GATE Biotechnology Fundamentals of Biological Engineering Flashcards

24 sample cards from the Fundamentals of Biological Engineering deck

Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.

1. Write the Goldman–Hodgkin–Katz (GHK) voltage equation for resting membrane potential.

   $$V_m = \frac{RT}{F}\ln\frac{P_K[K^+]_o + P_{Na}[Na^+]_o + P_{Cl}[Cl^-]_i}{P_K[K^+]_i + P_{Na}[Na^+]_i + P_{Cl}[Cl^-]_o}$$ It accounts for the relative permeabilities $P$ of multiple ions.

2. Relate the standard free energy change to the standard reduction potentials in a redox reaction.

   $$\Delta G^{\circ} = -nF\,\Delta E^{\circ}, \qquad \Delta E^{\circ} = E^{\circ}_{acceptor} - E^{\circ}_{donor}$$ A positive $\Delta E^{\circ}$ (electrons flow to higher reduction potential) gives negative $\Delta G^{\circ}$ (spontaneous).

3. How many ATP are generated per NADH and per FADH$_2$ via oxidative phosphorylation (standard P/O values)?

   Approximately $2.5$ ATP per $\ce{NADH}$ (P/O $\approx 2.5$) and $1.5$ ATP per $\ce{FADH2}$ (P/O $\approx 1.5$). Older textbook values are 3 and 2 respectively.

4. State the net ATP and reducing-equivalent yield of glycolysis (glucose to 2 pyruvate).

   Net per glucose: $+2$ ATP (4 produced $-$ 2 invested), $+2\ \ce{NADH}$, and 2 pyruvate. Overall: $\ce{glucose + 2 NAD+ + 2 ADP + 2 Pi -> 2 pyruvate + 2 NADH + 2 ATP + 2 H2O}$.

5. What is the total ATP yield from complete aerobic oxidation of one glucose molecule (textbook value)?

   About $30$–$32$ ATP per glucose (glycolysis + pyruvate oxidation + TCA cycle + oxidative phosphorylation), depending on the shuttle used for cytosolic NADH and the assumed P/O ratios.

6. Distinguish a Newtonian from a non-Newtonian fluid.

   A Newtonian fluid has shear stress directly proportional to shear rate with constant viscosity: $\tau = \mu\dfrac{du}{dy}$. A non-Newtonian fluid has a viscosity that varies with shear rate (apparent viscosity is not constant).

7. Write the power-law (Ostwald–de Waele) model and classify fluids by the flow behavior index $n$.

   $$\tau = K\left(\frac{du}{dy}\right)^{n}$$ $n<1$: pseudoplastic (shear-thinning); $n=1$: Newtonian (then $K=\mu$); $n>1$: dilatant (shear-thickening). $K$ is the consistency index.

8. Define a Bingham plastic fluid.

   A Bingham plastic requires a finite yield stress $\tau_0$ before it flows: $$\tau = \tau_0 + \mu_p\frac{du}{dy} \quad (\tau > \tau_0)$$ Below $\tau_0$ it behaves as a solid. Many mycelial broths and toothpaste-like fluids are Bingham.

9. Define the Reynolds number for pipe flow and state laminar/turbulent transition values.

   $$Re = \frac{\rho u D}{\mu}$$ For pipe flow: laminar for $Re < 2100$, transitional $2100 < Re < 4000$, turbulent for $Re > 4000$.

10. Define the impeller Reynolds number for a stirred tank.

    $$Re_i = \frac{\rho N D^{2}}{\mu}$$ where $N$ is impeller rotational speed (rev/s) and $D$ is impeller diameter. Laminar regime $Re_i < 10$; turbulent $Re_i > 10^{4}$.

11. What is the Hagen–Poiseuille equation for laminar flow in a pipe?

    $$Q = \frac{\pi \Delta P\, R^{4}}{8\mu L}$$ The volumetric flow rate of laminar flow varies with the fourth power of the radius. Velocity profile is parabolic with $u_{max} = 2\bar{u}$.

12. Define the power number $N_p$ for an agitated vessel.

    $$N_p = \frac{P}{\rho N^{3} D^{5}}$$ where $P$ is power input, $N$ impeller speed, $D$ impeller diameter. In the turbulent regime $N_p$ is approximately constant for a given impeller geometry.

13. How does ungassed power input depend on impeller speed and diameter in the turbulent regime?

    With $N_p$ constant in turbulent flow: $$P = N_p\,\rho N^{3} D^{5}$$ Power scales with the cube of speed and the fifth power of impeller diameter.

14. Define mixing time in a bioreactor.

    Mixing time $t_m$ is the time required to achieve a specified degree of homogeneity (typically 95%) after a tracer pulse is added. Shorter $t_m$ means better, faster blending. It is often correlated as $N\,t_m \approx$ constant for a given geometry in turbulent flow.

15. State Fick's first law of molecular diffusion.

    $$J = -D\,\frac{dC}{dx}$$ The diffusive molar flux $J$ is proportional to the concentration gradient; $D$ is the diffusion coefficient (diffusivity). The minus sign indicates flux from high to low concentration.

16. State the key assumption of the film (two-film) theory of mass transfer.

    All resistance to mass transfer resides in a thin stagnant fluid film at the interface, across which transport is by steady molecular diffusion; the bulk fluid is well mixed. The mass transfer coefficient $k = D/\delta$, where $\delta$ is the film thickness.

17. Write the equation for the rate of oxygen transfer (OTR) from gas to liquid in a bioreactor.

    $$OTR = k_L a\,(C^{*} - C_L)$$ where $k_L a$ is the volumetric mass transfer coefficient, $C^{*}$ the saturation (equilibrium) dissolved $\ce{O2}$ concentration, and $C_L$ the bulk dissolved $\ce{O2}$ concentration.

18. At steady state in a fermenter, how do oxygen transfer rate (OTR) and oxygen uptake rate (OUR) relate?

    $$OTR = OUR \implies k_L a\,(C^{*} - C_L) = q_{O_2}\,X$$ where $q_{O_2}$ is the specific oxygen uptake rate and $X$ the biomass concentration. Oxygen supply must match consumption.

19. Describe the static gassing-out (dynamic) method for measuring $k_L a$.

    Stop aeration (or sparge $\ce{N2}$) to lower $C_L$, then resume aeration and record the dissolved $\ce{O2}$ rise. With no respiration, $\dfrac{dC_L}{dt} = k_L a(C^{*}-C_L)$; a plot of $\ln(C^{*}-C_L)$ vs $t$ gives slope $-k_L a$.

20. State Fourier's law of conduction and Newton's law of cooling (convection).

    Conduction: $$q = -kA\frac{dT}{dx}$$ Convection: $$q = hA(T_s - T_\infty)$$ where $k$ is thermal conductivity, $h$ the convective heat transfer coefficient, $A$ the area.

21. Define the overall heat transfer coefficient $U$ for a wall with two convective films (neglecting wall curvature).

    $$\frac{1}{U} = \frac{1}{h_i} + \frac{x_w}{k_w} + \frac{1}{h_o}$$ The total resistance is the sum of inside film, wall conduction, and outside film resistances. Then $q = U A\,\Delta T$.

22. Define the Log Mean Temperature Difference (LMTD) for a heat exchanger.

    $$\Delta T_{lm} = \frac{\Delta T_1 - \Delta T_2}{\ln\!\left(\dfrac{\Delta T_1}{\Delta T_2}\right)}$$ where $\Delta T_1$ and $\Delta T_2$ are the temperature differences at the two ends. Heat duty: $q = U A\,\Delta T_{lm}$.

23. For the same inlet and outlet temperatures, which gives a larger LMTD: counter-current or co-current flow, and why?

    Counter-current flow gives a larger LMTD and more uniform driving force, so it requires less area for the same duty. It can also cool/heat one stream beyond the other's outlet temperature, which co-current cannot.

24. Define heat exchanger effectiveness $\varepsilon$ in the $\varepsilon$-NTU method.

    $$\varepsilon = \frac{q_{actual}}{q_{max}} = \frac{q}{C_{min}(T_{h,in} - T_{c,in})}$$ where $C_{min}$ is the smaller of the two fluid heat capacity rates $\dot{m}c_p$. It is the ratio of actual to maximum possible heat transfer.

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