常见的情况是使用浸入管（dip tube）来添加物料；根据长度不同，浸入管实际上可以起到挡板的作用，即便容器的液位高度与直径之比（h:d）处于推荐范围内，它也能抑制涡旋的形成。叶轮形状也会影响其破坏涡旋的能力。在叶轮直径相同的情况下，某些形状的叶轮可能比其他形状更容易诱发涡旋。通常，叶片位置较高的叶轮有助于形成稳定的涡旋，即使其高径比接近或略低于 1:1。图 4 展示了为改变流型而对叶轮叶片形状进行的常见改进设计。

The need to generate a vortex is application dependent. A vortex is not a sign of ‘better mixing’. In many cases, a vortex should be avoided as it may entrap air. Process fluids with a tendency to foam are particularly sensitive to this condition. The exception to this rule is when dealing with light powder’s incorporation. Solids that tend to float, are hydrophobic and/or can clump would require a vortex to be sucked down towards the impeller. If that is required by the application, then it is extremely important that the h:d ratio selected is not below 1:1, as this will inhibit the mixer’s ability to form a vortex. This is a common mistake seen when designing agitated vessels in the biopharmaceutical industry. As there are multiple factors that may govern the vessel geometry, it is important to prioritize those that may have a larger effect on the mixing results. After all, an expensive biopharmaceutical-grade, agitated pressure vessel will become useless if the flow pattern cannot achieve the desired mixing outcome (e.g. incorporation of light solids into solution). Some of the main reasons vessels are designed with a h:d below the 1:1 ratio are related to head room, since the same working volume can be achieved with a shorter vessel. However, the consequences to the process shall be considered carefully. Vortex shape and depth is dependent on the agitator suction rate, the liquid viscosity and the vessel geometry. The dimensionless Froude number is used to describe surface condition and can be related to the formation of surface vortices. It represents the ratio of flow inertial forces to gravitational forces. For agitated vessels, the Froude number can be expressed as (nomenclature explanation in the end of this white paper):

Higher Froude numbers would be more conducive to the formation of surface vortices. However, this is a complex phenomenon that requires considering various additional parameters. Every appurtenance in the agitated vessel can potentially change the flow dynamics and help or inhibit vortex formation. A common case in biopharmaceutical vessels where this occurs is due to the use of dip tubes for ingredient additions. Depending on the length of it, the dip tube can effectively act as a baffle and can inhibit vortex formation even on the vessels with the recommended h:d ratio. The impeller shape has an influence in the ability to break a vortex. Given the same impeller diameter, some impeller shapes may be more conducive to create a vortex than others. Typically, higher wings may help in forming a stable vortex, even when close or slightly below the 1:1 ratio. Figure 4 shows common modifications done to impeller wing shape for obtaining different changes in the flow pattern.

图1展示了安装在碟形底容器中的搅拌器。这是生物工艺中最常用的底部形状（通常采用ASME标准的法兰碟形封头）。某些工艺也会采用其他形状的底部，例如锥形底。对于磁力驱动搅拌器，锥形底的角度可能会受到限制，以避免轴承承受不均匀的载荷。通常情况下，锥角与水平线的夹角不超过30度（见图5）。

其他类型的底部（如平底）较少见，因为它们无法实现容器的自排空（这是有效进行在线蒸汽灭菌的必要条件）。

半球形底部也曾用于底部安装的磁力搅拌器，但不常见。与碟形底相比，这种底部可能允许更低的最小混合体积。此外，对于涉及浓缩步骤的工艺（如各种过滤系统），常采用“郁金香形”容器（见图6）。

使用底部安装的磁力搅拌器时，郁金香形容器会增加设计的复杂性。必须考虑容器的小直径与大直径之差以及郁金香形部分的深度。对于郁金香形容器，同样的几何设计准则依然适用，因此应保持推荐的h:d（高径）比。特别是当使用底部进入式磁力搅拌器时，应避免采用过深且狭窄的郁金香形结构。当小直径与大直径的比值接近1时，通常仅需在底部安装一台搅拌器即可实现全容器范围内的混合。随着直径差的增大，单台搅拌器实现全容积混合的能力会降低；在某些情况下，可能需要使用两个叶轮（一个安装在底部，另一个安装在大直径侧壁上）。

Figure 1 depicts an agitator in a vessel with a dished bot tom. This is the most common bottom shape used in bioprocess (in most cases a ASME flange and dish head is used). Other bottom shapes are used in certain processes, such as conical. With magnetically driven agitators, the angle of the cone may be restricted to avoid uneven loads on the bearings. In general terms, the angle is no more than 30 degrees from the horizontal line (see figure 5).

Other type bottoms, such as flat ones are uncommon due to their inability to provide a self-draining vessel (needed to effectively steam in place).

Hemispherical bottoms have been used with bottom mount mag mixers, but are not common. These may offer a lower minimum mixing volume than dished bottoms. Alternatively, tulip vessels are often used for processes where there are concentration steps (such as various filtration systems). See figure 6.

Tulip vessels create an additional degree of complexity when trying to use bottom mount mag mixers. The difference between the small and large diameter, as well as the depth of the tulip shall be considered. For the tulip, the same vessel geometry rules apply, so the ratio of h:d should be maintained as recommended. In particular, deep and narrow tulips should be avoided if using a bottom entry mag mixer. When the small and large diameter ratio is closer to one, it is often possible to mix the entire vessel with one mixer installed in the bottom. As the difference between diameters increases, the ability to mix the entire volume with one mixer is reduced and in some instances, two impellers may be used (one installed in the bottom and one installed on the side of the larger diameter).