Pipette AnalysisProceduresG342 Sedimentation and Stratigraphy Name:________________________Laboratory 3Assoc. Prof. A Jay Kaufman14 February 2005Laboratory 3 – Pipette analysis of fine-grained sedimentsIntroductionSieve analysis is restricted largely to sediments coarser than 0.063 mm in diameter (4Ø, coarse-grained silt). Finer sediment grains are commonly cohesive or possess electrostatic charges,which make them unsuitable for dry sieving. Size analysis of fine-grained sediment is usuallyperformed when the sediment is dispersed in water and electrostatic charges or other attractiveforces between particles can be neutralized with chemical additives called dispersants. The mostwidely used analytical technique is the pipette method. This is a form of "sedimentation" analysisbecause particle size is estimated from the rate at which particles sink through a fluid.Pipette AnalysisTheoryThe theoretical basis of all sedimentation grain-size analysis is the predictable relationshipbetween particle grain size and settling velocity in a fluid medium. It is apparent that a particlefalling freely through a quiescent fluid will cease to accelerate when the frictional force exertedon the particle by the fluid exactly balances the downward force of gravity on the particle. Thevelocity of the particle under these conditions is called the fall or settling velocity. Stokescalculated a general equation for the fall velocity of small particles (< 0.1 mm diameter) by firstconsidering the frictional resistance which the fluid offers to movement of a settling sphere:R = 6rvwhere R = resistance (frictional drag) in gram cm/sec , r = sphere radius in cm,  = viscosity (0.01 at 20oC) of the fluid medium (g/cm sec) and v = settling velocity of the sphere in cm/sec.The force of gravity pulling the particle downward is:F = 4/3r3sgwhere s= density of the sphere and g = the acceleration due to gravity (cm/sec ).The buoyant force of the liquid is:F = 4/3r3fg where f = density of the liquid.The net result of upward buoyant and downward gravity forces acting on the particle is given byF = 4/3r3(s-f)gWhen this net force on the particle exactly equals the fluid resistance R, the settling velocity becomes constant. The relationship is expressed by equating the above forces:6rv = 4/3r3(s-f)gBy solving this equation for the settling velocity, v, we obtain an expression of Stokes' law, which is valid for particles smaller than fine sand (about 3Ø).If conditions of temperature and fluid density are constant and the density of the sphere is known,the equation can be stated asv = Cr2where C is a constant and equal to 2 (s- f)g/9At a temperature of 20oC and assuming a sphere density of 2.65 g/cm3 where C = 3.59 x 104v = 3.59 x 104r2This formula is used to compute the time required for a particle of given diameter to settle to a given depth.The assumptions implicit in derivation of Stokes' law merit some consideration. Perhapsthe greatest assumption is that the particles are spheres; few natural sedimentary grains are truespheres. This error is proportional to the deviation of the "effective" cross-sectional area fromthat of a sphere of the same mass. This deviation increases for smaller particles because mostsilt- and clay-sized grains have a platy shape. In addition, differences in local turbulence withinand near the wake of the particle may affect settling velocities; this effect varies with particle size,sorting and total sample weight.The particle should he allowed to behave as a discrete grain in a homogeneous medium ofinfinite extent. Boundary effects are generally considered negligible in settling tubes 5 cm ormore in diameter. Excessive material (greater than 2 percent) in suspension will result in particle-to-particle interference and suspensions should be kept as dilute as analytical procedures willpermit. The selection of 2.65 as the average particle density appears to be satisfactory for mostsediments. Standard values for the viscosity and density of pure water may be used if thesuspended particles are free of soluble salts and colloidal material. Precautions must be taken toassure that water temperature remains constant because viscosity varies markedly withtemperature changes. The student is referred to Krumbein and Pettijohn (1938, p. 95-102) forfurther considerations regarding assumptions involved in Stokes' law.The above theoretical discussion indicates that, from an originally homogeneous grain-fluid suspension, the coarsest grains will settle most rapidly with a predictable fall velocity. Aftersome time interval, t, all grains larger than some specified size, d, will have settled below somelevel, h, in the suspension whereas all finer size grades will, at level h, have the sameconcentration as in the original homogeneous suspension. The weight of sediment, w, in a knownvolume of the suspension, in common practice 20 cc or 1/50th of an original 1000 cc volume,withdrawn at level h at time t will thus contain 1/50th of the total sediment load finer than d. Thetotal weight of sediment finer than d will thus be 50w. A subsequent sample withdrawn at time titlevel h, for size d1 has a weight wl. It can easily be seen that the weight of sediment within thegrain size interval d - d1 will be equal to 50(w-w1). By taking a series of carefully timedwithdrawals, the weight of sediment within each 1/20 size grade, or any other interval of choice,can be calculated.By far the most important withdrawal is the first because it is taken when the suspension isstill statistically homogeneous and, hence, contains 1/50th of the total sediment load. This is theonly estimate you will have of the actual total weight of sediment in your sample. If you have notwet sieved the sample and suspect that some sand is present, this must be allowed to settle pastthe sample level, h. Hence, most pipette analyses begin with a first withdrawal at h = 20 cm and t= 58 sec. However, if your wet sieving has been done carefully and all sand-sized sediment hasbeen removed from your sample, your first withdrawal can be taken at h = 20 cm at any timefrom about 20 to 58 sec. after stirring. DO NOT WAIT UNTIL 58 SEC HAVE PAST TO STARTWITHDRAWING YOUR SAMPLE. If you do, you will obtain a low estimate of the