第三讲 离心与沉降 2学时一、通过本章学习应该掌握的内容
1、何谓沉降
2、沉降与离心的异同
3、沉降与离心的速度方程
4、离心设备可分为哪两大类
5、常用的离心沉降设备有哪些
6、常用的离心过滤设备有哪些二、离心的概念
The first step in most industrial bioseparations is the removal of insoluble solids from the fermentation beer,The concentration and size of these in solubles varies widely,（生物分离首先去除不溶物）
The size ranges from microorganisms of perhaps 1 um diameter up to insoluble nutrients characteristically 1mm in diameter（粒径从1um的到1mm）
When these insolubles are dilute,large & rigid,they can be easily separated by filtration,In the previous chapter,we described filtration,including the use of filter aids,For many beers,these filter aids facilitate filtration,For other beers,filter aids are ineffective.（不溶物浓度小，粒径大，硬度强时用过滤分离。使助滤剂过滤分离，对一些发酵液很有用）
When the beers are not easily filtered,they sometimes can be separated by centrifugation,which is the subject of this chapter.（不易过滤可用离心）
Centrifugation requires more expensive equipment than filtration,However,it is often effective way even when the solid particles are small & hence hard to filter.
基于固体颗粒和周围液体密度存在的差异，在离心场中使不同密度的固体颗粒加速沉降的分离过程实际上离心和过滤一样，也是固液分离的一种单元操作对于一些固体颗粒小、溶液粘度大的生物体系，过滤实际上是很难进行的，必须采用离心技术方能达到目的三、沉降的概念沉降：是指当悬浮液静置时，密度较大的固体颗粒在重力的作用下逐渐下沉，这一过程成为沉降沉降过程通常是十分缓慢的，对于一些固液密度差异很小的体系沉降往往需要很长时间四、沉降速率方程
When a solid particle moves through an infinite continuum,its velocity is affected by two forces.
当一固体微粒通过连续介质时，它的运动速度受到两种力的作用：
1、由于密度差引起的浮力
2、微粒受到的流体阻力当浮力与阻力达到平衡时，该微粒以恒定的速度沉降联立二式可得沉降速率方程：
五、重力沉降式液固分离设备
1、特点：
设备简单、运行成本低、能耗低体积庞大、分离效率低
2、传统的沉降设备：
（a）矩形水平流动池
（b）圆形径向流动池
（c）斜板与斜管式沉淀池六、离心式沉降分离
1、分类：
（a）离心沉降
（b）离心过滤
2、离心沉降利用悬浮液或乳浊液中密度不同的组分在离心力场中迅速沉降分层，实现固液分离操作方式：间歇式、连续式型式：管式、套筒、碟片式
（1）管式离心机（Tubular bowl）
Simple yet,can provide a very high centrifugal force.（最简单，可提供较大离心力）
Tubular centrifuges can be cool,a real advantage in protein work.（可用冷却水冷却），Suspension is usually fed through bottom,and clarified liquid is removed from the top.（悬浮液由管底进，澄清液由管口流出）
离心过程分析：
To begin this analysis,assume that this typical particle is located at
(1) A distance Z from the bottom of the centrifuge as show in Fig 3.2.1.
(2) Located at position r from the axis of rotation.（离旋转轴为r的微粒）
(3) This position is between the liquid surface R1 & the bowl radius R0.（位于液体界面半径r1和管心半径r0的微粒 ）
The particle is moving in both the Z & r directions,
Its movement in the Z direction comes from convection of the feed pumped in the bottom of the centrifuge,（Z方向的动力来源于离心机底部泵入料液的对流）
dz/dt=Q/[π(R02-R12)] (3.8)
Where Q is the feed flow.（料液流速）
The eq(3.8) implies that gravity has only a negligible effect in the Z direction.（ Z方向重力可忽略）
We will assume that the centrifugal force is so high that the liquid interface R1 is constant,independent of Z.（假定离心力很大，R1是常数）
The particle movement in the r direction is related to its radial position r by (3.7).（r方向上运动与半径r有关）
dr/dt= d2(ρs-ρ)rω2/(18μ) (3.9)
We will rewrite this eq,In terms of the velocity of a particle settling under the influence of gravity:
dr/dt=νg(rω2/g) (3.10)
Whereνg is velocity given by Eq.(3.6).
We combine (3.8) & (3.9) to find the trajectory of a particle within the centrifuge:（得出离心机内部微粒的运动轨迹）
dr/dz=(dr/dt)/(dz/dt)=νg(rω2/g)π(R02-R12)/Q (3.11)
（2）碟片式离心机（Disc type centrifuge.）
dx/dt=ν0-νcsinθ (3.15)
ν0=[Q/(2πrln)]f(y) （3.16）
n--- the number of discs（蝶片数）
r--- the distance from the axis of rotation（微粒与转鼓轴线间距离）
l--- the distance between discc
f(y)--- some function giving the velocity variation across the distance between discs, （蝶片间流速变化的函数）
3、离心过滤使悬浮液在离心力场作用下产生的离心力压力，作用在过滤介质上，使液体通过过滤介质成为滤液，而固体颗粒被截留在过滤介质表面，从而实现固液分离，是离心与过滤单元操作的集成，分离效率更高
This is the third,centrifugal filtration; the basket unit shown in fig 3.2-1 d,is really a combination of a centrifuge & a filter,It consists of a perforated basked which rotates rapidly,Suspension is again fed along the axis of the bowl & solid accumulate on the wall of the basket,
We begin the analysis by recalling that the pressure drop Δp in a flat cake is proportional to the fluid velocity v through that cake,
(根据过滤压差Δp和流体通过滤饼的速度成正比 )
有：
Δp/l=(μαρ0)ν (3.25)
Where
l--- the thickness of the cake (式中l-滤饼的厚度 )
μ--- the fluid velocity (u-料液的粘度)
α--- the specific resistance of the cake(a－滤饼的比阻力 )
ρ0 --- the mass of solid per volume of liquid feed (ρ0－单位体积料液所含的滤渣量)
-dp/dr=(μαρ0)ν (3.26)
2πrlυ=Q (3.27)
由（3.26）和（3.27）
-dp/dr=μαρ0Q/(2πrl) (3.28)
4、常见的离心过滤设备
（a）三足式离心机是最常见的过滤式离心机，立式有孔转鼓悬挂于三根支足上故而得名
（b）卧式刮刀离心机可连续生产，使用效率更高，功率消耗小
（c）螺旋卸料离心机主要用于需耐压的场合，具较高的分散因数七、本章作业
1、何谓沉降
2、沉降与离心的异同
3、沉降与离心的速度方程
4、离心设备可分为哪两大类
5、常用的离心沉降设备有哪些
6、常用的离心过滤设备有哪些
1、何谓沉降
2、沉降与离心的异同
3、沉降与离心的速度方程
4、离心设备可分为哪两大类
5、常用的离心沉降设备有哪些
6、常用的离心过滤设备有哪些二、离心的概念
The first step in most industrial bioseparations is the removal of insoluble solids from the fermentation beer,The concentration and size of these in solubles varies widely,（生物分离首先去除不溶物）
The size ranges from microorganisms of perhaps 1 um diameter up to insoluble nutrients characteristically 1mm in diameter（粒径从1um的到1mm）
When these insolubles are dilute,large & rigid,they can be easily separated by filtration,In the previous chapter,we described filtration,including the use of filter aids,For many beers,these filter aids facilitate filtration,For other beers,filter aids are ineffective.（不溶物浓度小，粒径大，硬度强时用过滤分离。使助滤剂过滤分离，对一些发酵液很有用）
When the beers are not easily filtered,they sometimes can be separated by centrifugation,which is the subject of this chapter.（不易过滤可用离心）
Centrifugation requires more expensive equipment than filtration,However,it is often effective way even when the solid particles are small & hence hard to filter.
基于固体颗粒和周围液体密度存在的差异，在离心场中使不同密度的固体颗粒加速沉降的分离过程实际上离心和过滤一样，也是固液分离的一种单元操作对于一些固体颗粒小、溶液粘度大的生物体系，过滤实际上是很难进行的，必须采用离心技术方能达到目的三、沉降的概念沉降：是指当悬浮液静置时，密度较大的固体颗粒在重力的作用下逐渐下沉，这一过程成为沉降沉降过程通常是十分缓慢的，对于一些固液密度差异很小的体系沉降往往需要很长时间四、沉降速率方程
When a solid particle moves through an infinite continuum,its velocity is affected by two forces.
当一固体微粒通过连续介质时，它的运动速度受到两种力的作用：
1、由于密度差引起的浮力
2、微粒受到的流体阻力当浮力与阻力达到平衡时，该微粒以恒定的速度沉降联立二式可得沉降速率方程：
五、重力沉降式液固分离设备
1、特点：
设备简单、运行成本低、能耗低体积庞大、分离效率低
2、传统的沉降设备：
（a）矩形水平流动池
（b）圆形径向流动池
（c）斜板与斜管式沉淀池六、离心式沉降分离
1、分类：
（a）离心沉降
（b）离心过滤
2、离心沉降利用悬浮液或乳浊液中密度不同的组分在离心力场中迅速沉降分层，实现固液分离操作方式：间歇式、连续式型式：管式、套筒、碟片式
（1）管式离心机（Tubular bowl）
Simple yet,can provide a very high centrifugal force.（最简单，可提供较大离心力）
Tubular centrifuges can be cool,a real advantage in protein work.（可用冷却水冷却），Suspension is usually fed through bottom,and clarified liquid is removed from the top.（悬浮液由管底进，澄清液由管口流出）
离心过程分析：
To begin this analysis,assume that this typical particle is located at
(1) A distance Z from the bottom of the centrifuge as show in Fig 3.2.1.
(2) Located at position r from the axis of rotation.（离旋转轴为r的微粒）
(3) This position is between the liquid surface R1 & the bowl radius R0.（位于液体界面半径r1和管心半径r0的微粒 ）
The particle is moving in both the Z & r directions,
Its movement in the Z direction comes from convection of the feed pumped in the bottom of the centrifuge,（Z方向的动力来源于离心机底部泵入料液的对流）
dz/dt=Q/[π(R02-R12)] (3.8)
Where Q is the feed flow.（料液流速）
The eq(3.8) implies that gravity has only a negligible effect in the Z direction.（ Z方向重力可忽略）
We will assume that the centrifugal force is so high that the liquid interface R1 is constant,independent of Z.（假定离心力很大，R1是常数）
The particle movement in the r direction is related to its radial position r by (3.7).（r方向上运动与半径r有关）
dr/dt= d2(ρs-ρ)rω2/(18μ) (3.9)
We will rewrite this eq,In terms of the velocity of a particle settling under the influence of gravity:
dr/dt=νg(rω2/g) (3.10)
Whereνg is velocity given by Eq.(3.6).
We combine (3.8) & (3.9) to find the trajectory of a particle within the centrifuge:（得出离心机内部微粒的运动轨迹）
dr/dz=(dr/dt)/(dz/dt)=νg(rω2/g)π(R02-R12)/Q (3.11)
（2）碟片式离心机（Disc type centrifuge.）
dx/dt=ν0-νcsinθ (3.15)
ν0=[Q/(2πrln)]f(y) （3.16）
n--- the number of discs（蝶片数）
r--- the distance from the axis of rotation（微粒与转鼓轴线间距离）
l--- the distance between discc
f(y)--- some function giving the velocity variation across the distance between discs, （蝶片间流速变化的函数）
3、离心过滤使悬浮液在离心力场作用下产生的离心力压力，作用在过滤介质上，使液体通过过滤介质成为滤液，而固体颗粒被截留在过滤介质表面，从而实现固液分离，是离心与过滤单元操作的集成，分离效率更高
This is the third,centrifugal filtration; the basket unit shown in fig 3.2-1 d,is really a combination of a centrifuge & a filter,It consists of a perforated basked which rotates rapidly,Suspension is again fed along the axis of the bowl & solid accumulate on the wall of the basket,
We begin the analysis by recalling that the pressure drop Δp in a flat cake is proportional to the fluid velocity v through that cake,
(根据过滤压差Δp和流体通过滤饼的速度成正比 )
有：
Δp/l=(μαρ0)ν (3.25)
Where
l--- the thickness of the cake (式中l-滤饼的厚度 )
μ--- the fluid velocity (u-料液的粘度)
α--- the specific resistance of the cake(a－滤饼的比阻力 )
ρ0 --- the mass of solid per volume of liquid feed (ρ0－单位体积料液所含的滤渣量)
-dp/dr=(μαρ0)ν (3.26)
2πrlυ=Q (3.27)
由（3.26）和（3.27）
-dp/dr=μαρ0Q/(2πrl) (3.28)
4、常见的离心过滤设备
（a）三足式离心机是最常见的过滤式离心机，立式有孔转鼓悬挂于三根支足上故而得名
（b）卧式刮刀离心机可连续生产，使用效率更高，功率消耗小
（c）螺旋卸料离心机主要用于需耐压的场合，具较高的分散因数七、本章作业
1、何谓沉降
2、沉降与离心的异同
3、沉降与离心的速度方程
4、离心设备可分为哪两大类
5、常用的离心沉降设备有哪些
6、常用的离心过滤设备有哪些
